2013
5
2
2
109
A Computational Wear Model of the Oblique Impact of a Ball on a Flat Plate
2
2
Many wearing processes are a result of the oblique impacts. Knowing the effective impact parameters on the wear mechanism would be helpful to have the more reliable designs. The HDD (HertzDi Maio Di Renzo) nonlinear model of impact followed by the time increment procedure is used to simulate the impact process of a ball on a flat plate. Restitution parameters are extracted and compared with the experimental data to ensure the accuracy of the impact model. The constant parameters of a wear equation are determined by comparing the results with the experimental data. The results obtained suggest that this simulation method could be used as a predictive way to study the practical design problems and to explain some phenomena associated with impact erosion.
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107
115


M
Akhondizadeh
Mechanical Engineering Department of Shahid Bahonar, University of Kerman
Mechanical Engineering Department of Shahid
Iran
m.akhondizadeh@gmail.com


M
Fooladi Mahani
Mechanical Engineering Department of Shahid Bahonar, University of Kerman
Mechanical Engineering Department of Shahid
Iran


S.H
Mansouri
Mechanical Engineering Department of Shahid Bahonar, University of Kerman
Mechanical Engineering Department of Shahid
Iran


M
Rezaeizadeh
Graduate University of Advanced Technology ,Kerman
Graduate University of Advanced Technology
Iran
Contact
Impact wear
Wear modeling
Steel
Indentation
[ [1] Bayer R. G., Engel P. A., Sirico J. L., 1971, Impact wear testing machine, Wear 24:343354.##[2] Engel P. A., Lyons T. H., Sirico J. L., 1973, Impact wear for steel specimens, Wear 23:185201.##[3] Engel P. A., Millis D.B., 1982, Study of surface topology in impact wear, Wear 75:423442.##[4] Goryacheva I.G., Contact Mechanics in Tribology, Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia, Kluwer Academic Publishers.##[5] Mindlin R. D., Deresiewicz H., 1953, Elastic spheres in contact under varying oblique forces, Applied Mechanics 16:259268.##[6] Maw N., 1975, The oblique impact of elastic spheres, Wear 25: 101114.##[7] Gorham D. A., Kharaz A. H., 2000, The measurement of particle rebound characteristics, Powder Technology 112:193202.##[8] Kharaz A.H., Gorham D.A., Salman A.D., 2001, An experimental study of the elastic rebound of spheres, Powder Technology 120(3):281291.##[9] Levy A., 1993, The erosion–corrosion of tubing steels in combustion boiler environments, Corrosion Science 35:10351056.##[10] Bellman R., Levy A., 1981, Erosion mechanism in ductile metals, Wear 70(1): 127.##[11] Lindsley B.A., Marder A.R., 1999, The effect of velocity on the solid particle erosion rate of alloys, Wear 225–229: 510516.##[12] Head W.J., Harr M.E., 1970, The development of a model to predict the erosion of materials by natural contaminants, Wear 15: 146.##[13] Xie Y., Clark H.McI., Hawthorne H.M., 1999, Modelling slurry particle dynamics in the Coriolis erosion tester, Wear 225–229: 405416.##[14] Talia M., Lankarani H., Talia J.E., 1999, New experimental technique for the study and analysis of solid particle erosion mechanisms, Wear 225–229 (2):10701077.##[15] Di Maio F. P., Di Renzo A., 2005, Modeling particle contacts in distinct element simulations, Chemical Engineering Research and Design 83:12871297.##[16] Chuanyu W., Longyuan L., Colin T., 2003, Rebound behaviour of spheres for plastic impacts, International Journal of Impact Engineering 28: 929946.##[17] Lewis A.D., Rogers R. J., 1988, Experimental and numerical study of forces during oblique impact, Journal of Sound and 125(3): 403412.##[18] Mesarovic SDJ., Johnson KL., 2000, Adhesive contact of elastic–plastic spheres, Journal of Mechanical Physic Solids 24: 127138##[19] Ashrafizadeh H., Ashrafizadeh F., 2012, A numerical 3D simulation for prediction of wear caused by solid particle impact, Wear 276277: 7584.## ##]
Levy Type Solution for Nonlocal ThermoMechanical Vibration of Orthotropic MonoLayer Graphene Sheet Embedded in an Elastic Medium
2
2
In this paper, the effect of the temperature change on the vibration frequency of monolayer graphene sheet embedded in an elastic medium is studied. Using the nonlocal elasticity theory, the governing equations are derived for singlelayered graphene sheets. Using Levy and Navier solutions, analytical frequency equations for singlelayered graphene sheets are obtained. Using Levy solution, the frequency equation and mode shapes orthotropic rectangular nanoplate are considered for three cases of boundary conditions. The obtained results are subsequently compared with valid result reported in the literature. The effects of the small scale, temperature change, different boundary conditions, Winkler and Pasternak foundations, material properties and aspect ratios on natural frequencies are investigated. It has been shown that the nondimensional frequency decreases with increasing temperature change. It is seen from the figure that the influence of nonlocal effect increases with decreasing of the length of nanoplate and also all results at higher length converge to the local frequency. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration proper ties of the nanoplates.
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116
132


