2016
8
4
0
230
1

Vibration Analysis of Carotid Arteries Conveying NonNewtonian Blood Flow Surrounding by Tissues
http://jsm.iauarak.ac.ir/article_527015.html
1
The high blood rate that often occurs in arteries may play a role in artery failure and tortuosity which leads to blackouts, transitory ischemic attacks and other diseases. However, vibration and instability analysis of carotid arteries are lacking. The objective of this study is to investigate the vibration and instability of the carotid arteries conveying blood under axial tension with surrounding tissue support. Arteries are modeled as elastic cylindrical vessels based on first order shear deformation theory (FSDT) within an elastic substrate. The elastic medium is simulated with viscoPasternak foundation. The blood flow in carotid artery is modeled with nonNewtonian fluid based on Carreau, power law and Casson models. Applying energy method, Hamilton principle and differential quadrature method (DQM), the frequency, critical blood velocity and transverse displacement of the carotid arteries are obtained. It can be seen that increasing the tissue stiffness would delay critical blood velocity. The current model provides a powerful tool for further experimental investigation arteries tortuosity. In addition, the dimensionless transverse displacement predicted by Newtonian model is lower than that of nonNewtonian models.
0

693
704


A.H
Ghorbanpour Arani
Faculty of Mechanical Engineering, University of Tehran, Tehran, Iran
Iran


A
Rastgoo
Faculty of Mechanical Engineering, University of Tehran, Tehran, Iran
Iran


A.
Ghorbanpour Arani
Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran 
Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan, Iran
Iran
aghorban@kashanu.ac.ir


R
Kolahchi
Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Iran
Carotid artery
NonNewtonian fluid
Critical blood velocity
FSDT
Tissue matrix
[[1] Pancera P., Ribul M., Presciuttini B., Lechi A., 2000, Prevalence of carotid artery kinking in 590 consecutive subjects evaluated by Echocolordoppler. Is there a correlation with arterial hypertension, Journal of Internal Medicine 248:712.##[2] Brown W.R., Moody D.M., Challa V.R., Thore C.R., Anstrom J.A., 2002, Venous collagenosis and arteriolar tortuosity in leukoaraiosis, Journal of the Neurological Sciences 203:159163.##[3] Hiroki M., Miyashita K., Oda M., 2002, Tortuosity of the white matter medullary arterioles is related to the severity of hypertension, Cerebrovascular Disease 13:242250.##[4] Aleksic M., Schutz G., Gerth S., Mulch J., 2004, Surgical approach to kinking and coiling of the internal carotid artery, The Journal of Cardiovascular Surgery 45:4348.##[5] Helisch A., Schaper W., 2003, Arteriogenesis: the development and growth of collateral arteries, Microcirculation 10:8397.##[6] Weibel J., Fields W.S., 1965, Tortuosity, coiling, and kinking of the internal carotid artery. Ii. relationship of morphological variation to cerebrovascular insufficiency, Neurology 15:462468.##[7] Jackson Z.S., Dajnowiec D., Gotlieb A.I., Langille B.L., 2005, Partial offloading of longitudinal tension induces arterial tortuosity, Arteriosclerosis, Thrombosis, and Vascular Biology 25:957962.##[8] Han H.Ch., 2007, A biomechanical model of artery buckling, Journal of Biomechanics 40:36723678.##[9] Han H.Ch., 2008, Nonlinear buckling of blood vessels: A theoretical study, Journal of Biomechanics 41:27082713.##[10] Han H.Ch., 2009, Blood vessel buckling within soft surrounding tissue generates tortuosity, Journal of Biomechanics 42:27972801.##[11] Han H.Ch., 2012, Mechanical buckling of artery under pulsatile pressure, Journal of Biomechanics 45:11921198.##[12] Han H.Ch., 2013, Mechanical buckling of arterioles in collateral development, Journal of Theoretical Biology 316:4248.##[13] Pedley T.J., 1980, The Fluid Mechanics of Large Blood Vessels, Cambridge University Press, Cambridge.##[14] Cho Y.I., Kensey R., 1991, Effects of the nonnewtonian viscosity of blood flows in a diseased arterial vessel. Part 1: steady flows, Biorheology 28:241262.##[15] Dash R.K., Jayaraman G., Metha K.N., 1999, Flow in a catheterized curved artery with stenosis, Journal of Biomechanics 32:4961.##[16] Chen J., Lu X.Y., 2004, Numerical investigation of the nonNewtonian blood flow in a bifurcation model with a nonplanar branch, Journal of Biomechanics 37:18991911.##[17] Barbara Johnston M., Johnston P.R., Corney S., Kilpatrick D., 2004, NonNewtonian blood flow in human right coronary arteries: steady state simulations, Journal of Biomechanics 37:709720.##[18] Mandal P.K., 2005, An unsteady analysis of nonNewtonian blood flow through tapered arteries with a stenosis, International Journal of NonLinear Mechanics 40:151164.##[19] Sankar D.S., Hemalatha K., 2007, A nonNewtonian fluid flow model for blood flow through a catheterized artery—Steady flow, Applied Mathematical Modeling 31:18471864.##[20] Boyd J., Buick J.M., Green S., 2007, Analysis of the Casson and CarreauYasuda nonNewtonian blood models in steady and oscillatory flows using the lattice Boltzmann method, Physics of Fluids 19:093103.##[21] Abdollahian M., Ghorbanpour Arani A., Mosallaie Barzoki A.A., Kolahchi R., Loghman A., 2013, Nonlocal wave propagation in embedded armchair TWBNNTs conveying viscous fluid using DQM, Physica B 418:115.##[22] Ghorbanpour Arani A., Abdollahian M., Kolahchi R., Rahmati A.H., 2013, Electrothermotorsional buckling of an embedded armchair DWBNNT using nonlocal shear deformable shell model, Composite Part B: Engineering 51:291299.##[23] Taj M., Zhang J.Q., 2012, Analysis of vibrational behaviors of microtubules embedded within elastic medium by Pasternak model, Biochemical and Biophysical Research Communications 424:8993.##[24] Ghorbanpour Arani A., Shiravand A., Rahi M., Kolahchi R., 2012, Nonlocal vibration of coupled DLGS systems embedded on ViscoPasternak foundation, Physica B 407:41234131.##[25] Wang L., Ni Q., 2009, A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid, Mechanics Research Communication 36:833837.##[26] Ghorbanpour Arani A., Kolahchi R., Khoddami Maraghi Z., 2013, Nonlinear vibration and instability of embedded doublewalled boron nitride nanotubes based on nonlocal cylindrical shell theory, Applied Mathematical Modeling 37:76857707.##[27] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., Mozdianfard M.R., Noudeh Farahani S.M., 2012, Elastic foundation effect on nonlinear thermovibration of embedded doublelayered orthotropic graphene sheets using differential quadrature method, Journal of Mechanical Engineering Science 227:862879.##[28] Jozwik K., Obidowski D., 2010, Numerical simulations of the blood flow through vertebral arteries, Journal of Biomechanics 43:177185.##[29] Cho Y.I., Kensey K.R., 1991, Effects of the nonNewtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: steady flows, Biorheology 28:241262.##[30] Han H.C., Zhao L., Huang M., Hou L.S., Huang Y.T., Kuang Z.B., 1998, Postsurgical changes of the opening angle of canine autogenous vein graft, Journal of Biomechanical Engineering 120:211216.##]
1

Mechanical Stresses in a Linear Plastic FGM Hollow Cylinder Due to NonAxisymmetric Loads
http://jsm.iauarak.ac.ir/article_527016.html
1
In this paper, an analytical solution for computing the linear plastic stresses and critical pressure in a FGM hollow cylinder under the internal pressure due to nonAxisymmetric Loads is developed. It has been assumed that the modulus of elasticity was varying through thickness of the FGM material according to a power law relationship. The Poisson's ratio was considered constant throughout the thickness. The general form of mechanical boundary conditions is considered on the inside surfaces. In the analysis presented here the effect of nonhomogeneity in FGM cylinder was implemented by choosing a dimensionless parameter, named m, which could be assigned an arbitrary value affecting the stresses in the cylinder. Distribution of stresses in radial, circumferential and shear directions for FGM cylinders under the influence of internal pressure were obtained. Graphs of variations of stress versus radius of the cylinder were plotted. The direct method is used to solve the Navier equations.
0

705
718


M
Shokouhfar
South Tehran Branch, Islamic Azad University,Tehran, Iran
Iran
miladshokouhfar@gmail.com


M
Jabbari
South Tehran Branch, Islamic Azad University,Tehran, Iran
Iran
Hollow cylinder
NonHomogenous
Non Axisymmetri
FGM
Elasticplastic analysis
[[1] Lutz M.P., Zimmerman R.W., 1996, Thermal stresses and effective thermal expansion coefficient of functionally graded sphere, Journal of Thermal Stresses 19:3954.##[2] Zimmerman R.W., Lutz M. P., 1999, Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder, Journal of Thermal Stresses 22:177188.##[3] Jabbari M., Sohrabpour S., Eslami M.R., 2003, General solution for mechanical and thermal stresses in functionally graded hollow cylinder due to nonaxisymmetric steadystate loads, Journal of Applied Mechanics 70:111118.##[4] Poultangari R., Jabbari M., Eslami M.R. 2008, Functionally graded hollow spheres under nonaxisymmetric thermomechanical loads, International Journal of Pressure Vessels and Piping 85: 295305.##[5] Lu Y., Zhang K., Xiao J., Wen D., 1999, Thermal stresses analysis of ceramic/metal functionally gradient material cylinder, Applied Mathematics and Mechanics 20(4): 413417.##[6] Shariyat M., Lavasani S.M.H., Khaghani M., 2010, Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperaturedependent FGM cylinders, using a secondorder pointcollocation method, Applied Mathematical Modelling 34:898918.##[7] Shariyat M., 2009, A nonlinear Hermitian transfinite element method for transient behavior analysis of hollow functionally graded cylinders with temperaturedependent materials under thermomechanical loads, International Journal of Pressure Vessels and Piping 86: 280289.##[8] Lü C.F., Chen W.Q., Lim C.W., 2009, Elastic mechanical behavior of nanoscaled FGM films incorporating surface energies, Composites Science and Technology 69: 11241130.##[9] Afsar A.M., Sekine H., 2002, Inverse problems of material distributions for prescribed apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media, Composites Science and Technology 62:10631077.##[10] Tajeddini V., Ohadi A., Sadighi M., 2011, Threedimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation, International Journal of Mechanical Sciences 53:300308.##[11] Nosier A., Fallah F., 2009, Nonlinear analysis of functionally graded circular plates under asymmetric transverse loading, International Journal of NonLinear Mechanics 44:928942.##[12] Zhang D.G., Zhou Y. H., 2008, A theoretical analysis of FGM thin plates based on physical neutral surface ,Computational Materials Science 44 :716720.##[13] Fazelzadeh S.A., Hosseini M., 2007, Aero thermo elastic behavior of supersonic rotating thinwalled beams made of functionally graded materials, Journal of Fluids and Structures 23:12511264.##[14] Ootao Y., Tanigawa Y., 2004, Transient thermo elastic problem of functionally graded thick strip due to Non uniform heat supply , Composite Structures 63(2):139146.##[15] Jabbari M., Sohrabpour S., Eslami M.R., 2002, Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads , International Journal of Pressure Vessels and Piping 79:493497.##[16] Farid M. , Zahedinejad P. , Malekzadeh P., 2010, Threedimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on twoparameter elastic foundation using a hybrid semianalytic, differential quadrature method, Materials and Design 31:213.##[17] Bagri A., Eslami M.R., 2008, Generalized coupled thermo elasticity of functionally graded annular disk considering the Lord–Shulman theory, Composite Structures 83:168179.##[18] Jabbari M., Bahtui A., Eslami M.R., 2009, Axisymmetric mechanical and thermal stresses in thick short length functionally graded material cylinder, International Journal of Pressure Vessels and Piping 86: 296306.##[19] Zamani Nejad M., Rahimi G.H., 2009, Deformations and stresses in rotating FGM pressurized thick hollow cylinder under thermal load, Scientific Research and Essay 4(3): 131140.##[20] Batra R.C., Iaccarino G.L., 2008, Exact solutions for radial deformations of a functionally graded isotropic and incompressible secondorder elastic cylinder, International Journal of NonLinear Mechanics 43:383398.##[21] Shao Z.S., Wang T.J., 2006, Threedimensional solutions for the stress fields in functionally graded cylindrical panel with finite length and subjected to thermal/mechanical loads, International Journal of Solids and Structures 43: 38563874.##[22] Shabanaa Y.M., Noda N., 2001, Thermoelastoplastic stresses in functionally graded materials subjected to thermal loading taking residual stresses of the fabrication process into consideration, Composites: Part B 32: 111121.##[23] Eraslan A.N., Akis T., 2006, Plane strain analytical solutions for a functionally graded elastic–plastic pressurized tube, International Journal of Pressure Vessels and Piping 83: 635644.##[24] Eraslan A.N., Arselan E., 2007, Plane strain analytical solutions to rotating partially plastic graded hollow shafts, Turkish Journal of Engineering and Environmental Sciences 31: 273288.##[25] Eraslan A.N., Akis T., 2005, Elastoplastic response of a long functionally graded tube subjected to internal pressure, Turkish Journal of Engineering and Environmental Sciences 29(6): 361368.##[26] Alla M.N., Ahmed K. I. E., Allah I. H., 2009, Elastic–plastic analysis of twodimensional functionally graded materials under thermal loading, International Journal of Solids and Structures 46: 27742786.##[27] Lu H. Ç., 2011, Stress analysis in a functionally graded disc under mechanical loads and a steady state temperature distribution, Indian Academy of Sciences Sadhana 36: 5364.##[28] Jahromi B. H., 2012, Elastoplastic stresses in a functionally graded rotating disk, Journal of Engineering Materials and Technology 134: 021004021015.##[29] Sadeghian M., Toussi H. E., 2012, Elastoplastic axisymmetric thermal stress analysis of functionally graded cylindrical vessel, Journal of Basic and Applied Scientific Research 2(10): 1024610257.##[30] Mendelson A., 1986, Plasticity: Theory and Application, New York, MacMillan.##]
1

Finite Difference Method for Biaxial and Uniaxial Buckling of Rectangular Silver Nanoplates Resting on Elastic Foundations in Thermal Environments Based on Surface Stress and Nonlocal Elasticity Theories
http://jsm.iauarak.ac.ir/article_527017.html
1
In this article, surface stress and nonlocal effects on the biaxial and uniaxial buckling of rectangular silver nanoplates embedded in elastic media are investigated using finite difference method (FDM). The uniform temperature change is utilized to study thermal effect. The surface energy effects are taken into account using the GurtinMurdoch’s theory. Using the principle of virtual work, the governing equations considering small scale for both nanoplate bulk and surface are derived. The influence of important parameters including, the Winkler and shear elastic moduli, boundary conditions, inplane biaxial and uniaxial loads, and widthtolength aspect ratio, on the surface stress effects are also studied. The finite difference method, uniaxial buckling, nonlocal effect for both nanoplate bulk and surface, silver material properties, and belowmentioned results are the novelty of this investigation. Results show that the effects of surface elastic modulus on the uniaxial buckling are more noticeable than that of biaxial buckling, but the influences of surface residual stress on the biaxial buckling are more pronounced than that of uniaxial buckling.
0

719
733


M
karimi
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
Iran
morteza.karimi@me.iut.ac.ir


A.R
Shahidi
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
Iran
Biaxial and uniaxial buckling
Surface stress theory
finite difference method
Thermal environment
Nonlocal elasticity theory
[[1] SakhaeePour A., Ahmadian M. T., Vafai A., 2008, Applications of singlelayered graphene sheets as mass sensors and atomistic dust detectors, Solid State Communications 145:168172.##[2] Ball P., 2001, Roll up for the revolution, Nature 414:142144.##[3] Baughman R. H., Zakhidov A. A., DeHeer W. A., 2002, Carbon nanotubes–the route toward applications, Science 297: 787792.##[4] Li C., Chou T. W., 2003, A structural mechanics approach for the analysis of carbon nanotubes, International Journal of Solids and Structures 40: 24872499.##[5] Govindjee S., Sackman J. L., 1999, On the use of continuum mechanics to estimate the properties of nanotubes, Solid State Communications 110: 227230.##[6] He X. Q., Kitipornchai S., Liew K. M., 2005, Buckling analysis of multiwalled carbon nanotubes: a continuum model accounting for van der Waals interaction, Journal of Mechanics and Physics of solids 53: 303326.##[7] Gurtin M. E., Murdoch A. I., 1975, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis 57: 291323.##[8] Gurtin M. E, Murdoch A. I., 1978, Surface stress in solids, International Journal of Solids and Structures 14: 431440.##[9] Assadi A., Farshi B., AliniaZiazi A., 2010, Size dependent dynamic analysis of nanoplates, Journal of Applied Physics 107: 124310.##[10] Assadi A., 2013, Size dependent forced vibration of nanoplates with consideration of surface effects, Applied Mathematical Modelling 37: 35753588.##[11] Assadi A., Farshi B., 2010, Vibration characteristics of circular nanoplates, Journal of Applied Physics 108: 074312.##[12] Assadi A., Farshi B., 2011, Size dependent stability analysis of circular ultrathin films in elastic medium with consideration of surface energies, Physica E 43: 11111117.##[13] Gheshlaghi B., Hasheminejad S. M., 2011, Surface effects on nonlinear free vibration of nanobeams, Composites Part B: Engineering 42: 934937.##[14] Nazemnezhad R., Salimi M., Hosseini Hashemi S. h., Asgharifard Sharabiani P., 2012, An analytical study on the nonlinear free vibration of nanoscale beams incorporating surface density effects, Composites Part B: Engineering 43: 28932897.##[15] HosseiniHashemi S., Nazemnezhad R., 2013, An analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects, Composites Part B: Engineering 52: 199206.##[16] Asgharifard Sharabiani P., Haeri Yazdi M. R., 2013, Nonlinear free vibrations of functionally graded nanobeams with surface effects, Composites Part B: Engineering 45: 581586.##[17] Ansari R., Sahmani S., 2011, Bending behavior and buckling of nanobeams including surface stress effects corresponding to different beam theories, International Journal of Engineering Science 49: 12441255.##[18] Karimi M., Shokrani M.H., Shahidi A.R., 2015, Sizedependent free vibration analysis of rectangular nanoplates with the consideration of surface effects using finite difference method, Journal of Applied and Computational Mechanics 1: 122133.##[19] Challamel N., Elishakoff I., 2012, Surface stress effects may induce softening: Euler–Bernoulli and Timoshenko buckling solutions, Physica E 44: 18621867.##[20] Park H.S., 2012, Surface stress effects on the critical buckling strains of silicon nanowires, Computational Materials Science 51: 396401.##[21] Ansari R., Shahabodini A., Shojaei M. F., Mohammadi V., Gholami R., 2014, On the bending and buckling behaviors of Mindlin nanoplates considering surface energies, Physica E 57: 126137.##[22] Ansari R., Mohammadi V., Faghih Shojaei M., Gholami R., Sahmani S., 2014, On the forced vibration analysis of Timoshenko nanobeams based on the surface stress elasticity theory, Composites Part B: Engineering 60: 158166.##[23] Mouloodi S., Khojasteh J., Salehi M., Mohebbi S., 2014, Size dependent free vibration analysis of Multicrystalline nanoplates by considering surface effects as well as interface region, International Journal of Mechanical Sciences 85: 160167.##[24] Mouloodi S., Mohebbi S., Khojasteh J., Salehi M., 2014, Sizedependent static characteristics of multicrystalline nanoplates by considering surface effects, International Journal of Mechanical Sciences 79: 162167.##[25] Wang K. F., Wang B. L., 2013, A finite element model for the bending and vibration of nanoscale plates with surface effect, Finite Elements in Analysis and Design 74: 2229.##[26] Wang K.F., Wang B.L., 2011, Combining effects of surface energy and nonlocal elasticity on the buckling of nanoplates, Micro and Nano Letters 6: 941943.##[27] Wang K.F., Wang B.L., 2011, Vibration of nanoscale plates with surface energy via nonlocal elasticity, Physica E 44: 448453.##[28] Farajpour A., Dehghany M., Shahidi A. R., 2013, Surface and nonlocal effects on the axisymmetric buckling of circular graphene sheets in thermal environment, Composites Part B: Engineering 50: 333343.##[29] Asemi S. R., Farajpour A., 2014, Decoupling the nonlocal elasticity equations for thermomechanical vibration of circular graphene sheets including surface effects, Physica E 60: 8090.##[30] Juntarasaid C., Pulngern T., Chucheepsakul S., 2012, Bending and buckling of nanowires including the effects of surface stress and nonlocal elasticity, Physica E 46: 6876.##[31] Mahmoud F.F., Eltaher M.A., Alshorbagy A.E., Meletis E.I., 2012, Static analysis of nanobeams including surface effects by nonlocal finite element, Journal of Mechanical Science and Technology 26: 35553563.##[32] Eltaher M.A., Mahmoud F.F., Assie A.E., Meletis E.I., 2013, Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams, Applied Mathematics and Computation 224:760774.##[33] Karimi M., Haddad H.A., Shahidi A.R., 2015, Combining surface effects and nonlocal two variable refined plate theories on the shear/biaxial buckling and vibration of silver nanoplates, Micro and Nano Letters 10: 276281.##[34] Hosseini–Hashemi S. h., Fakher M., Nazemnezhad R., 2013, Surface effects on free vibration analysis of nanobeams using nonlocal elasticity: a comparison between EulerBernoulli and Timoshenko, Journal of Solid Mechanics 5: 290304.##[35] Ghorbanpour Arani A., Kolahchi R., Hashemian M.,2014, Nonlocal surface piezoelasticity theory for dynamic stability of doublewalled boron nitride nanotube conveying viscose fluid based on different theories, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 203:228245.##[36] Ghorbanpour Arani A., Fereidoon A., Kolahchi R., 2014, Nonlinear surface and nonlocal piezoelasticity theories for vibration of embedded singlelayer boron nitride sheet using harmonic differential quadrature and differential cubature methods, Journal of Intelligent Material Systems and Structures 26:11501163.##[37] Mohammadi M., Moradi A., Ghayour M., Farajpour A., 2014, Exact solution for thermomechanical vibration of orthotropic monolayer graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures 11: 437458.##[38] Mohammadi M., Farajpour A., Goodarzi M., Dinari F., 2014, Thermomechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures 11: 659682.##[39] Mohammadi M., Farajpour A., Goodarzi M., Heydarshenas R., 2013, Levy type solution for nonlocal thermomechanical vibration of orthotropic monolayer graphene sheet embedded in an elastic medium, Journal of Solid Mechanics 5: 116132.##[40] Asemi S. R., Farajpour A., Borghei, M., Hassani A. H., 2014, Thermal effects on the stability of circular graphene sheets via nonlocal continuum mechanics, Latin American Journal of Solids and Structures 11: 704724.##[41] Ghorbanpour Arani A.H., Maboudi M.J., Ghorbanpour Arani A., Amir S., 2013, 2Dmagnetic field and biaxiall inplane preload effects on the vibration of double bonded orthotropic graphene sheets, Journal of Solid Mechanics 5: 193205.##[42] Ghorbanpour Arani A., Amir S., 2013, Nonlocal vibration of embedded coupled CNTs conveying fluid Under thermomagnetic fields via Ritz method, Journal of Solid Mechanics 5:206215.##[43] Ghorbanpour Arani A., Kolahchi R., Allahyari S.M.R., 2014, Nonlocal DQM for large amplitude vibration of annular boron nitride sheets on nonlinear elastic medium, Journal of Solid Mechanics 6:334346.##[44] Anjomshoa A., Shahidi A.R., Shahidi S.H., Nahvi H., 2015, Frequency analysis of embedded orthotropic circular and elliptical micro/nanoplates using nonlocal variational principle, Journal of Solid Mechanics 7:1327.##[45] Naderi A., Saidi A.R., 2014, Nonlocal postbuckling analysis of graphene sheets in a nonlinear polymer medium, International Journal of Engineering Science 81: 4965.##[46] Naderi A., Saidi A.R., 2013, Modified nonlocal mindlin plate theory for buckling analysis of nanoplates, Journal of Nanomechanics and Micromechanics 4:130150130158.##[47] Eringen A.C., Edelen D.G.B., 1972, On nonlocal elasticity, International Journal of Engineering Science 10: 233248.##[48] Malekzadeh P., Shojaee M., 2013, A twovariable firstorder shear deformation theory coupled with surface and nonlocal effects for free vibration of nanoplates, Journal Vibration and Control 21(14): 27552772.##[49] Karamooz Ravari M. R., Talebi S. A., Shahidi R., 2014, Analysis of the buckling of rectangular nanoplates by use of finitedifference method, Meccanica 49: 14431455.##[50] Karamooz Ravari M.R., Shahidi R., 2013, Axisymmetric buckling of the circular annular nanoplates using finite difference method, Meccanica 48: 135144.##[51] GreeJ.R, Street R.A., 2007, Mechanical characterization of solutionderived nanoparticle silver ink thin films, Journal of Applied Physics 101: 103529.##]
1

Finite Element Analysis of Reinforced RC Bracket Using CFRP Plates
http://jsm.iauarak.ac.ir/article_527018.html
1
CFRP composites have unique application qualities such as high resistance and durability to environmental conditions, having relatively low weight and easy to install in strengthening concrete structure elements. The brackets should be strengthen sufficiently if they are not calculated and implemented well. Application of the CFRP is one of the methods for such purposes. The study involves using five different configurations of CFRP sheets as a means of strengthening bracket, using finite element and nonlinear dynamic analysis method within the ABAQUS software. Comparative analysis results of nonstrengthened bracket model, show a 24.06% increase in the loadcarrying capacity of strengthened models using the CFRP compared with the initial model (without CFRP). Results further show an increase of 24.96% of energy absorption in the strengthened models compared with the nonstrengthened model.
0

734
743


A
Rafati
Department of Civil, Dezful Branch, Islamic Azad university, Dezful, Iran
Iran


S.V
Razavi
Department of Civil Engineering, Jundishapor University of Technology, Dezful, Iran
Iran
vrazavi@jsu.ac.ir
Bracket
Load carrying capacity
energy absorption
CFRP
ABAQUS
[[1] Zeinoldini M. 2010, The Investigation of Performance of FRP Materials in Strengthening Concrete Buildings, MA Thesis, Shahid Bahonar University of Kerman.##[2] Abou Elez Y., 1997 , Behavior of Reinforced Concrete Columns Confined with Advanced Composite Materials, Ph.D. Thesis, Minia University, Egypt.##[3] Norris T., Saadatmanesh H., Ehsani M., 1997 , Shear and flexural strengthening of R/C beams with carbon fiber sheets, Journal of Structural Engineering 123(7 ): 903911.##[4] Dolan Ch., Corry R., 2001 , Strengthening and repair of a column bracket using a carbon fiber reinforced polymer(CFRP)fabric , PCI Journal 46: 5463.##[5] Erfan A., Abdel Rahman G., Nassifand M., Hammad Y., 2010 , Behaviour of Reinforced Concrete Corbels Strengthened with CFRP Fabrics, Benha University.##[6] Elgwady M., Rabie M., Mostafa M., 2009 , Strengthening of Corbels Using CFRP an Experimental Program, Cairo University, Giza, Egypt.##[7] Ozden S., Meydanli Atalay H., 2001 , Strengthening and Repair of a column Bracket using a Carbon Fiber Reinforced Polymer Fabric, PCI Journal 46(1): 5463.##[8] Yao L., Wan Y., Liang Ch., Hwan Y., Sin L., 2012 , Reinforced concrete corbels strengthened with carbon fiber reinforced plastics, Computers and Concrete 10(3): 259276.##[9] Halvaey Far M.R. , Razavi T. V., 2011 , Nonlinear analysis of loaddeflection testing of reinforced oneway slab strengthened by carbon fiber reinforced polymer (CFRP) and using artificial neural network (ANN) for prediction , International Journal of the Physical Sciences 6(13): 30543061.##[10] Hansen E., Willam K. , Carol I., 2001 , A twosurface anisotropic damage/plasticity model for plain covcrete , Proceedings of Framcos4 Conference Paris , Fracture Mechanics of Concrete Materials.##[11] ABAQUS V6.13 Manuals, 2013 , Providence, RI: Dassault Systemes.##[12] Taqieddin Z., 2008 , ElastoPlastic and Damage Modeling of Reinforced Concrete, Ph.D. Dissertation, Louisiana State University, Baton Rouge, LA.##[13] Mander J.B., Priestley M.J.N., Park R., 1988 , Theoretical StressStrain Model for Confined Concrete , Fellow, ASCE.##[14] Tosonos A. G., Tegos I. A., Penelis G. G., 1992, Seismic Resistance of Type 2 Exterior BeamColumn Reinforced with Inclined Bars, ACI Structural Journal 89(1): 312.##]
1