M
Mohammadi
Department of Engineering, Ahvaz Branch, Islamic Azad University
Department of Engineering, Ahvaz Branch,
Iran
m.mohamadi@me.iut.ac.ir


A
Farajpour
Young Researches and Elites Club, North Tehran Branch, Islamic Azad University
Young Researches and Elites Club, North Tehran
Iran


M
Goodarzi
Department of Engineering, Ahvaz Branch, Islamic Azad University
Department of Engineering, Ahvaz Branch,
Iran


R
Heydarshenas
Department of Engineering, Ahvaz Branch, Islamic Azad University
Department of Engineering, Ahvaz Branch,
Iran
Thermomechanical vibration
Orthotropic singlelayered graphene sheets
Elastic medium
Analytical Modeling
[[1] Wong E.W., Sheehan P.E., Lieber C.M., 1997, Nanobeam mechanics: elasticity, strength and toughness of nanorods and nanotubes, Science 277: 1971–1975.##[2] Sorop T.G., Jongh L.J., 2007, Sizedependent anisotropic diamagnetic screening in superconducting nanowires, Physical Review B 75: 014510014515.##[3] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354: 56–58.##[4] Kong X.Y, Ding Y, Yang R, Wang Z.L., 2004, SingleCrystal Nanorings Formed by Epitaxial SelfCoiling of Polar Nanobelts, Science 303: 13481351.##[5] Zhou S.J., Li Z.Q., 2001, Metabolic response of Platynota stultanapupae during and after extended exposure to elevated CO2 and reduced O2 atmospheres, Shandong University Technology 31: 401409.##[6] Fleck N.A., Hutchinson J.W., 1997, Strain gradient plasticity, Applied Mechanics 33: 295–361.##[7] 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 Structure 39: 27312743.##[8] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 47034711.##[9] 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 (1): 2327.##[10] 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.##[11] 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 (5): 16051615.##[12] Farajpour A., Danesh M., Mohammadi M., 2011, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E: LowDimensional Systems and Nanostructures 44(3): 719727.##[13] 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: LowDimensional Systems and Nanostructures 44(1): 135140.##[14] 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(1): 3242.##[15] 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: Engineering 51: 121129.##[16] 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.##[17] Mohammadi M., Farajpour A., Moradi A., Ghayour M., 2014, Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment, Composites Part B: Engineering 56: 629637.##[18] 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.##[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): 659683.##[20] Mohammadi M., Farajpour A., Goodarzi M., Shehni nezhad pour H., 2014, Numerical study of the effect of shear inplane load on the vibration analysis of graphene sheet embedded in an elastic medium, Computational Material Science 52: 510520.##[21] Mohammadi M., Ghayour M., Farajpour A., 2011, Analysis of free vibration sector plate based on elastic medium by using new version differential quadrature method, Journal of Solid Mechanics in Engineering 3(2): 4756.##[22] Wang C.M., Duan W.H., 2008, Free vibration of nanorings/arches based on nonlocal elasticity, Journal of Applied Physics 104(1): 014303.##[23] Reddy J.N., Pang S.D., 2008, Nonlocal continuum theories of beams for the analysis of carbon nanotubes,Journal of Applied Physics 103(2): 023511.##[24] Murmu T., Pradhan S. C., 2009, Buckling analysis of singlewalled carbon nanotubes embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Physica E 41: 12321239.##[25] Wang L., 2009, Dynamical behaviors of doublewalled carbon nanotubes conveying fluid accounting for the role of small length scale, Computational Material Science 45: 584588.