Ductile Failure and Safety Optimization of Gas Pipeline
http://jsm.iauarak.ac.ir/article_527020.html
1
Safety and failure in gas pipelines are very important in gas and petroleum industry. For this reason, it is important to study the effect of different parameters in order to reach the maximum safety in design and application. In this paper, a three dimensional finite element analysis is carried out to study the effect of crack length, crack depth, crack position, internal pressure and pipe thickness on failure mode and safety of API X65 gas pipe. Four levels are considered for each parameter and finite element simulations are carried out by using design of experiments (DOE). Then, multiobjective Taguchi method is conducted in order to minimize x and y coordinates of Failure Assessment Diagram (FAD). So, desired levels that minimize the coordinates and rises the possibility of safety are derived for each parameter. The variation in FAD coordinates according to the changes in each parameter are also found. Finally, comparisons between the optimum design and all other experiments and simulations have shown a good safety situation. It is also concluded that the more design parameters close to optimum levels, the better safety condition will occur in FAD. A verification study is performed on the safety of longitudinal semielliptical crack and the results has shown a good agreement between numerical and experimental results.
0

744
755


P
Zamani
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Iran


A
Jaamialahmadi
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Iran
jaamia@um.ac.ir


M
Shariati
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Iran
mshariati44@gmail.com
SemiElliptical Crack
Finite Element Analysis
Taguchi Method
Failure assessment diagram
[[1] Underwood J.H., 1972, Stress intensity factors for internally pressurized thickwalled cylinders, American Society for Testing and Materials 513 : 5970.##[2] Raju I.S., Newman J.C., 1980, Stressintensity factors for internal and external surface cracks in cylindrical vessels, Journal of Pressure Vessel Technology 102(4): 293298.##[3] Newman J.C., 1976, Fracture analysis of surface and through cracks in cylindrical pressure vessels, National Aeronautics and Space Administration 39: 2133.##[4] Liu A., 1996, Rockwell International Science Center, ASM Handbook Fatigue and Fracture.##[5] Lee S.L., Ju J.B., Kim W.S., Kwon D., 2004, Weld crack assessments in API X65 pipeline: failure assessments diagrams with variations in representative mechanical properties, Materials Science and Engineering 373(1): 122130.##[6] Oh C.K, Kim Y.J, Baek J.H., Kim Y.P., Kim W.S., 2007, Ductile failure analysis of API X65 pipes with notchtype defects using a local fracture criterion, International Journal of Pressure Vessels and Piping 84: 512525.##[7] Sandvik A., Ostby E., Thaulow C., 2008, A probabilistic fracture mechanics model including 3D ductile tearing of biaxially loaded pipes with surface cracks, Engineering Fracture Mechanics 75: 7696.##[8] Pluvinage G., Capelle J., Schmitt G., Mouwakeh M., 2012, Doman failure assessment diagrams for defect assessment of gas pipes, 19th European Conference on Fracture, Kazan, Russia.##[9] Zhang B., Ye C., Liang B., Zhang Z., Zhi Y., 2014, Ductile failure analysis and crack behavior of X65 buried pipes using extended finite element method, Engineering Failure Analysis 45: 2640.##[10] Ghajar R., Mirone G., Keshavarz A., 2013, Ductile failure of X100 pipeline steelExperiments and fractography, Materials & Design 43: 513525.##[11] Sharma K., Singh I.V., Mishra B.K., Maurya S.K., 2014, Numerical simulation of semielliptical axial crack in pipe bend using XFEM, Journal of Solid Mechanics 6(2): 208228.##[12] Dimic I., Medjo B., Rakin M., Arsic M., Sarkocevic Z., Sedmak A., 2014, Failure prediction of gas and oil drilling rig pipelines with axial defects, Procedia Materials Science 3: 955960.##[13] Ainsworth R.A., 1984, The assessment of defects in structures of strain hardening material, Engineering Fracture Mechanics 19(4):633642.##[14] Anderson T.L., Osage D.A., 2000, API 579: a comprehensive fitnessforservice guide , International Journal of Pressure Vessels and Piping 77(14):953963.##[15] API 579, 2000, Recommended Practice for Fitness for Service, American Petroleum Institute.##[16] BS7910, 1999, Guide and Methods for Assessing the Acceptability of Flaws in Fusion Welded Structures, British Standard Institutions.##[17] R6,1998, Assessment of the Integrity of Structures Containing Defects, British Energy.##[18] BS EN ISO 7448, 1999, Metallic Materials Determination of PlanStrain Fracture Toughness, British Standard Institution.##[19] Shahraini S.I., Hashemi S.H., 2014, Effects of surface crack length and depth variations on gas transmission pipeline safety, Modares Mechanical Engineering 14:2632.##[20] Habbit, Karlsson, Sorensen, 2007, Abaqus/Standard Analysis User’s Manual, USA.##]
1

On the Stability of an ElectrostaticallyActuated Functionally Graded MagnetoElectroElastic MicroBeams Under MagnetoElectric Conditions
http://jsm.iauarak.ac.ir/article_527021.html
1
In this paper, the stability of a functionally graded magnetoelectroelastic (FGMEE) microbeam under actuation of electrostatic pressure is studied. For this purpose EulerBernoulli beam theory and constitutive relations for magnetoelectroelastic (MEE) materials have been used. We have supposed that material properties vary exponentially along the thickness direction of the microbeam. Governing motion equations of the microbeam are derived by using of Hamilton’s principle. Maxwell’s equation and magnetoelectric boundary conditions are used in order to determine and formulate magnetic and electric potentials distribution along the thickness direction of the microbeam. By using of magnetoelectric potential distribution, effective axial forces induced by external magnetoelectric potential are formulated and then the governing motion equation of the microbeam under electrostatic actuation is obtained. A Galerkinbased step by step linearization method (SSLM) has been used for static analysis. For dynamic analysis, the Galerkin reduced order model has been used. Static pullin instability for 5 types of MEE microbeam with different gradient indexes has been investigated. Furthermore, the effects of external magnetoelectric potential on the static and dynamic stability of the microbeam are discussed in detail.
0

756
772


A
Amiri
Mechanical Engineering Department, Urmia University, Urmia, Iran
Iran
amiri.ahd@gmail.com


G
Rezazadeh
Mechanical Engineering Department, Urmia University, Urmia, Iran
Iran


R
Shabani
Mechanical Engineering Department, Urmia University, Urmia, Iran
Iran


A
Khanchehgardan
Mechanical Engineering Department, Urmia University, Urmia, Iran
Iran
Functionally graded
MEE
MEMS
Maxwell’s Equation
Pullin instability
[[1] Davi G., Milazzo A., 2011, A regular variational boundary model for free vibrations of magnetoelectroelastic structures, Engineering Analysis with Boundary Elements 35: 303312.##[2] Fakhzan M.N., Muthalif Asan G.A., 2013, Harvesting vibration energy using piezoelectric material: Modeling, simulation and experimental verifications, Mechatronics 23: 6166.##[3] Amiri A., Fakhari S.M., Pournaki I.J., Rezazadeh G., Shabani R., 2015, Vibration analysis of circular magnetoelectroelastic Nanoplates based on Eringen's nonlocal theory, International Journal of Engineering, Transactions C: Aspects 28(12): 18081817.##[4] Liu C., Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2013, Thermoelectromechanical vibration of piezoelectric nanoplates based on the nonlocal theory, Composite Structures 106: 167174.##[5] Daga A., Ganesan N., Shankar K., 2009, Behavior of magnetoelectroelastic sensors under transient mechanical loading, Sensors and Actuators A: Physical 150: 4655.##[6] Li Y.S., Cai Z.Y., Shi S.Y., 2014, Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory, Composite Structures 111: 522529.##[7] Linnemann K., Klinkel S., Wagner W., 2009, A constitutive model for magnetostrictive and piezoelectric materials, International Journal of Solids and Structures 46: 11491166.##[8] Xue C.X., Pan E., Zhang S.Y., 2011, Large deflection of a rectangular magnetoelectroelastic thin plate, Mechanics Research Communications 38: 518523.##[9] Pan E., Heyliger P.R., 2003, Exact solutions for magnetoelectroelastic laminates in cylindrical bending, International Journal of Solids and Structures 40: 68596876.##[10] Ke L.L., Wang Y.S., 2014, Free vibration of sizedependent magnetoelectroelastic nanobeams based on the nonlocal theory, Physica E 63: 5261.##[11] Amiri A., Pournaki I.J., Jafarzadeh E., Shabani R., Rezazadeh G., 2016, Vibration and instability of fluidconveyed smart microtubes based on magnetoelectroelasticity beam model, Microfluidics and Nanofluidics 20(2): 110.##[12] Liu M.F., 2011, An exact deformation analysis for the magnetoelectroelastic fiberreinforced thin plate, Applied Mathematical Modelling 35: 24432461.##[13] Huang D.J., Ding H.J., Chen W.Q., 2007, Analytical solution for functionally graded magnetoelectroelastic plane beams, International Journal of Engineering Science 45: 467485.##[14] Chang T.P., 2013, On the natural frequency of transversely isotropic magnetoelectroelastic plates in contact with fluid, Applied Mathematical Modelling 37: 25032515.##[15] Alaimo A., Milazzo A., Orlando C., 2013, A fournode MITC finite element for magnetoelectroelastic multilayered plates, Computers and Structures 129: 120133.##[16] Li Y.S., 2014, Buckling analysis of magnetoelectroelastic plate resting on Pasternak elastic foundation, Mechanics Research Communications 56: 104114.##[17] Chang T.P., 2013, Deterministic and random vibration analysis of fluidcontacting transversely isotropic magnetoelectroelastic plates, Computers and Fluids 84: 247254.##[18] Zhou Z.G., Wang B., Sun Y.G., 2004, Two collinear interface cracks in magnetoelectroelastic composites, International Journal of Engineering Science 42: 11551167.##[19] Li J.Y., 2000, Magnetoelectroelastic multiinclusion and inhomogeneity problems and their applications in composite materials, International Journal of Engineering Science 38: 19932011.##[20] Milazzo A., 2014, Large deflection of magnetoelectroelastic laminated plates, Applied Mathematical Modelling 38: 17371752.##[21] Xue C.X., Pan E., 2013, On the longitudinal wave along a functionally graded magnetoelectroelastic rod, International Journal of Engineering Science 62: 4855.##[22] Raeisifard H., Bahrami M.N., YousefiKoma A., Raeisi Fard H., 2014, Static characterization and pullin voltage of a microswitch under both electrostatic and piezoelectric excitations, European Journal of Mechanics A/Solids 44: 116124.##[23] Mobki H., Sadeghi M.H., Rezazadeh G., Fathalilou M., Keyvanijanbahan A.A., 2014, Nonlinear behavior of a nanoscale beam considering length scaleparameter, Applied Mathematical Modelling 38: 18811895.##[24] Rezazadeh G., Madinei H., Shabani R., 2012, Study of parametric oscillation of an electrostatically actuated microbeam using variational iteration method, Applied Mathematical Modelling 36: 430443.##[25] Zhang W.M., Yan H., Peng Z.K., Meng G., 2014, Electrostatic pullin instability in MEMS/NEMS: A review, Sensors and Actuators A: Physical 214: 187218.##[26] Khanchehgardan A., Rezazadeh G., Shabani R., 2014, Effect of mass diffusion on the damping ratio in microbeam resonators, International Journal of Solids and Structures 51: 31473155.##[27] Khanchehgardan A., ShahMohammadiAzar A., Rezazadeh G., Shabani R., 2013, Thermoelastic damping in nanobeam resonators based on nonlocal theory, International Journal of Engineering 26(12): 15051514.##[28] Duan J.S., Rach R., 2013, A pullin parameter analysis for the cantilever NEMS actuator model including surface energy, fringing field and Casimir effects, International Journal of Solid and Structures 50: 35113518.##[29] Taghavi N., Nahavi H., 2013, Pullin instability of cantilever and fixedfixed nanoswitches, European Journal of Mechanics A/Solids 41: 123133.##[30] Wang K.F., Wang B.L., 2014, Influence of surface energy on the nonlinear pullin instability of nanoswitches, International Journal of Nonlinear Mechanics 59: 6975.##[31] Yu Y.P., Wu B.S., 2014, An approach to predicting static responses of electrostatically actuated microbeam under the effect of fringing field and Casimir force, International Journal of Mechanical Science 80: 183192.##[32] Zamanzadeh M., Rezazadeh G., Jafarsadeghipoornaki I., Shabani R., 2013, Static and dynamic stability modeling of a capacitive FGM microbeam in presence of temperature changes, Applied Mathematical Modelling 37: 69646978.##[33] Mobki H., Rezazadeh G., Sadeghi M., VakiliTahami F., SeyyedFakhrabadi M.S., 2013, A comprehensive study of stability in an electrostatically actuated microbeam, International Journal of Nonlinear Mechanics 48: 7885.##[34] Osterberg P.M., Senturia S.D., 1997, Mtest: A test chip for MEMS material property measurement using electrostatically actuated test structure, Journal of Microelectromechanical Systems 6 (2): 107118.##]
1