##[26] Xiaohu Y., Qiang H., 2007, Investigation of axially compressed buckling of a multiwalled carbon nanotube under temperature field, Composite Science Technology 67: 125134.##[27] Sudak L.J., 2003, Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics, Journal of Applied Physics 94(11): 72817287.##[28] 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(6): 064319.##[29] 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: 1062–1069.##[30] Wang Y. Z., Li F. M., Kishimoto K., 2011, Thermal effects on vibration properties of doublelayered nanoplates at small scales, Composites Part B: Engineering 42:1311–1317.##[31] Reddy C.D., Rajendran S., Liew K.M., 2006, Equilibrium configuration and continuum elastic properties of finite sized graphene, Nanotechnology 17: 864–870.##[32] 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 Structure 93: 2083–2089.##[33] Aksencer T., Aydogdu M., 2011, Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory, Physica E 43 954 –959.##[34] Satish N., Narendar S., Gopalakrishnan S., 2012, Thermal vibration analysis of orthotropic nanoplates based on nonlocal continuum mechanics, Physica E 44:1950 –1962.##[35] 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 :332–342.##[36] Chen Y., Lee J.D., Eskandarian A., 2004, Atomistic viewpoint of the applicability of microcontinuum theories, International Journal of Solids Structures 41:20852097.##[37] SakhaeePour A., Ahmadian M.T., Naghdabadi R., 2008, Vibrational analysis of single layered graphene sheets, Nanotechnology 19: 957–964.##[38] Pradhan S.C., Kumar A., 2010, Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method, Computational Material Science 50:239245.##[39] Liew K. M., He X. Q., Kitipornchai S., 2006, Predicting nanovibration of multilayered graphene sheets embedded in an elastic matrix, Acta Material 54: 42294236.##[40] Zhang Y.Q., Liu X., Liu G.R., 2007, Thermal effect on transverse vibrations of double walled carbon nanotubes, Nanotechnology 18(44):445701.##[41] Benzair A., Tounsi A., Besseghier A., Heireche H., Moulay N., Boumia L., 2008, The thermal effect on vibration of singlewalled carbon nanotubes using nonlocal Timoshenko beam theory, Journal of Applied Physics 41(22):225404.##[42] Lee H.L., Chang W.J., 2009, A closedform solution for critical buckling temperature of a singlewalled carbon nanotube, Physica E 41:1492–1494.##[43] Pradhan S. C., Kumar A., 2011, Vibration analysis of orthotropic graphene sheets using nonlocal theory and differential quadrature method, Composite Structure 93: 774779.## ##]
Rheological Response and Validity of Viscoelastic Model Through Propagation of Harmonic Wave in NonHomogeneous Viscoelastic Rods
2
2
This study is concerned to check the validity and applicability of a five parameter viscoelastic model for harmonic wave propagating in the nonhomogeneous viscoelastic rods of varying density. The constitutive relation for five parameter model is first developed and validity of these relations is checked. The nonhomogeneous viscoelastic rods are assumed to be initially unstressed and at rest. In this study, it is assumed that density, rigidity and viscosity of the specimen i.e. rod are space dependent. The method of nonlinear partial differential equation (Eikonal equation) has been used for finding the dispersion equation of harmonic waves in the rods. A method for treating reflection at the free end of the finite nonhomogeneous viscoelastic rod is also presented. All the cases taken in this study are discussed numerically and graphically with MATLAB.
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133
151


R
Kakar
Principal, DIPS Polytechnic College, Hoshiarpur
Principal, DIPS Polytechnic College, Hoshiarpur
Iran
rkakar_163@rediffmail.com


K
Kaur
Faculty of Applied Sciences, BMSCE, Muktsar152026, India
Faculty of Applied Sciences, BMSCE, Muktsar152026
Iran
Harmonic waves
Viscoelastic media
Friedlander series
Inhomogeneous
Varying density
[[1] Alfrey T., 1944, Nonhomogeneous stress in viscoelastic media, Quarterly of Applied Mathematics 2: 113119.##[2] Barberan J., Herrera J., 1966, Uniqueness theorems and speed of propagation of signals in viscoelastic materials, Archive for Rational Mechanics and Analysis 23(3): 173190.##[3] Achenbach J.D., Reddy D. P., 1967, Note on the wavepropagation in linear viscoelastic media, Zeitschrift für angewandte Mathematik und Physik (ZAMP), 18(1):141144.##[4] Bhattacharya S., Sengupta P.R., 1978, Disturbances in a general viscoelastic medium due to impulsive forces on a spherical cavity, Gerlands Beitr Geophysik Leipzig 87(8): 5762.##[5] Acharya D. P., Roy I., Biswas P. K., 2008, Vibration of an infinite inhomogeneous transversely isotropic viscoelastic medium with a cylindrical hole, Applied Mathematics and Mechanics 29(3): 112.##[6] Bert C. W., Egle D. M., 1969, Wave propagation in a finite length bar with variable area of crosssection, Journal of Applied Mechanics 36: 908909.##[7] Biot M.A., 1940, Influence of initial stress on elastic waves, Journal of Applied Physics 11(8):522530.##[8] Batra R. C., 1998, Linear constitutive relations in isotropic finite elasticity, Journal of Elasticity 51: 243245.##[9] White J.E., Tongtaow C., 1981, Cylindrical waves in transversely isotropic media, The Journal of the Acoustical Society of America 70(4):11471155.##[10] Mirsky I., 1965, Wave propagation in transversely isotropic circular cylinders, part I: Theory, Part II: Numerical results, The Journal of the Acoustical Society of America 37:10161026.##[11] Tsai Y.M., 1991, Longitudinal motion of a thick transversely isotropic hollow cylinder, Journal of Pressure Vessel Technology 113:585589.##[12] Murayama S., Shibata T., 1961, Rheological properties of clays, 5th International Conference of Soil Mechanics and Foundation Engineering, Paris, France 1:269 – 273.##[13] Schiffman R.L., Ladd C.C., Chen A.T.F., 1964, The secondary consolidation of clay, rheology and soil mechanics, Proceedings of the International Union of Theoretical and Applied Mechanics Symposium, Grenoble, Berlin 273 – 303.##[14] Gurdarshan S., Avtar S., 1980, Propagation, reflection and transmission of longitudinal waves in nonhomogeneous five parameter viscoelastic rods, Indian Journal of Pure and Applied Mathematics 11(9): 12491257.##[15] Kakar R., Kaur K., Gupta K.C., 2012, Analysis of fiveparameter viscoelastic model under dynamic loading, Journal of Solid Mechanics 4(4): 426440.##[16] Kaur K., Kakar R., Gupta K.C., 2012, A dynamic nonlinear viscoelastic model, International Journal of Engineering Science and Technology 4(12): 47804787.