Analyzing Frequency of Conical (∆ shaped) Tanks
http://jsm.iauarak.ac.ir/article_527022.html
1
A finite element analysis is presented for sloshing and impulsive motion of liquidfilled conical tanks during lateral antisymmetric excitation. The performed analyses led to the development of a number of charts which can be used to identify the natural frequency, the mode shapes of conical tanks for both fundamental and the cos(θ)modes of vibration. Conical tank geometry was described with several parameters namely, bottom radius( Rb) total height of liquid (h), angle of inclination of the tanks(θi), as variables. Numerical result of the free vibration was obtained for the cases of conical tanks with θi=0 and compared with existing experiments and other predicated results, showing a good agreement between the experiment and numerical results.
0

773
780


F
Saljughi
National Iranian Oil Company (NIOC), Iran
Iran
saljughi.f@nisoc.ir
Conical shell
Modal characteristic
Finite Element Method
Apex angle
Natural frequency
[[1] Jacobson L.S., Ayre R.S., 1951, Hydrodynamic experiments with rigid cylindrical tanks subjected to transient motion, Bulletin of the Seismological Society of America 41: 1535.##[2] Graham E.W., Rodriguez A. M., 1979, The characteristics of fuel motion which affect airplane dynamics, Journal of Applied Mechanics 19(3): 381388.##[3] Abramson H.N, 1966, The Dynamic Behavior of Liquid in Moving Containers with Applications to Space Vehicle Technology, NASA SP106, National Aeronautic and Space Administration, Washington.##[4] Feschenko S. F., Lukovsky I. A., Rabinovich B. I., Dokuchaev L. V, 1969, The methods for determining the added fluid masses in mobile cavities Kiev, Naukova Dumka 250: 13.##[5] Dokuchaev L. V, 1964, On the solution of a boundary value problem on the sloshing of a liquid in conical cavities, Applied Mathematics and Mechanics 28: 151154.##[6] Abramson H. N., 1968, NASA Space Vehicle Design Criteria (Structures), NASA SP8009 Propellant Slosh Loads, Washington.##[7] Mikishev G. N., Dorozhkin N. Y, 1961, An experimental investigation of free oscillations of a liquid in containers, Izvestiya Akademii Nauk SSSr, Otdelenie Tekhnicheskikh Nauk, Mekhanika, Mashinostroenie 4: 4853.##[8] Bauer H. F, 1982, Sloshing in conical tanks, Acta Mechanica 43(34): 185200.##[9] Bauer H. F., Eidel W, 1988, Non–linear liquid motion in conical container, Acta Mechanica 73 (14): 1131.##[10] Lukovsky I. A., Bilyk A. N., 1985, Forced nonlinear oscillation of a liquid in moving axialsymmetric conical tanks in book: NumericalAnalytical Methods of Studying the Dynamics and Stability of Multidimensional Systems, Institute of Mathematics, Kiev.##[11] Schiffner K, 1983, A modified boundary element method for the threedimensional problem of fluid oscillation, Proceedings of the Fifth International Conference Berlin, Hiroshima, Japan.##[12] Yamaki N., Tani J., Yamaji T., 1984, Free vibration of a clampedclamped circular cylindrical shell partially filled with liquid, Journal of Sound Vibration 94: 531550.##[13] Gupta R. K., Hutchinson G. L., 1988, Free vibration analysis of liquid storage tanks, Journal of Sound Vibration 122: 491506.##[14] Mazuch T., Horacek J., Trnka J., Vesely J., 1996, Natural modes and frequencies of a thin clampedfree steel cylindrical storage tank partially filled with water, FEM and measurement, Journal of Sound and Vibration 193: 669690.##[15] Han R. P. S., Liu J. D., 1994, Free vibration analysis of a fluidloaded variable thickness cylindrical tank, Journal of Sound and Vibration 176: 235253.##[16] Jeong K. H., Kim K. J., 1998, Free vibration of a circular cylindrical shell filled with bounded compressible fluid, Journal of Sound and Vibration 217: 197221.##[17] Jeong K. H., Kim K. S., Park K. B., 1997, Natural frequency characteristics of a cylindrical tank filled with bounded compressible fluid, Journal of the Computational Structural Engineering Institute of Korea 10(4): 291302.##[18] Dutta S., Mandal A., Dutta S.C., 2004, Soil structure interaction in dynamic behavior of elevated tanks with alternate frame staging configurations, Journal of Sound and Vibration 277: 825853.##[19] Shrimali M.K., Jangid R.S., 2003, Earthquake response of isolated elevated liquid storage steel tanks, Journal of Constructional Steel Research 59: 12671288.##[20] Damatty El A.A., Sweedan A.M.I., 2006, Equivalent mechanical analog for dynamic analysis of pure conical tanks, ThinWalled Structures 44: 429440.##[21] Damatty El A., Korol R. M., Tang L. M., 2000, Analytical and experimental investigation of the dynamic response of liquidfilled conical tanks, Proceedings of the World Conference of Earthquake Engineering, New Zelan.##[22] Housner G.W., 1963, Dynamic behavior of water tanks, Bulletin of the Seismological Society of America 53:381387.##[23] Haroun M.A., Housner G.W., 1981, Seismic design of liquid storage tanks, Proceeding of the Journal of Technical Councils, ASCE.##[24] Yih C.S., 1980, Stratified Flows, Academic Press Inc, New York.##]
1

Dynamic Simulation and Mechanical Properties of Microtubules
http://jsm.iauarak.ac.ir/article_527023.html
1
This work is conducted to obtain mechanical properties of microtubule. For this aim, interaction energy in alphabeta, betaalpha, alphaalpha, and betabeta dimers was calculated using the molecular dynamic simulation. Forcedistance diagrams for these dimers were obtained using the relation between potential energy and force. Afterwards, instead of each tubulin, one sphere with 55 KDa weight connecting to another tubulin with a nonlinear connection such as nonlinear spring could be considered. The mechanical model of microtubule was used to calculate Young’s modulus based on finite element method. Obtained Young’s modulus has good agreement with previous works. Also, natural frequency of microtubules was calculated based on finite element method.
0

781
787


M
Motamedi
Faculty of Engineering, University of Shahreza, P. O. Box 8614956841, Isfahan, Iran
Iran
mmotamedi@ut.ac.ir


M
Mosavi Mashhadi
Department of Mechanical Engineering, University of Tehran, P.O. Box 113654563, Tehran, , Iran
Iran
Microtubules
Finite Element
Molecular dynamic
Mechanical Properties
[[1] Yiting D., Zhiping X., 2011, Mechanics of microtubules from a coarsegrained model, BioNanoScience 1: 173182.##[2] Downing K.H. , Nogales E., 1998, New insights into microtubule structure and function from the atomic model of tubulin, European Biophysics Journal 27: 431436.##[3] David S., Nathan A., Andrew J., 2003, The physical basis of microtubule structure and stability, Protein Science 12: 22572261.##[4] Lin Y., Gijsje H., Frederick C., David A., 2007, Viscoelastic properties of microtubule networks, Macromolecules 40: 77147720.##[5] Chretien D., Fuller S.D., 2000, Microtubules switch occasionally into unfavorable configurations during elongation, Journal of Molecular Biology 298: 663676.##[6] Iva M.T., 2008, Pushmepullyou: how microtubules organize the cell interior, European Biophysics Journal 37: 12711278.##[7] Chrétien D., Wade R.H., 1991, New data on the microtubule surface lattice, Biology of the Cell 71: 161174.##[8] Nogales E., Wolf S. G., Downing K. H., 1998, Structure of the α, β tubulin dimer by electron crystallography, Nature 391: 199203.##[9] Li H., DeRosier D.J., Nicholson W.V., Nogales E., Downing K.H., 2002, Microtubule structure at 8 Å resolution, Structure 10: 13171328.##[10] Löwe J., Li H., Downing K. H., Nogales E., 2001, Refined structure of αβtubulin at 3.5 Å resolutions, Journal of Molecular Biology 313: 10451057.##[11] De Pablo P.J., Schaap I. A.T., MacKintosh F.C., Schmidt C. F., 2003, Deformation and collapse of microtubules on the nanometer scale, Physical Review Letters 91: 098101.##[12] Ja´nosi M., Chre´tien D., Flyvbjerg H., 2002, Structural microtubule cap: stability, catastrophe, rescue, and third state, Biophysical Journal 83: 13171330.##[13] Ying X., Dong X., Jie L., 2007, Computational Methods for Protein Structure Prediction and Modeling, Basic Characterization, Springer Science. NewYork.##[14] Karplus M., McCammon J.A., 2002, Molecular dynamics simulations of biomolecules, Nature Structural Biology 9: 646  652##[15] Zeiger A.S., Layton B.E., 2008, Molecular modeling of the axial and circumferential elastic moduli of tubulin, Biophysical Journal 95: 36063618.##[16] Bekir A., Ömer C., 2014, Mechanical analysis of isolated microtubules based on a higherorder shear deformation beam theory, Composite Structures 118: 918.##[17] Kis A., Kasas S., Babic B., Kulik A.J., Benoit W., 2002, Nanomechanics of microtubules, Physical Review Letters 89: 248101.##[18] Kasas S., Kis A., Riederer B. M., Forro L., Dietler G., Catsicas S., 2004, Mechanical properties of microtubules explored using the finite elements method, ChemPhysChem 5: 252257.##[19] Nogales E., Whittaker M., Milligan R. A., Downing K. H., 1999, Highresolution model of the microtubule, Cell 96: 7988.##[20] Howard J., 2001, Mechanics of Motor Proteins and the Cytoskeleton, Sinauer, Sunderland.##[21] Dominguez C., Boelens R., Bonvin A.M.J.J., 2003, HADDOCK: a proteinprotein docking approach based on biochemical or biophysical information, Journal of the American Chemical Society 125: 17311737.##[22] Pronk S., Páll S., Schulz R., Larsson P., Bjelkmar P., Apostolov R., Shirts M.R., Smith J.C., Kasson P.M., Vander Spoel D., Hess B., Lindahl E., 2013, GROMACS 4.5: a highthroughput and highly parallel open source molecular simulation toolkit, Bioinformatics 29: 845854.##[23] Walter R.P., Philippe H. , Ilario G., Alan E., Salomon R., Jens F., Andrew E., Thomas H., Peter K., Wilfred F., 1999, The GROMOS biomolecular simulation program package, The Journal of Physical Chemistry A 103: 35963607.##[24] Berendsen H.J.C., Postma J.P.M., DiNola A., Haak J.R., 1984, Molecular dynamics with coupling to an external bath, The Journal of Chemical Physics 81:3684.##[25] Meriam J., Kraige L., 2012, Engineering MechanicsDynamic, Wiley, 7 edition.##[26] Russell C., 2013, Mechanics of Materials, Prentice Hall, 9 edition.##[27] Gitte F., Mickey B., Nettleton J., Howard J., 1993, Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape, The Journal of Cell Biology 120: 923934.##[28] Mickey B., Howard J., 1995, Rigidity of microtubules is increased by stabilizing agent, The Journal of Cell Biology 130: 909917.##]
1

ThermoMechanical Vibration Analysis of FG Circular and Annular Nanoplate Based on the ViscoPasternak Foundation
http://jsm.iauarak.ac.ir/article_527024.html
1
In this study, the vibration behavior of functional graded (FG) circular and annular nanoplate embedded in a ViscoPasternak foundation and coupled with temperature change is studied. The effect of inplane preload and temperature change are investigated on the vibration frequencies of FG circular and annular nanoplate. To obtain the vibration frequencies of the FG circular and annular nanoplate, two different size dependent theories are utilized. The material properties of the FGM nanoplates are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique. The FG circular and annular nanoplate is coupled by an enclosing viscoelastic medium which is simulated as a Visco Pasternak foundation. By using the modified strain gradient theory (MSGT) and the modified couple stress theory (MCST), the governing equation is derived for FG circular and annular nanoplate. The differential quadrature method (DQM) and the Galerkin method (GM) are utilized to solve the governing equation to obtain the frequency vibration of FG circular and annular nanoplate. The results are subsequently compared with valid result reported in the literature. The effects of the size dependent, the inplane preload, the temperature change, the power index parameter, the elastic medium and the boundary conditions on the natural frequencies are investigated. The results show that the size dependent parameter has an increasing effect on the vibration response of circular and annular nanoplate. The temperature change also play an important role in the mechanical behavior of the FG circular and annular nanoplate. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the nanoplate
0

788
805


M
Goodarzi
Department of Engineering, College of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
Iran
m.goodarzi.iau@gmail.com


M
Mohammadi
Department of Engineering, College of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
Iran