##[17] Kakar R., Kaur K., 2013, Mathematical analysis of five parameter model on the propagation of cylindrical shear waves in nonhomogeneous viscoelastic media, International Journal of Physical and Mathematical Sciences 4(1): 4552.##[18] Kaur K., Kakar R., Kakar S., Gupta K.C., 2013, Applicability of four parameter viscoelastic model for longitudinal wave propagation in nonhomogeneous rods, International Journal of Engineering Science and Technology 5(1): 7590.##[19] Friedlander F.G., 1947, Simple progressive solutions of the wave equation, Mathematical Proceedings of the Cambridge Philosophical Society 43: 36073.##[20] Karl F. C., Keller J. B., 1959, Elastic waves propagation in homogeneous and inhomogeneous media, Journal of Acoustical Society America 31: 694705.##[21] Moodie T.B., 1973, On the propagation, reflection and transmission of transient cylindrical shear waves in nonhomogeneous fourparameter viscoelastic media, Bulletin of the Australian Mathematical Society 8: 397411.##[22] Carslaw H. S., Jaeger, J. C., 1963, Operational Methods in Applied Math, Second Ed., Dover Pub, New York.##[23] Bland D. R., 1960, Theory of Linear Viscoelasticity, Pergamon Press, Oxford.##[24] Christensen R. M., 1971, Theory of Viscoelasticity, Academic Press.## ##]
Dynamics of a Running BelowKnee Prosthesis Compared to Those of a Normal Subject
2
2
The normal human running has been simulated by twodimensional biped model with 7 segments. Series of normal running experiments were performed and data of ground reaction forces measured by force plate was analyzed and was fitted to some Fourier series. The model is capable to simulate running for different ages and weights at different running speeds. A proportional derivative control algorithm was employed to grant stabilization during each running step. For calculation of control algorithm coefficients, an optimization method was used which minimized cinematic differences between normal running model and that of the experimentally obtained from running cycle data. This yielded the estimated torque coefficients of the different joints. The estimated torques and the torque coefficients were then applied to specific belowknee prosthesis (a SACH foot) to simulate healthyrunning motion of joints. Presently the SACH foot is designed for amputee’s walking; our data was used to modify such construct for running purposes. The goal was to minimize the differences between normal human model and a subject wearing a SACH foot during running. Kinematical curves of models for the obtained optimum mechanical properties indicated that prosthetic leg can reasonably produce the kinematics of normal running under normal joint driving torques.
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152
160