M
Khooran
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Iran
Iran


F
Saadi
Department of Engineering, College of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
Iran
Circular and annular nanoplate
Functional graded nanoplate
Modified strain gradient theory
Modified couple stress theory
[[1] Sallese J.M., Grabinski W., Meyer V., Bassin C., Fazan P., 2001, Electrical modeling of a pressure sensor MOSFET, Sensors and Actuators A: Physical 94: 5358.##[2] Nabian A., Rezazadeh G., Haddadderafshi M., Tahmasebi A., 2008, Mechanical behavior of a circular microplate subjected to uniform hydrostatic and nonuniform electrostatic pressure, Microsystem Technologies 14: 235240.##[3] Bao M., Wang W., 1996, Future of microelectromechanical systems (MEMS), Sensors and Actuators A: Physical 56: 135141.##[4] Younis M.I., AbdelRahman E.M., Nayfeh A., 2003, A reducedorder model for electrically actuated microbeambased MEMS, Journal of Microelectromechanical Systems 12: 672680.##[5] Batra R.C., Porﬁri M., Spinello D, 2006, Electromechanical model of electrically actuated narrow microbeams, Journal of Microelectromechanical Systems 15: 11751189.##[6] Nayfeh A.H., Younis M.I., AbdelRahman E.M., 2007, Dynamic pullin phenomenon in MEMS resonators, Nonlinear Dynamics 48: 153163.##[7] Nayfeh A.H., Younis M.I., 2004, Modeling and simulations of thermoelastic damping in microplates, Journal of Micromechanics and Microengineering 14: 17111717.##[8] Zhao X.P., AbdelRahman E.M., Nayfeh A.H., 2004, A reducedorder model for electrically actuated microplates, Journal of Micromechanics and Microengineering 14: 900906.##[9] Machauf A., Nemirovsky Y., Dinnar U., 2005, A membrane micropump electrostatically actuated across the working ﬂuid, Journal of Micromechanics and Microengineering 15: 23092316.##[10] Wong E.W., Sheehan P.E., Lieber C.M., 1997, Nanobeam mechanics: elasticity, strength and toughness of nanorods and nanotubes, Science 277: 19711975.##[11] Zhou S.J., Li Z.Q., 2001, Metabolic response of Platynota stultana pupae during and after extended exposure to elevated CO2 and reduced O2 atmospheres, Shandong University Technology 31: 401409.##[12] Mohammadi V., Ansari R., Faghih Shojaei M., Gholami R., Sahmani S., 2013, Sizedependent dynamic pullin instability of hydrostatically and electrostatically actuated circular microplates, Nonlinear Dynamics 73: 15151526.##[13] Yang F., Chong A.C.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39: 27312743.##[14] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal Applied Physics 54: 47034711.##[15] Asemi H.R., Asemi S.R., Farajpour A., Mohammadi M., 2015, Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermoelectromechanical loads, Physica E 68: 112122.##[16] Danesh M., Farajpour A., Mohammadi M., 2012, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications 39: 2327.##[17] Aydogdu M., 2009, Axial vibration of the nanorods with the nonlocal continuum rod model, Physica E 41: 861864.##[18] Mohammadi M., Farajpour A., Goodarzi M., Heydarshenas R., 2013, Levy type solution for nonlocal thermomechanical vibration of orthotropic monolayer graphene sheet embedded in an elastic medium, Journal of Solid Mechanics 5(2): 116132.##[19] Mohammadi M., Farajpour A., Goodarzi M., Dinari F., 2014, Thermomechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures 11 (4): 659682.##[20] Duan W. H., Wang C. M., 2007, Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory, Nanotechnology 18: 385704.##[21] Mohammadi M., Moradi A., Ghayour M., Farajpour A., 2014, Exact solution for thermomechanical vibration of orthotropic monolayer graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures 11(3): 437458.##[22] Asemi S.R., Farajpour A., Asemi H.R., Mohammadi M., 2014, Influence of initial stress on the vibration of doublepiezoelectricnanoplate systems with various boundary conditions using DQM, Physica E 63: 169179.##[23] Mohammadi M., Goodarzi M., Ghayour M. Farajpour A., 2013, Inﬂuence of inplane preload on the vibration frequency of circular graphene sheet via nonlocal continuum theory, Composites Part B 51: 121129.##[24] Goodarzi M., Mohammadi M., Farajpour A., Khooran M., 2014, Investigation of the effect of prestressed on vibration frequency of rectangular nanoplate based on a visco pasternak foundation, Journal of Solid Mechanics 6: 98121.##[25] Farajpour A., Shahidi A. R., Mohammadi M., Mahzoon M., 2012, Buckling of orthotropic micro/nanoscale plates under linearly varying inplane load via nonlocal continuum mechanics, Composite Structures 94: 16051615.##[26] Mohammadi M., Farajpour A., Goodarzi M., Mohammadi H., 2013, Temperature effect on vibration analysis of annular graphene sheet embedded on viscoPasternak foundation, Journal of Solid Mechanics 5(3): 305323.##[27] Wang C.M., Duan W.H., 2008, Free vibration of nanorings/arches based on nonlocal elasticity, Journal of Applied Physics 104: 014303.##[28] Moosavi H., Mohammadi M., Farajpour A., Shahidi S. H., 2011, Vibration analysis of nanorings using nonlocal continuum mechanics and shear deformable ring theory, Physica E 44: 135140.##[29] Mohammadi M., Goodarzi M., Ghayour M., Alivand S., 2012, Small scale effect on the vibration of orthotropic plates embedded in an elastic medium and under biaxial inplane preload via nonlocal elasticity theory, Journal of Solid Mechanics 4(2) : 128143.##[30] Wang B., Zhao J., Zhou S., 2010, A micro scale Timoshenko beam model based on strain gradient elasticity theory, European Journal of Mechanics A/Solids 29: 591599.##[31] Ansari R., Gholami R., Sahmani S., 2011, Free vibration of sizedependent functionally graded microbeams based on a strain gradient theory, Composite Structures 94: 221228.##[32] Ansari R., Gholami R., Sahmani S., 2012, Study of small scale effects on the nonlinear vibration response of functionally graded Timoshenko microbeams based on the strain gradient theory, Journal of Computational and Nonlinear Dynamics 7: 031010 .##[33] Sahmani S., Ansari R., 2013, On the free vibration response of functionally graded higherorder shear deformable microplates based on the strain gradient elasticity theory, Composite Structures 95: 430442.##[34] Ghayesh M.H., Amabili M., Farokhi H., 2013, Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory, International Journal of Engineering Science 63: 5260.##[35] Mohammadi M., Farajpour A., Moradi M., Ghayour M., 2013, Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment, Composites Part B: Engineering 56: 629637.##[36] Civalek Ö., Akgöz B., 2013, Vibration analysis of microscaled sector shaped graphene surrounded by an elastic matrix, Computational Materials Science 77: 295303.##[37] Murmu T., Pradhan S.C., 2009, Vibration analysis of nanosinglelayered graphene sheets embedded in elastic medium based on nonlocal elasticity theory, Journal of Applied Physics 105: 064319.##[38] Pradhan S.C., Phadikar J.K., 2009, Small scale effect on vibration of embedded multi layered graphene sheets based on nonlocal continuum models, Physics Letters A 373: 10621069.##[39] Wang Y. Z., Li F. M., Kishimoto K., 2011, Thermal effects on vibration properties of doublelayered nanoplates at small scales, Composites Part B: Engineering 42: 13111317.##[40] Reddy C.D., Rajendran S., Liew K.M., 2006, Equilibrium configuration and continuum elastic properties of finite sized graphene, Nanotechnology 17: 864870.##[41] Aksencer T., Aydogdu M., 2011, Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory, Physica E 43: 954959.##[42] Malekzadeh P., Setoodeh A.R., Alibeygi Beni A., 2011, Small scale effect on the thermal buckling of orthotropic arbitrary straightsided quadrilateral nanoplates embedded in an elastic medium, Composite Structures 93: 20832089.##[43] Satish N., Narendar S., Gopalakrishnan S., 2012, Thermal vibration analysis of orthotropic nanoplates based on nonlocal continuum mechanics, Physica E 44: 19501962.##[44] Prasanna Kumar T.J., Narendar S., Gopalakrishnan S., 2013, Thermal vibration analysis of monolayer graphene embedded in elastic medium based on nonlocal continuum mechanics, Composite Structures 100: 332342.##[45] Farajpour A., Mohammadi M., Shahidi A.R., Mahzoon M., 2011, Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E 43: 18201825.##[46] Mohammadi M., Ghayour M., Farajpour A., 2013, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites Part B: Engineering 45: 3242.##[47] Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids 51: 14771508.##[48] Timoshenko S.P., Goodier J.N., 1970, Theory of Elasticity, McGrawHill, New York.##[49] Saadatpour M. M., Azhari M., 1998, The Galerkin method for static analysis of simply supported plates of general shape, Computers and Structures 69: 19.##[50] Farajpour A., Danesh M., Mohammadi M., 2011, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E 44: 719727.##[51] Shu C., 2000, Differential Quadrature and its Application in Engineering, Berlin, Springer.##[52] Bert C.W., Malik M., 1996, Differential quadrature method in computational mechanics: a review, Applied Mechanics Reviews 49: 127.##[53] Malekzadeh P., Setoodeh A. R., Alibeygi Beni A., 2011, Small scale effect on the thermal buckling of orthotropic arbitrary straightsided quadrilateral nanoplates embedded in an elastic medium, Composite Structures 93: 20832089.##[54] Wang Y. Z., Li F. M., Kishimoto K., 2011, Thermal effects on vibration properties of doublelayered nanoplates at small scales, Composites Part B: Engineering 42: 13111317.##[55] Ke L. L., Yang J., Kitipornchai S., Bradford M. A., 2012, Bending, buckling and vibration of sizedependent functionally graded annular microplates, Composite Structures 94: 32503257.##[56] Leissa A.W., Narita Y., 1980, Natural frequencies of simply supported circular plates, Journal of Sound and Vibration 70: 221229.##[57] Kim C.S., Dickinson S.M., 1989, On the free, transverse vibration of annular and circular, thin, sectorial plates subject to certain complicating effects, Journal of Sound and Vibration 134: 407421.##[58] Qiang L.Y., Jian L., 2007, Free vibration analysis of circular and annular sectorial thin plates using curve strip Fourier Pelement, Journal of Sound and Vibration 305: 457466.##[59] Zhou Z.H., Wong K.W., Xu X.S., Leung A.Y.T., 2011, Natural vibration of circular and annular thin plates by Hamiltonian approach, Journal of Sound and Vibration 330: 10051017.##[60] Carrington H., 1925, The frequencies of vibration of ﬂat circular plates ﬁxed at the circumference, Philosophical Magazine 6: 12611264.##[61] Leissa A.W., 1969, Vibration of Plates, Ofﬁce of Technology Utilization, Washington.##[62] Chakraverty S., Bhat R.B., Stiharu I., 2001, Free vibration of annular elliptic plates using boundary characteristic orthogonal polynomials as shape functions in the Rayleigh–Ritz method, Journal of Sound and Vibration 241: 524539.##]
1

Effects of Gravitational and Hydrostatic Initial Stress on a TwoTemperature FiberReinforced Thermoelastic Medium for ThreePhaseLag
http://jsm.iauarak.ac.ir/article_527027.html
1
The threephaselag model and Green–Naghdi theory without energy dissipation are employed to study the deformation of a twotemperature fiberreinforced medium with an internal heat source that is moving with a constant speed under a hydrostatic initial stress and the gravity field. The modulus of the elasticity is given as a linear function of the reference temperature. The exact expressions for the displacement components, force stresses, thermal temperature and conductive temperature are obtained by using normal mode analysis. The variations of the considered variables with the horizontal distance are illustrated graphically. A comparison is made with the results of the two theories for two different values of a hydrostatic initial stress. Comparisons are also made with the results of the two theories in the absence and presence of the gravity field as well as the linear temperature coefficient.
0

806
822


S.M
Said
Department of Mathematics, Faculty of Science and Arts, Almithnab, Qassim University, P.O. Box 931, Buridah 51931, Almithnab, Kingdom of Saudi Arabia
Saudi Arabia
samia_said59@yahoo.com


M.I.A
Othman
Department of Mathematics, Faculty of Science, Taif University 888, Saudi Arabia
Saudi Arabia
Fiberreinforced
Gravity field
GreenNaghdi theory
Hydrostatic initial stress
Threephaselag model
Twotemperature
[[1] Chen P.J., Gurtin M. E., 1968, On a theory of heat conduction involving two temperatures, Zeitschrift für Angewandte Mathematik und Physik 19: 614627.##[2] Chen P.J., Williams W.O., 1968, A note on non simple heat conduction, Zeitschrift für angewandte Mathematik und Physik 19: 969970.##[3] Chen P.J., Gurtin M. E., Williams W.O., 1969, On the thermodynamics of nonsimple elastic materials with twotemperatures, Zeitschrift für Angewandte Mathematik und Physik 20: 107112.##[4] Warren W. E., Chen P. J., 1973, Wave propagation in the two temperatures theory of thermoelasticity, Journal of Acta Mechcanica 16: 2133.##[5] Youssef H. M., 2005, Theory of twotemperature generalized thermoelasticity, Journal of Applied Mathematics 71: 383390.##[6] Puri P., Jordan P.M., 2006, On the propagation of harmonic plane wanes under the two temperature theory, International Journal of Engineering Science 44: 11131126.##[7] Abbas I. A., Youssef H. M., 2009, Finite element method of twotemperature generalized magnetothermoelasticity, Journal Archive of Applied Mechanics 79: 917925.##[8] Kumar R., Mukhopadhyay S., 2010, Effects of thermal relaxation time on plane wave propagation under twotemperature thermoelasticity, International Journal of Engineering Science 48: 128139.##[9] Das P., Kanoria M., 2012, Twotemperature magnetothermoelastic response in a perfectly conducting medium based on GNIII Model, International Journal of Pure and Applied Mathematics 81: 199229.##[10] Abbas I. A., Zenkour A. M., 2014, Twotemperature generalized thermoplastic interaction in an infinite fiberreinforced anisotropic plate containing a circular cavity with two relaxation times, Journal of Computational and Theoretical Nanoscience 11: 17.##[11] Othman M. I. A., Hasona W.M., AbdElaziz E.M., 2014, Effect of rotation on micropolar generalized thermoelasticity with two temperatures using a dualphaselag model, Canadian Journal of Physics 92: 149158.##[12] Zenkour A. M., Abouelregal A. E., 2015, The fractional effects of a twotemperature generalized thermoelastic semiinfinite solid induced by pulsed laser heating, Archive of Mechanics 67: 5373.##[13] Biot M. A., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27: 240253.##[14] Lord H. W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal Mechanics Physics of Solid 15: 299309.##[15] Green A. E., Lindsay K. A., 1972, Thermoelasticity, Journal of Elasticity 2: 17.##[16] Hetnarski R. B., Ignaczak J., 1994, Generalized thermoelasticity: response of semispace to a short laser pulse, Journal of Thermal Stresses 17: 377396.##[17] Green A. E., Naghdi P. M., 1991, A reexamination of the basic postulate of thermomechanics, Proceedings of the Royal Society of London A 432: 171194.##[18] Green A. E., Naghdi P. M., 1992, On undamped heat waves in an elastic solid, Journal of Thermal Stresses 15: 253264.##[19] Green A. E., Naghdi P. M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31: 189208.##[20] Tzou D.Y., 1995, A unified approach for heat conduction from macroto microscales, ASME Journal of Heat Transfer 117: 816.##[21] Chandrasekharaiah D.S., 1998, Hyperbolic thermoelasticity: a review of recent literature, Journal of Applied Mechanics Review 51: 705729.##[22] Roy Choudhuri S., 2007, On a thermoelastic threephaselag model, Journal of Thermal Stresses 30: 231238.##[23] Quintanilla R., Racke R., 2008, A note on stability in threephaselag heat conduction, International Journal of Heat and Mass Transfer 51: 2429.##[24] Kar A., Kanoria M., 2009, Generalized thermoviscoelastic problem of a spherical shell with threephaselag effect, Journal of Applied Mathematical Modelling 33: 32873298.##[25] Quintanilla R., 2009, Spatial behaviour of solutions of the threephaselag heat equation, Journal of Applied Mathematics and Computation 213: 153162.##[26] Abbas I. A., 2014, Threephaselag model on thermoelastic interaction in an unbounded fiberreinforced anisotropic medium with a cylindrical cavity, Journal of Computational and Theoretical Nanoscience 11: 987992.##[27] Othman M. I. A., Said S.M., 2014, 2D problem of magnetothermoelasticity fiberreinforced medium under temperature dependent properties with threephaselag model, Journal of Meccanica 49: 12251241.##[28] Kumar A., Kumar R., 2015, A domain of influence theorem for thermoelasticity with threephaselag model, Journal of Thermal Stresses 38: 744755.##[29] Noda N., 1986, Thermal Stresses in Materials with TemperatureDependent Properties, NorthHolland, Amsterdam.##[30] Jin Z. H., Batra R.C., 1998, Thermal fracture of ceramics with temperaturedependent properties, Journal of Thermal Stresses 21: 157176.##[31] Othman M. I. A., 2002, LordShulman theory under the dependence of the modulus of elasticity on the reference temperature in two dimensional generalized thermoelasticity, Journal of Thermal Stresses 25: 10271045.##[32] Othman M. I. A., Song Y., 2008, Reflection of magnetothermoelastic waves with two relaxation times and temperature dependent elastic moduli, Journal of Applied Mathematical Modelling 32: 483500.##[33] Othman M. I. A., Lotfy Kh., Farouk R. M., 2010, Generalized thermomicrostretch elastic medium with temperature dependent properties for different theories, Engineering Analysis Boundary Elements 34: 229237.##[34] Othman M. I. A., Elmaklizi Y. D., Said S. M., 2013, Generalized thermoelastic medium with temperature dependent properties for different theories under the effect of gravity Field, International Journal of Thermophysics 34: 521553.##[35] Wang Y. Z., Liu D., Wang Q., Zhou J. Z., 2015, Fractional order theory of thermoelasticity for elastic medium with variable material properties, Journal of Thermal Stresses 38: 665676.##[36] Belfield A. J., Rogers T. G., Spencer A. J. M., 1983, Stress in elastic plates reinforced by fibers lying in concentric circles, Journal Mechanics Physics of Solid 31: 2554.##[37] Montanaro A., 1999, On singular surface in isotropic linear thermoelasticity with initial Stress, The Journal of the Acoustical Society of America 106: 15861588.##]
1