A
Ebrahimi Mamaghani
Mechanical Engineering, Tarbiat Modares University, Tehran
Mechanical Engineering, Tarbiat Modares University
Iran


H
Zohoor
Sharif University of Technology, Tehran
Sharif University of Technology, Tehran
Iran
zohoor@sharif.ir


K
Firoozbakhsh
Biomechanics, Mechanical Engineering Sharif University
Biomechanics, Mechanical Engineering Sharif
Iran


R
Hosseini
Mechanical Engineering Department, University of Tehran
Mechanical Engineering Department, University
Iran
Dynamic simulation
Human running
Belowknee prosthesis
Mathematical Modeling
Passive controller
Optimization
SACH Foot
[[1] Stein J. L., Flowers W. C., 1987, Stance phase control of aboveknee prostheses: knee control versus SACH Foot design, Journal of Biomechanics 20(1):1928.##[2] Blumentritt S., Werner S. H., Michael J., Schmalz T., 1998, Transfemoral amputees walking on a rotary hydraulic prosthetic knee mechanism: a preliminary report, American Academy of Orthotists & Prosthetists10(3): 6170.##[3] Sutherland J. L., Sutherland D. H., Kaufman K., Teel M., 1997, Case study forum: gait comparison of two prosthetic knee units, American Academy of Orthotists & Prosthetists 9(4): 168 173.##[4] Pejhan S., Farahmand F., Parnianpour M., 2008, Design optimization of an aboveknee prosthesis based on the kinematics of gait, Proceedings of the 30th Annual International Conference of the IEEE EMBS, Vancouver, British Columbia, Canada.##[5] Peasgood M.E., 2007, Stabilization of a dynamic walking gait simulation, Journal of Computational and Nonlinear Dynamics 2(1):6572.##[6] Tsai C.S., Mansour J.M., 1986, Swing phase simulation and design of aboveknee prostheses, Journal of Biomechanical Engineering, 108(1): 6572.##[7] Dundass C., Yao G.Z., Mechefske C.K., 2003, Initial biomechanical analysis and modeling of transfemoral amputee gait, American Academy of Orthotists & Prosthetists 15(1): 2026.##[8] Gard S.A, Childress D.S., Ullendahl J.E., 1996, The influence of fourbar linkage knees on prosthetic swingphase floor clearance, American Academy of Orthotists & Prosthetists 8(2), 34 40.##[9] Wojtyra M., 2000, Dynamical analysis of human walking, 15th European ADAMS Users Conference, University Technology, Warsaw.##[10] Iidaa F., Rummel J., Seyfarth A., 2008, Bipedal walking and running with springlike biarticular muscles, Journal of Biomechanical 41(3):656667.##[11] Peter S., Grimmer S., Lipfert W., 2009, Variable joint elasticities in running, Informatik Aktuell, Autonome Mobile Systeme 2009:29136.##[12] Gerrit S., Mombaur K., Knöthig J., 2010 , Modeling and optimal control of humanlike running, IEEE/ASME Transactions on Mechatronics 15(5).##[13] Akbari M., Farahmand F., Zohoor H., 2008, Dynamic simulation of the biped normal and amputee human gait, 12th International Conference on Climbing and and Walking Robots and the Support Technologies for Mobile Machines, Istanbul, Turkey.## ##]
Frequency Analysis of FG Sandwich Rectangular Plates with a FourParameter PowerLaw Distribution
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2
An accurate solution procedure based on the threedimensional elasticity theory for the free vibration analysis of Functionally Graded Sandwich (FGS) plates is presented. Since no assumptions on stresses and displacements have been employed, it can be applied to the free vibration analysis of plates with arbitrary thickness. The twoconstituent FGS plate consists of ceramic and metal graded through the thickness, from one surface of the each sheet to the other according to a generalized powerlaw distribution with four parameters. The benefit of using generalized powerlaw distribution is to illustrate and present useful results arising from symmetric, asymmetric and classic profiles. Using the Generalized Differential Quadrature (GDQ) method through the thickness of the plate, further allows one to deal with FG plates with an arbitrary thickness distribution of material properties. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The effects of different geometrical parameters such as the thicknesstolength ratio, different profiles of materials volume fraction and four parameters of powerlaw distribution on the vibration characteristics of the FGS plates are investigated. Interesting result shows that by utilizing a suitable fourparameter model for materials volume fraction, frequency parameter can be obtained more than the frequency parameter of the similar FGS plate with sheets made of 100% ceramic and at the same time lighter. Also, results show that frequencies of symmetric and classic profiles are smaller and larger than that of other types of FGS plates respectively. The solution can be used as benchmark for other numerical methods and also the refined plate theories.
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161
173


S
Kamarian
Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University
Young Researchers and Elite Club, Kermanshah
Iran


M.H
Yas
Department of Mechanical Engineering, Razi University, Kermanshah
Department of Mechanical Engineering, Razi
Iran
yas@razi.ac.ir