Coupled Vibration of Partially FluidFilled Laminated Composite Cylindrical Shells
http://jsm.iauarak.ac.ir/article_527091.html
1
In this study, the free vibration of partially fluidfilled laminated composite circular cylindrical shell with arbitrary boundary conditions has been investigated by using RayleighRitz method. The analysis has been carried out with straindisplacement relations based on Love’s thin shell theory and the contained fluid is assumed irrotational, incompressible and inviscid. After determining the kinetic and potential energies of fluid filled laminated composite shell, the eigenvalue problem has been obtained by means of RayleighRitz method. To demonstrate the validity and accuracy of the results, comparison has been made with the results of similar works for the empty and partially fluidfilled shells. Finally, an extensive parameter study on a typical composite tank is accomplished and some conclusions are drawn.
0

823
839


M.R
Saviz
Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran
Iran
saviz@azaruniv.ac.ir
Laminated composite
RayleighRitz
Partially fluidfilled
Cylindrical shell
Vibration analysis
[[1] Amabili M., 1996, Free vibration of partially filled, horizontal cylindrical shells, Journal of Sound and Vibration 191(5): 757780.##[2] Amabili M., 1997, Shellplate interaction in the free vibrations of circular cylindrical tanks partially filled with a liquid: The artificial spring method, Journal of Sound and Vibration 199(3): 431452.##[3] Amabili M., Paidoussis M. P., Lakis A. A., 1998,Vibrations of partially filled cylindrical tanks with ringstiffeners and flexible bottom, Journal of Sound and Vibration 213(2): 259299.##[4] Balamurugan V., Narayanan S., 2001, Shell finite element for smart piezoelectric composite plate/shell structures and its application to the study of active vibration control, Finite Elements in Analysis and Design 37: 713738.##[5] Chiba M., Abe K., 1999, Nonlinear hydroelastic vibration of a cylindrical tank with an elastic bottom containing liquidanalysis using harmonic balance method, ThinWalled Structure 34: 233260.##[6] Gupta R. K., Hutchinson G. L., 1988, Free vibration analysis of liquid storage tanks, Journal of Sound and Vibration 122: 491506.##[7] Goncalves P. B., Ramos N. R. S. S., 1996, Free vibration analysis of cylindrical tanks partially filled with liquid, Journal of Sound and Vibration 195(3): 429444.##[8] Jafari A. A., Bagheri M., 2006, Free vibration of nonuniformly ring stiffened cylindrical shells using analytical, experimental and numerical methods, ThinWalled Structures 44: 8290.##[9] Jeong K. H., Kim K. J., 1998, Free vibration of a circular cylindrical shell filled with bounded compressible fluid, Journal of Sound and Vibration 217(2): 197221.##[10] Kondo H., 1981, Axisymmetric vibration analysis of a circular cylindrical tank, Bulletin of the Japan Society of Mechanical Engineers 24: 215221.##[11] Kim Y. W., Lee Y. S., 2002,Transient analysis of ringstiffened composite cylindrical shells with both edges clamped, Journal of Sound and Vibration 252(1): 117.##[12] Kim Y. W., Lee Y. S., Ko S. H., 2004, Coupled vibration of partially fluidfilled cylindrical shells with ringstiffeners, Journal of Sound and Vibration 276:869897.##[13] Leissa A. W., 1973, Vibration of Shells, NASA SP288, Washington, Government Printing Office.##[14] Lee L. T., Lu J. C., 1995, Free vibration of cylindrical shells filled with liquid, Computers & Structures 54(5): 9971001.##[15] Liu M. L., To C. W. S., 2003, Free vibration analysis of laminated composite shell structures using hybrid strain based layerwise finite elements, Finite Elements in Analysis and Design 40(1): 83120.##[16] Mazuch T., Horacek J., Trnka J., Vesely J., 1996, Natural modes and frequencies of thin clampedfree steel cylindrical storage tank, Journal of Sound and Vibration 193:669690.##[17] Ramasamy R., Ganesan N., 1999,Vibration and damping analysis of fluid filled orthotropic cylindrical shells with constrained viscoelastic damping, Computers and Structures 70: 363376.##[18] Wang R. T., Lin Z. X., 2006, Vibration analysis of ringstiffened crossply laminated cylindrical shells, Journal of Sound and Vibration 295: 964987.##[19] Yu L., Cheng L., Yam L. H., Yan Y. J., Jiang J. S., 2007, Experimental validation of vibrationbased damage detection for static laminated composite shells partially filled with fluid, Computers and Structures 79: 288299.##[20] Zhao X., Liew K. M., Ng T. Y., 2002,Vibrations of rotating crossply laminated circular cylindrical shells with stringer and ring stiffeners, International Journal of Solids and Structures 39:529545.##]
1

Thermomechanical Interactions Due to Hall Current in Transversely Isotropic Thermoelastic with and Without Energy Dissipation with Two Temperatures and Rotation
http://jsm.iauarak.ac.ir/article_527092.html
1
The present paper is concerned with the investigation of disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperatures, in the presence of the combined effects of Hall currents and magnetic field due to thermomechanical sources. The formulation is applied to the thermoelasticity theories developed by GreenNaghdi Theories of TypeII and TypeIII. Laplace and Fourier transform technique is applied to solve the problem. As an application, the bounding surface is subjected to concentrated and distributed sources (mechanical and thermal sources). The analytical expressions of displacement, stress components, temperature change and current density components are obtained in the transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show a comparison of effect of Hall current on the two theories GNII and GNIII on resulting quantities. Some special cases are also deduced from the present investigation.
0

840
858


R
Kumar
Department of Mathematics, Kurukshetra University , Kurukshetra, Haryana, India
India
rajneesh_kuk@rediffmail.com


N
Sharma
Department of Mathematics, MM University, Mullana, Ambala, Haryana, India
India


P
Lata
Department of Basic and Applied Sciences, Punjabi University, Patiala, Punjab, India
India
parveenlata@pbi.ac.in
Transversely isotropic thermoelastic
Laplace and fourier transform
Concentrated and distributed sources
Rotation
Hall current
[Abbas I.A., Kumar R., Reen L,S., 2014, Response of thermal sources in transversely isotropic thermoelastic materials without energy dissipation and with two temperatures, Canadian Journal of Physics 92(11): 13051311.##[2] Abbas I.A., 2011, A two dimensional problem for a fibre reinforced anisotropic thermoelastic halfspace with energy dissipation, Sadhana(c) Indian academy of sciences 36(3): 411423.##[3] Attia H.A., 2009, Effect of Hall current on the velocity and temperature distributions of couette flow with variable properties and uniform suction and injection, Computational and Applied Mathematics 28(2): 195212.##[4] Atwa S.Y., Jahangir A., 2014, Two temperature effects on plane waves in generalized thermomicrostretch elastic solid, International Journal of Thermophysics 35: 175193.##[5] Boley B.A., Tolins I.S., 1962, Transient coupled thermoelastic boundary value problem in the half space, Journal of Applied Mechanics 29: 637646.##[6] Chandrasekharaiah D. S., 1998, Hyperbolic thermoelasticity: A review of recent literature, Applied Mechanics Reviews 51: 705729.##[7] Chen P.J., Gurtin M.E., 1968, On a theory of heat conduction involving two parameters, Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 19: 614627.##[8] Chen P.J., Gurtin M.E., WilliamsW.O., 1968, A note on simple heat conduction, Journal of Applied Mathematics and Physics 19: 969970.##[9] Chen P.J., Gurtin M.E., Williams W.O., 1969, On the thermodynamics of non simple elastic materials with two temperatures, Journal of Applied Mathematics and Physics 20: 107112.##[10] Das P., Kanoria M., 2014, Study of finite thermal waves in a magnetothermoelastic rotating medium, Journal of Thermal Stresses 37(4): 405428.##[11] Dhaliwal R.S., Singh A., 1980, Dynamic Coupled Thermoelasticity, Hindustance Publisher Corp, New Delhi, India.##[12] Ezzat M.A, Awad E.S.,2010, Constitutive relations, uniqueness of solutionand thermal shock application in the linear theory of micropolar generalized thermoelasticity involving two temperatures, Journal of Thermal Stresses 33(3): 225250.##[13] Green A.E., Naghdi P.M., 1991, A reexamination of the basic postulates of thermomechanics, Proceedings of the Royal Society of London A 432: 171194.##[14] Green A.E., Naghdi P.M., 1992, On undamped heat waves in an elastic solid, Journal of Thermal Stresses 15: 253264.##[15] Green A.E., Naghdi P.M.,1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31:189208.##[16] Honig G., Hirdes U., 1984, A method for the inversion of Laplace transform, Journal of Computational and Applied Mathematics 10:113132.##[17] Kaushal S., Kumar R., Miglani A., 2011, Wave propagation in temperature rate dependent thermoelasticity with two temperatures, Mathematical Sciences 5:125146.##[18] Kaushal S.,Sharma N., Kumar R., 2010, Propagation of waves in generalized thermoelastic continua with two temperature, International Journal of Applied Mechanics and Engineering 15:11111127.##[19] Kumar R., Devi S., 2010, Magnetothermoelastic (TypeII AND III) halfspace in contact with vacuum, Applied Mathematical Sciences 69(4): 34133424.##[20] Kumar R., Kansal T., 2010, Effect of rotation on rayleigh lamb waves in an isotropic generalized thermoelastic diffusive plate, Journal of Applied Mechanics and Technical Physics 51(5):751761.##[21] Kumar R., Mukhopdhyay S., 2010, Effects of thermal relaxation times on plane wave propagation under two temperature thermoelasticity, International Journal of Engineering Sciences 48(2): 128139.##[22] Kumar R., Rupender., 2009, Effect of rotation in magnetomicropolar thermoelastic medium due to mechanical and thermal sources, Solitons and Fractals 41:16191633.##[23] Kumar R., Sharma K.D., Garg S.K., 2014, Effect of two temperature on reflection coefficient in micropolar thermoelastic media with and without energy dissipation, Advances in Acoustics and Vibrations ID846721.##[24] Mahmoud S.R., 2013, An analytical solution for effect of magnetic field and initial stress on an infinite generalized thermoelastic rotating non homogeneous diffusion medium, Abstract and Applied Analysis ID 284646.##[25] Press W.H., Teukolshy S.A., Vellerling W.T., Flannery B.P., 1986, Numerical Recipes in Fortran, Cambridge University Press, Cambridge.##[26] Quintanilla R., 2002, Thermoelasticity without energy dissipation of materials with microstructure, Journal of Applied Mathematical Modeling 26:11251137.##[27] Salem A.M., 2007, Hall current effects on MHD flow of a PowerLaw fluid over a rotating disk, Journal of the Korean Physical Society 50(1): 2833.##[28] Sarkar N., Lahiri A., 2012, Temperature rate dependent generalized thermoelasticity with modified Ohm's law, International Journal of Computational Materials Science and Engineering 1(4): 1250031.##[29] Sharma K., Bhargava R.R., 2014, Propagation of thermoelastic plane waves at an imperfect boundary of thermal conducting viscous liquid/generalized thermolastic solid, Afrika Matematika 25: 81102.##[30] Sharma K., Marin M., 2013, Effect of distinct conductive and thermodynamic temperatures on the reflection of plane waves in micropolar elastic halfspace, UPB Scientific Bulletin 75(2):121132.##[31] Sharma K., Kumar P., 2013, Propagation of plane waves and fundamental solution in thermoviscoelastic medium with voids, Journal of Thermal Stresses 36: 94111.##[32] Sharma N., Kumar R., 2012, Elastodynamics of an axisymmetric problem in generalised thermoelastic diffusion , International Journal of Advanced Scientific and Technical Research 2(3): 478492.##[33] Sharma N., Kumar R., Ram P., 2012, Interactions of generalised thermoelastic diffusion due to inclined load, International Journal of Emerging Trends in Engineering and Development 5(2): 583600.##[34] Sharma S., Sharma K., Bhargava R.R., 2013, Effect of viscousity on wave propagation in anisotropic thermoelastic with GreenNaghdi theory TypeII and TypeIII, Materials Physics and Mechanics 16:144158.##[35] Slaughter W.S., 2002, The Linearised Theory of Elasticity, Birkhausar.##[36] Warren W.E., Chen P.J., 1973, Wave propagation in the two temperature theory of thermoelasticity, Journal of Acta Mechanica 16: 2133.##[37] Youssef H.M., 2006, Theory of two temperature generalized thermoelasticity, IMA Journal of Applied Mathematics 71(3): 383390.##[38] Youssef H.M., AILehaibi E.A.,2007, State space approach of two temperature generalized thermoelasticity of one dimensional problem, International Journal of Solids and Structures 44:15501562.##[39] Youssef H.M., AIHarby A.H., 2007, State space approach of two temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading, Journal of Archives of Applied Mechanics 77(9): 675687.##[40] Youssef H.M., 2011, Theory of two  temperature thermoelasticity without energy dissipation, Journal of Thermal Stresses 34:138146.##[41] Youssef H.M.,2013, Variational principle of two  temperature thermoelasticity without energy dissipation, Journal of Thermoelasticity 1(1): 4244.##[42] Zakaria M., 2012, Effects of hall current and rotation on magnetomicropolar generalized thermoelasticity due to ramptype heating, International Journal of Electromagnetics and Applications 2(3): 2432.##[43] Zakaria M., 2014, Effect of hall current on generalized magnetothermoelasticity micropolar solid subjected to ramptype heating, International Applied Mechanics 50(1):92104.##]
1

NonLocal ThermoElastic Buckling Analysis of MultiLayer Annular/Circular NanoPlates Based on First and Third Order Shear Deformation Theories Using DQ Method
http://jsm.iauarak.ac.ir/article_527096.html
1
In present study, thermoelastic buckling analysis of multilayer orthotropic annular/circular graphene sheets is investigated based on Eringen’s theory. The moderately thick and also thick nanoplates are considered. Using the nonlocal first and third order shear deformation theories, the governing equations are derived. The van der Waals interaction between the layers is simulated for multilayer sheets. The stability governing equations are obtained according to the adjacent equilibrium estate method. The constitutive equations are solved by applying the differential quadrature method (DQM). Applying the differential quadrature method, the ordinary differential equations are transformed to algebraic equations. Then, the critical temperature is obtained. Since there is not any research in thermoelastic buckling analysis of multilayer graphene sheets, the results are validated with available single layer articles. The effects of nonlocal parameter, the values of van der Waals interaction between the layers, third to first order shear deformation theory analyses, nonlocal to local analyses, different values of Winkler and Pasternak elastic foundation and analysis of bilayer and triple layer sheets are investigated. It is concluded that the critical temperature increases and tends to a constant value along the rise of van der Waals interaction between the layers.
0

859
874


Sh
Dastjerdi
Department of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran
Iran


M
Jabbarzadeh
Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
Iran
jabbarzadeh@mshdiau.ac.ir
Multilayer orthotropic annular/circular graphene sheets
Nonlocal first and third order shear deformation theories
Thermoelastic buckling analysis
Differential quadrature method (DQM)
[[1] Boehm H.P., Setton R., Stumpp E., 1994, Nomenclature and terminology of graphite intercalation compounds, Pure and Applied Chemistry 66: 18931901.##[2] Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Zhang Y., Dubonos S.V., Grigorieva I.V., Firsov A.A., 2004, Electric field effect in atomically thin carbon films, Science 306: 666669.##[3] Reddy J.N., 2011, Microstructuredependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids 59(11): 23822399.##[4] Akgöz B., Civalek Ö., 2013, A sizedependent shear deformation beam model based on the strain gradient elasticity theory, International Journal of Engineering Science 70: 114.##[5] Akgöz B., Civalek Ö., 2013, Buckling analysis of functionally graded micro beams based on the strain gradient theory, Acta Mechanica 224: 21852201.##[6] Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids 51(8): 14771508.##[7] Ke L.L., Yang J., Kitipornchai S., 2011, Free vibration of size dependent Mindlin micro plates based on the modified couple stress theory, Journal of Sound and Vibration 331: 94106.##[8] Akgöz B., Civalek Ö., 2011, Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro scaled beams, International Journal of Engineering Science 49: 12681280.##[9] Akgöz B., Civalek Ö., 2013, Free vibration analysis of axially functionally graded tapered BernoulliEuler microbeams based on the modified couple stress theory, Composite Structures 98: 314322.##[10] Yang F., Chong A.C.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39: 27312743.##[11] Eringen A.C., Edelen D.G.B., 1972, On nonlocal elasticity, International Journal of Engineering Science 10: 233248.##[12] Eringen A.C., 1983, On differential equations of nonlocal elasticity, solutions of screw dislocation, surface waves, Journal of Applied Physics 54: 47034710.##[13] Eringen A.C., 2002, NonLocal Continuum Field Theories, SpringerVerlag, New York.##[14] Eringen A.C., 2006, Nonlocal continuum mechanics based on distributions, International Journal of Engineering Science 44: 141147.##[15] Wen C.C., Chang T.W., Kuo W.S., 2014, Experimental study on mechanism of buckling and Kinkband formation in graphene nanosheets, Applied Mechanics & Materials 710: 1924.##[16] Ghorbanpour Arani A., Kolahchi R., Allahyari S.M.R., 2014, Nonlocal DQM for large amplitude vibration of annular boron nitride sheets on nonlinear elastic medium, Journal of Solid Mechanics 6(4): 334346.##[17] Mohammadi M., Goodarzi M., Ghayour M., AlivandS., 2012, Small scale effect on the vibration of orthotropic plates embedded in an elastic medium and under biaxial inplane preload via nonlocal elasticity theory, Journal of Solid Mechanics 4(2): 128143.##[18] Dastjerdi S., Jabbarzadeh M., Tahani M., Nonlinear bending analysis of sector graphene sheet embedded in elastic matrix based on nonlocal continuum mechanics, IJE Transaction B: Applications 28: 802811.##[19] Anjomshoa A., Shahidi A.R., Shahidi S.H., Nahvi H., 2014, Frequency analysis of embedded orthotropic circular and elliptical micro/nanoplates using nonlocal variational principle, Journal of Solid Mechanics 7(1): 1327.##[20] Pradhan S.C., 2009, Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory, Physics letters A 373: 41824188.##[21] He X.Q., Kitipornchai S., Liew K.M., 2005, Buckling analysis of multiwalled carbon nanotubes: a continuum model accounting for van der Waals interaction, Journal of the Mechanics and Physics of Solids 53: 303326.##[22] Scarpa F., Adhikari S., Gil A.J., Remillat C., 2010, The bending of single layer graphene sheets: The lattice versus continuum approach, Nanotechnology 21(12): 125702.##[23] Samaei A.T., Abbasian S., Mirsayar M.M., 2011, Buckling analysis of a single layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory, Mechanics Research Communications 38: 481485.##[24] Zenkour A.M., Sobhy M., 2013, Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium, Physica E 53: 251259.##[25] Wang Y., Cui H.T., Li F.M., Kishimoto K., 2013, Thermal buckling of a nanoplate with smallscale effects, Acta Mechanica 224(6): 12991307.##[26] Pradhan S.C., Phadikar J.K., 2009, Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models, Physics Letters A 373: 10621069.##[27] Bellman R.E., Casti J., 1971, Differential quadrature and longterm integration, Journal of Mathematical Analysis & Applications 34: 235238.##[28] Bellman R.E., Kashef B.G., Casti J., 1972, Differential quadrature: A technique for the rapid solution of nonlinear partial differential equation, Journal of Computational Physics 10: 4052.##[29] Sepahi O., Forouzan M.R., Malekzadeh P., 2011, Thermal buckling and postbuckling analysis of functionally graded annular plates with temperaturedependent material properties, Materials and Design 32: 40304041.##[30] Wang C.M., Xiang Y., Kitipornchai S., Liew K.M., 1994, Buckling solutions for Mindlin plates of various shapes, Engineering Structures 16: 119127.##]
1

Lateral Vibrations of SingleLayered Graphene Sheets Using Doublet Mechanics
http://jsm.iauarak.ac.ir/article_527098.html
1
This paper investigates the lateral vibration of singlelayered graphene sheets based on a new theory called doublet mechanics with a length scale parameter. After a brief reviewing of doublet mechanics fundamentals, a sixth order partial differential equation that governs the lateral vibration of singlelayered graphene sheets is derived. Using doublet mechanics, the relation between natural frequency and length scale parameter is obtained in the lateral mode of vibration for singlelayered graphene. It is shown that length scale parameter plays a significant role in the lateral vibration behavior of singlelayered graphene sheets. Such effect decreases the natural frequency compared to the predictions of the classical continuum mechanics models. However with increasing the length of the plate, the effect of scale parameter on the natural frequency decreases. For validating the results of this method, the results obtained herein are compared with the existing nonlocal and molecular dynamics results and good agreement with the latter is observed.
0

875
894


A
FatahiVajari
Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Iran


A.
Imam
Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Iran
aimam@srbiau.ac.ir
Doublet mechanics
Natural frequency
Length scale parameter
Lateral vibration
Singlelayered graphene sheets
[[1] Granik V.T., 1997, Microstructural mechanics of granular media, Technique Report IM/MGU 78241, Institute of Mechanics of Moscow State University, in Russian.##[2] Granik V.T., Ferrari M., 1993, Microstructural mechanics of granular media, Mechanics of Materials 15: 301322.##[3] Ferrari M., Granik V.T., Imam A., Nadeau J., 1997, Advances in Doublet Mechanics, Springer, Berlin.##[4] Kojic M., Vlastelica I., Decuzzi P., Granik V.T., Ferrari M., 2011, A ﬁnite element formulation for the doublet mechanics modeling of microstructural materials, Computer Methods in Applied Mechanics and Engineering 200: 14461454.##[5] Xin J., Zhou L.X., Ru W.J., 2009, Ultrasound attenuation in biological tissue predicted by the modified doublet mechanics model, Chinese Physics Letters 26(7): 074301.1074301.4.##[6] Ferrari M., 2000, Nanomechanics, and biomedical nanomechanics: Eshelby's inclusion and inhomogeneity problems at the discrete continuum interface, Biomedical Microdevices 2(4): 273281.##[7] Gentile F., Sakamoto J., Righetti R., Decuzzi P., Ferrari M., 2011, A doublet mechanics model for the ultrasound characterization of malignant tissues, Journal of Biomedical Science and Engineering 4: 362374.##[8] Lin S.S., Shen Y.C., 2005, Stress fields of a halfplane caused by moving loadsresolved using doublet mechanics, Soil Dynamics and Earthquake Engineering 25: 893904.##[9] Sadd M.H., Dai Q., 2005, A comparison of micromechanical modeling of asphalt materials using ﬁnite elements and doublet mechanics, Mechanics of Materials 37: 641662.##[10] Fang J.Y., Jue Z., Jing F., Ferrari M., 2004, Dispersion analysis of wave propagation in cubicTetrahedral assembly by doublet mechanics, Chinese Physics Letters 21(8): 15621565.##[11] Sadd M. H., 2005, Elasticity Theory Applications, and Numeric, Elsevier ButterworthHeinemann, Burlington.##[12] Eringen A.C., 1972, Nonlocal Polar Elastic Continua, International Journal of Engineering Science 10: l16.##[13] Iijima S., 1991, Helical microtubes of graphitic carbon, Nature 354: 5658.##[14] Katsnelsona M.I., Novoselov K.S., 2007, Graphene: New bridge between condensed matter physics and quantum electrodynamics, Solid State Communications 143: 313.##[15] Heersche H.B., Herrero P.J., Oostinga J.B., Vandersypen L.M.K., Morpurgo A.F., 2007, Induced superconductivity in graphene, Solid State Communications 143: 7276.##[16] Stankovich S., Dikin D.A., Piner R.D., Kohlhaas K.A., Kleinhammes A., Jia Y., Wu Y., Nguyen S.T., Ruoff R.S., 2007, Synthesis of graphenebased nanosheets via chemical reduction of exfoliated graphite oxide, Carbon 45: 15581565.##[17] Danesh M., Farajpour A., Mohammadi M., 2012, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications 39: 2327.##[18] Wang Q, C Wang M., 2007, The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes, Nanotechnology 18: 075702.1075702.4.##[19] Ghannadpour S.A.M., Mohammadi B., Fazilati J., 2013, Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method, Composite Structures 96: 584589.##[20] Malekzadeh P., Mohebpour S. R., Heydarpour Y., 2012, Nonlocal effect on the free vibration of short nanotubes embedded in an elastic medium, Acta Mechanica 223: 13411350.##[21] Stankovich S., Piner R.D, Nguyen S.T., Ruoff R.S., 2006, Synthesis and exfoliation of isocyanatetreated graphene oxide nanoplatelets, Carbon 44: 33423347.##[22] Wang J., Tian M., He X., Tang Z., 2014, Free vibration analysis of singlelayered graphene sheets based on a continuum model, Applied Physics Frontier 2(1): 17.##[23] Rao S.S., 2007, Vibration of Continuous Systems, John Wiley and Sons, New Jersey.##[24] Green A.E., Zerna W., 1992, Theoretical Elasticity, Dover publications, New York.##[25] Reddy J.N., 2010, Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates International Journal of Engineering Science 48(11): 15071518.##[26] Aghababaei R., Reddy J.N., 2009, Nonlocal thirdorder shear deformation plate theory with application to bending and vibration of plates, Journal of Sound and Vibration 326(12): 277289.##[27] Farajpour A., Mohammadi M., Shahidi A.R., Mahzoon M., 2011, Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E: Lowdimensional Systems and Nanostructures 43(10): 18201825.##[28] Pradhan S.C., Phadikar J. K., 2009, Nonlocal elasticity theory for vibration of nanoplates, Journal of Sound and Vibration 325: 206223.##[29] Alibeigloo A., 2011, Free vibration analysis of nanoplate using threedimensional theory of elasticity, Acta Mechanica 222: 149159.##[30] Aksencer T., Aydogdu M., 2011, Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory, Physica E 43: 954959.##[31] Ansari R., Sahmani S., Arash B., 2010, Nonlocal plate model for free vibrations of singlelayered graphene sheets, Physics Letters A 375: 5362.##[32] Jalali S.K., Rastgoo A., Eshraghi I., 2011, Large amplitude vibration of imperfect shear deformable nanoplates using nonlocal theory, Journal of Solid Mechanics 3(1): 6473.##[33] Rouhi S., Ansari R., 2012, Atomistic finite element model for axial buckling and vibration analysis of singlelayered graphene sheets, Physica E 44: 764772.##[34] Aksencer T., Aydogdu M., 2012, Forced transverse vibration of nanoplates using nonlocal elasticity, Physica E 44: 17521759.##[35] Daneshmand F., Rafiei M., Mohebpour S.R., Heshmati M., 2013, Stress and straininertia gradient elasticity in free vibration analysis of single walled carbon nanotubes with first order shear deformation shell theory, Applied Mathematical Modelling 37: 79838003.##[36] Bouyge F., Jasiuk I., Boccara S., OstojaStarzewski M., 2002, A micromechanically based couplestress model of an elastic orthotropic twophase composite, European Journal of Mechanics A/Solids 21: 465481.##[37] Bandow S., Asaka S., Saito Y., Rao A., Grigorian L., Richter E., Eklund P., 1998, Effect of the growth temperature on the diameter distribution and chirality of singlewall carbon nanotubes, Physical Review Letters 80(17): 37793782.##]
1