A
Pourasghar
Young Researchers and Elite Club, Central Tehran Branch, Islamic Azad University
Young Researchers and Elite Club, Central
Iran
Elasticity solution
Sandwich plate
Functionally Graded Materials
Generalized powerlaw distribution
GDQ Method
[[1] Tornabene F., Viola E., 2009, Free vibration analysis of fourparameter functionally graded parabolic panels and shells of revolution, European Journal of Mechanics  A/Solids 28:9911013.##[2] Sobhani B., Yas M.H., 2010, Threedimensional analysis of thermal stresses in fourparameter continuous grading fiber reinforced cylindrical panels, International Journal of Mechanical Sciences 52:10471063.##[3] Sobhani B., Yas M.H., 2010, Static and free vibration analyses of continuously graded fiberreinforced cylindrical shells using generalized powerlaw distribution, Acta Mechanica 215:155173.##[4] Pourasghar A., Yas M.H., Kamarian S., 2013, Local aggregation effect of CNT on the vibrational behavior of fourparameter continuous grading nanotube reinforced cylindrical panels, Polymer Composites 34(5):707721.##[5] Malekzadeh P., 2008, Threedimensional free vibrations analysis of thick functionally graded plates on elastic foundations, Composite Structures 89(3):367373.##[6] Yas M.H., Sobhani B., 2010, Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation, International Journal of Engineering Science 48:18811895.##[7] Matsunaga H., 2008, Free vibration and stability of functionally graded plates according to a 2D higherorder deformation theory, Composite Structures 82:499512.##[8] Li Q, Iu VP, Kou KP, 2008, Threedimensional vibration analysis of functionally graded material sandwich plates, The Journal of Sound and Vibration 311(1–2):498–515.##[9] Zenkour AM., 2005, A comprehensive analysis of functionally graded sandwich plates: Part1 deflection and stresses. International Journal of Solids and Structures 42:5224–5242.##[10] Zenkour AM., 2005, A comprehensive analysis of functionally graded sandwich plates: Part2 buckling and free vibration deflection and stresses, International Journal of Solids and Structures 42:5243–5258.##[11] Khalili S.M.R., Mohammadi Y., 2012, Free vibration analysis of sandwich plates with functionally graded face sheets and temperature dependent material properties: A new approach, European Journal of Mechanics  A/Solids 35:61–74.##[12] Natarajan S., Manickam G., 2012, Bending and vibration of functionally graded material sandwich plates using an accurate theory, Finite Elements in Analysis and Design 57:32–42.##[13] Neves A.M.A., Ferreira A.J.M., Carrera E., Cinefra M., Roque C.M.C., Jorge R.M.N., Soares C.M.M., 2013, Static free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi3D higherorder shear deformation theory and a meshless technique, Composites Part B: Engineering 44(1):657–674.##[14] Sobhy M., 2012, Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions, Composite Structures 99:7687.##[15] Song X., Guiwen K., Mingsui Y., Yan Z., 2013, Natural frequencies of sandwich plate with functionally graded face and homogeneous core, Composite Structures 96:226–231.##[16] Bellman R, Kashef B.G., Casti J., 1972, Differential Quadrature: a technique for a rapid solution of non linear partial differential equations, Journal of Computational Physics 10:40–52.##[17] Shu C., 2000, Differential Quadrature and Its Application in Engineering, Berlin, Springer.##[18] Kamarian S., Yas M.H., Pourasghar A., 2012, Free Vibrations of Continuous Grading Fiber Orientation Beams on Variable Elastic Foundations, Journal of Solid Mechanic 4(1): 7583.##[19] Bert CW., Malik M., 1996, Differential quadrature method in computational mechanics, a review, Applied Mechanics Reviews 49:128.##[20] Yas M. H., Kamarian S., Eskandari J., Pourasghar A., 2011, Optimization of functionally graded beams resting on elastic foundations, Journal of Solid Mechanic 3(4):365378.##[21] Yas M.H., Kamarian S., Pourasghar A.,2012, Application of imperialist competitive algorithm a and neural networks to optimize the volume fraction of threeparameter functionally graded beams, Journal of Experimental & Theoretical Artificial Intelligence , doi:10.1080/0952813X.2013.782346.## ##]
Design and Dynamic Modeling of Planar Parallel MicroPositioning Platform Mechanism with Flexible Links Based on Euler Bernoulli Beam Theory
2
2
This paper presents the dynamic modeling and design of micro motion compliant parallel mechanism with flexible intermediate links and rigid moving platform. Modeling of mechanism is described with closed kinematic loops and the dynamic equations are derived using Lagrange multipliers and Kane’s methods. EulerBernoulli beam theory is considered for modeling the intermediate flexible link. Based on the Assumed Mode Method theory, the governing differential equations of motion are derived and solved using both RungeKuttaFehlberg4, 5th and Perturbation methods. The mode shapes and natural frequencies are calculated under clampedclamped boundary conditions. Comparing perturbation method with RungeKuttaFehlberg4, 5th leads to same results. The mode frequency and the effects of geometry of flexure hinges on intermediate links vibration are investigated and the mode frequency, calculated using Fast Fourier Transform and the results are discussed.
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192


N.S
Viliani
Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University
Department of Mechanical and Aerospace Engineering
Iran
navid.viliani@gmail.com


H
Zohoor
Center of Excellence in Design, Robotics, and Automation, Sharif University of Technology; Fellow, The Academy of Sciences of Iran,
Center of Excellence in Design, Robotics,
Iran
zohoor@sharif.ir