Free and Forced Transverse Vibration Analysis of Moderately Thick Orthotropic Plates Using Spectral Finite Element Method
http://jsm.iauarak.ac.ir/article_527099.html
1
In the present study, a spectral finite element method is developed for free and forced transverse vibration of Levytype moderately thick rectangular orthotropic plates based on firstorder shear deformation theory. Levy solution assumption was used to convert the twodimensional problem into a onedimensional problem. In the first step, the governing outofplane differential equations are transformed from time domain into frequency domain by discrete Fourier transform theory. Then, the spectral stiffness matrix is formulated, using frequencydependent dynamic shape functions which are obtained from the exact solution of the governing differential equations. An efficient numerical algorithm, using drawing method is used to extract the natural frequencies. The frequency domain dynamic responses are obtained from solution of the spectral element equation. Also, the time domain dynamic responses are derived by using inverse discrete Fourier transform algorithm. The accuracy and excellent performance of the spectral finite element method is then compared with the results obtained from closed form solution methods in previous studies. Finally, comprehensive results for outofplane natural frequencies and transverse displacement of the moderately thick rectangular plates with six different combinations of boundary conditions are presented. These results can serve as a benchmark to compare the accuracy and precision of the numerical methods used.
0

895
915


M.R
Bahrami
Civil Engineering Department, Yasouj University, Yasouj, Iran
Iran


S
Hatami
Civil Engineering Department, Yasouj University, Yasouj, Iran
Iran
hatami@yu.ac.ir
Spectral finite element method
Firstorder shear deformation theory
Orthotropic plate
Exact solution
Dynamic stiffness matrix
Discrete Fourier transform
Transverse vibration
[[1] Reddy J.N., Phan N.D., 1985, Stability and vibration of isotropic, orthotropic and laminated plates according to a higherorder shear deformation theory, Journal of Sound and Vibration 98(2): 157170.##[2] Xiang Y., Wei G.W., 2004, Exact solutions for buckling and vibration of stepped rectangular Mindlin plates, International Journal of Solids and Structures 41: 279294.##[3] HosseiniHashemi Sh., Arsanjani M., 2005, Exact characteristic equations for some of classical boundary conditions of vibrating moderately thick rectangular plates, International Journal of Solids and Structures 42: 819853.##[4] HosseiniHashemi Sh., Fadaee M., Eshaghi M., 2010, A novel approach for inplane/outofplane frequency analysis of functionally graded circular/annular plates, International Journal of Mechanical Sciences 52: 10251035.##[5] HosseiniHashemi Sh., Rokni Damavandi Taher H., Akhavan H., Omidi M., 2010, Free vibration of functionally graded rectangular plates using firstorder shear deformation plate theory, Applied Mathematical Modelling 34: 12761291.##[6] HosseiniHashemi Sh., Fadaee M., Atashipour, S.A., 2011, A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates, International Journal of Mechanical Sciences 53: 1122.##[7] HosseiniHashemi Sh., Fadaee M., Atashipour S.A., 2011, Study on the free vibration of thick functionally graded rectangular plates according to a new exact closedform procedure, Composite Structure 93: 722735.##[8] HosseiniHashemi Sh., Fadaee M., Rokni Damavandi Taher H., 2011, Exact solutions for free flexural vibration of Lévytype rectangular thick plates via thirdorder shear deformation plate theory, Applied Mathematical Modelling 35: 708727.##[9] Akhavan H., HosseiniHashemi Sh., Rokni Damavandi Taher H., Alibeigloo A., Vahabi Sh., 2009, Exact solutions for rectangular Mindlin plates under inplane loads resting on Pasternak elastic foundation. Part II: frequency analysis, Computational Materials Science 44: 951961.##[10] Hatami S., Azhari M., Saadatpour M.M., 2007, Free vibration of moving laminated composite plates, Composite Structures 80: 609620.##[11] Hatami S., Ronagh H.R., Azhari M., 2008, Exact free vibration analysis of axially moving viscoelastic plates, Computers and Structures 86: 17381746.##[12] Boscolo M., Banerjee J.R., 2011, Dynamic stiffness elements and their applications for plates using ﬁrst order shear deformation theory, Computers and Structures 89: 395410.##[13] Boscolo M., Banerjee J.R., 2012, Dynamic stiffness formulation for composite Mindlin plates for exact modal analysis of structures. Part I: Theory, Computers and Structures 9697: 6173.##[14] Boscolo M., Banerjee J.R., 2012, Dynamic stiffness formulation for composite Mindlin plates for exact modal analysis of structures. Part II: Results and application, Computers and Structures 9697: 7483.##[15] Leung A.Y.T., Zhou W.E., 1996, Dynamic stiffness analysis of laminated composite plates, ThinWalled Structures 25(2): 109133.##[16] Fazzolari F.A., Boscolo M., Banerjee J.R., 2013, An exact dynamic stiffness element using a higher order shear deformation theory for free vibration analysis of composite plate assemblies, Composite Structures 96: 262278.##[17] Kolarevic N., NefovskaDanilovic M., Petronijevic M., 2015, Dynamic stiffness elements for free vibration analysis of rectangular Mindlin plate assemblies, Journal of Sound and Vibration 359: 84106.##[18] Kolarevic N., Marjanovic M., NefovskaDanilovic M., Petronijevic M., 2016, Free vibration analysis of plate assemblies using the dynamic stiffness method based on the higher order shear deformation theory, Journal of Sound and Vibration 364: 110132.##[19] Ghorbel O., Casimir J.B., Hammami L., Tawfiq I., Haddar M., 2015, Dynamic stiffness formulation for free orthotropic plates, Journal of Sound and Vibration 346: 361375.##[20] Ghorbel O., Casimir J.B., Hammami L., Tawfiq I., Haddar M., 2016, Inplane dynamic stiffness matrix for a free orthotropic plate, Journal of Sound and Vibration 364: 234246.##[21] Doyle J.F., 1997, Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms, SpringerVerlag, New York, Second Edition.##[22] Lee U., Lee J., 1998, Vibration analysis of the plates subject to distributed dynamic loads by using spectral element method, KSME International Journal 12(4): 565571.##[23] Kim J., Cho J., Lee U., Park, S., 2003, Modal spectral element formulation for axially moving plates subjected to inplane axial tension, Computers and Structures 81: 20112020.##[24] Chakraborty A., Gopalakrishnan S., 2005, A spectrally formulated plate element for wave propagation analysis in anisotropic material, Computer Methods in Applied Mechanics and Engineering 194: 44254446.##[25] Kwon K., Lee U., 2006, Spectral element modeling and analysis of an axially moving thermo elastic beamplate, Journal of Mechanics of Materials and Structures 1: 605632.##[26] Wang G., Unal A., 2013, Free vibration of stepped thickness rectangular plates using spectral finite element method, Journal of Sound and Vibration 332: 43244338.##[27] Hajheidari H., Mirdamadi H.R., 2012, Free and transient vibration analysis of an unsymmetric crossply laminated plate by spectral finite elements, Acta Mechanica 223: 24772492.##[28] Hajheidari H., Mirdamadi H.R., 2013, Frequencydependent vibration analysis of symmetric crossply laminated plate of Levytype by spectral element and ﬁnite strip procedures, Applied Mathematical Modelling 37: 71937205.##[29] Liu X., Banerjee J.R., 2015, An exact spectraldynamic stiffness method for free flexural vibration analysis of orthotropic composite plate assemblies. Part I: Theory, Composite Structures 132: 12741287.##[30] Liu X., Banerjee J.R., 2015,An exact spectraldynamic stiffness method for free flexural vibration analysis of orthotropic composite plate assemblies . Part II: Applications, Composite Structures 132: 12881302.##[31] Liu X., Banerjee J.R., 2016, Free vibration analysis for plates with arbitrary boundary conditions using a novel spectraldynamic stiffness method, Computers & Structures 164: 108126.##[32] Park I., Lee U., 2015, Spectral element modeling and analysis of the transverse vibration of a laminated composite plate, Composite Structures 134: 905917.##[33] Shirmohammadi F., Bahrami S., Saadatpour M.M., Esmaeily A., 2015, Modeling wave propagation in moderately thick rectangular plates using the spectral element method, Applied Mathematical Modelling 39(12): 34813495.##[34] Bahrami S., Shirmohammadi F., Saadatpour M.M., 2015, Modeling wave propagation in annular sector plates using spectral strip method, Applied Mathematical Modelling 39(21): 65176528.##[35] Reddy J.N., 2007, Theory and Analysis of Elastic Plates and Shells, CRC Press, Boca Raton, Second Edition.##[36] Reissner, E., 1944, On the theory of bending of elastic plates, Journal Math Physics 23(4): 184191.##[37] Lee U., 2009, Spectral Element Method in Structural Dynamics, John Wiley & Sons.##[38] Szilard R., 2004, Theories and Applications of Plate Analysis: Classical, Numerical and Engineering Methods, John wiley & Sons, Inc, New Jersey.##]
1

Calculation of Collision Speed Corresponded to Maximum Penetration Using Hydrodynamic Theory
http://jsm.iauarak.ac.ir/article_527100.html
1
One of the most valid and efficient models of long rod projectile penetration in homogeneous targets is Tate and Alekseevskii’s (A&t) model. Based on Tate’s model, the present research tries to calculate the optimum speeds to achieve the maximum penetration depth in the homogeneous targets. The proposed collision speedpenetration depth diagrams are developed using Tate’s model. In this way, various collision speedpenetration depth diagrams for different projectile dynamic resistances and targets are calculated and the optimum speed envelope is derived. According to Tate’s diagrams, the increase of collision speed is not followed by the increase of penetration depth; instead, it causes erosion phenomenon to happen. The comparison of the resulted optimum penetration speeds and the available data confirms the findings. Speed and rigidity both have a positive impact on the increase of penetration depth. With the increase of speed, the erosion issue finds a higher significance due to the increase of pressure on the projectile tip. Therefore, higher speed and erosion are opposed to each other; for the case of Y>R, there are some maximum points which indicate the optimum reciprocity of the two mentioned factors to obtain a maximum penetration depth. In the present research, an equation is developed indicating the optimum speeds resulting in the maximum penetration rate in the case of Y>R. For the reciprocity of speed and erosion, the target resistance against an erosive projectile should be 4 to 5 fold higher than the same target resistance against a rigid projectile penetration. [1]
0

916
922


A.R
Nezamabadi
Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran
Iran
anezamabadi@iauarak.ac.ir
Hydrodynamic theory
Tate and Alekseevskii’s theory
Erosion
Rigidity
Optimum speed
Maximum penetration depth
[[1] Rosenberg and Z., Dekel E., 2008, A numerical study of the cavity expansion process and its application to longrod penetration mechanics, International Journal of Impact Engineering 35: 147154.##[2] Forrestal M. J., Frew D. J., Hickerson J. P. Rohwer T. A., 2003,Penetration of concrete targets with decelerationtime, International Journal of Impact Engineering 28: 479497.##[3] Frew D.J., Forrestal M.J. Cargile J.D., 2006,The effect of concrete target diameter on projectile deceleration and penetration depth, International Journal of Impact Engineering 32: 15841594.##[4] Forrestal M. J., Frew D. J., Hanchak S. J. Brar N. S., 1996, Penetration of grout and concrete targets with ogivenose steel projectiles, International Journal of Impact Engineering 18: 465476.##[5] Vladimir M.G., 1996, Concrete penetration by eroding projectiles: experiments and analysis, Technical Report ARAEDTR96014.##[6] Alekseeveskii V.P., 1966, Penetration of a Rod into a Target at High Velocity, Combus Explos Shock Waves 2: 6366.##[7] Dullum O., Haugstad B., 1981, On the Effect of Finite Strength in Long Rod Penetration, Forsvarets Forskningstitutt, FFI/Rapport81/4001, Kjeller, Norway .##[8] Tate A., 1967, A theory for the deceleration of long rods after impact, Journal of the Mechanics and Physics of Solids 15: 387399.##[9] Tate A.,1969, Further results in the theory of long rod penetration, Journal of the Mechanics and Physics of Solids 17: 141150.##[10] Zukas J. A., 1990, High Velocity Impact Dynamics, John Wiley & Sons.##[11] Williams A. E., 1976, Impact tests with mathematics method , Proceedings, 27th Meeting of the Aeroballistic Range Association, Centre, d Etudes de Vaujours, Sevran, France.##]