M.H
Kargarnovin
School of Mechanical Engineering, Sharif University of Technology
School of Mechanical Engineering, Sharif
Iran
Compliant mechanism
Flexible link
Kane’s method
Micro positioning
Lagrange multipliers
[[1] Lobontiu N., 2003, Compliant Mechanisms Design of Flexure Hinges, CRC Press, Florida.##[2] Yi B.J., Chung G.B., Na H.Y., Kim W.K., Suh I.H., 2003, Design and experiment of a 3DOF parallel micromechanism utilizing flexure hinges, IEEE Transactions on Robotics and Automation 19: 604612.##[3] Yong Y.K., Fu L.T., 2009, Kinetostatic modeling of a 3RRR compliant micromotion stages with flexure hinges, Mechanism and Machine Theory 44: 11561175.##[4] Yong Y.K., Fu L.T., 2008, The effect of the accuracies of ﬂexure hinge equations on the output compliances of planar micromotion stages, Mechanism and Machine Theory 43: 347363.##[5] Yong Y.K., Fu L.T., 2009, Comparison of circular ﬂexure hinge design equations and the derivation of empirical stiffness formulations, IEEE/ASME International Conference on Advanced Intelligent Mechatronics Suntec Convention and Exhibition Center, doi:10.1109/AIM.2009.5229961.##[6] Paros J.M., Weisbord L., 1965, How to design flexure hinges, Machine Design 37: 151156.##[7] Anathasuresh G.K., Kota S., 1995, Designing compliant mechanisms, ASME Mechanical Engineering117: 9396.##[8] Murphy M.D., Midha A., Howell L.L., 1996, The topological synthesis of compliant mechanisms, Mechanism and Machine Theory 31: 185199.##[9] Tokin, 1996, Multilayer Piezoelectric Actuators, User’s Manual, Tokin Corporate Publisher.##[10] Saggere L., Kota S., 1997, Synthesis of distributed compliant mechanisms for adaptive structures application: an elastokinematic approach, Proceedings of the DETC 1997, ASME Design Engineering Technical Conferences, Sacramento, CA.##[11] Kota S., Joo J., Li Z., Rodgers S.M., Sniegowski J., 2001, Design of compliant mechanisms: applications to MEMS, Analog Integrated Circuits and Signal ProcessingAn international journal 29: 715.##[12] Rong Y.,Zhu Y., Luo Z., Xiangxi L., 1994, Design and analysis of flexure hinge mechanism used in micropositioning stages, ASME proceeding of the 1994 international Mechanical Engineering Congress and Exposition 68: 979985.##[13] Her I., Cheng J.C., 1994, A linear scheme for the displacement analysis of micro positioning stages with flexure hinges, ASME Journal of Mechanical Design 116: 770776.##[14] Trindade M.A., Sampaio R., 2002, Dynamics of beams undergoing large rotations accounting for arbitrary axial deformation, AIAA journal of Guidance, Control and dynamics 25: 634643.##[15] Yong Y.K., Lu T.F., Handley D.C., 2008, Review of circular ﬂexure hinge design equations and derivation of empirical formulations, Precision Engineering 32: 63–70.##[16] Lobontiu N., Paine J.S.N., Garcia E., Goldfarb M., 2001, Cornerfilleted flexure hinges, Transactions of the ASME, Journal of Mechanical Design 123: 346352.##[17] Shim J., Song S.K., Kwon D.S., Cho H.S., 1997, Kinematic feature analysis of a 6degree of freedom inparallel manipulator for micropositioning surgical, Proceedings of 1997 IEEE/RSJ International Conference on Intelligent Robots and Systems 3:16171623.##[18] Ryu J.W., Gweon D., Moon K.S., 1997, Optimal design of a flexure hinge based xyθ wafer stage, Precision Engineering 21: 1828.##[19] Meirovitch L., 2001, Fundamentals of Vibrations, MC Grow Hill, New York.##[20] Yu H.Y., Bi S., Zong G., Zhao W., 2004, Kinematics feature analysis of a 3 DOF compliant mechanism for micro manipulation, Chinese Journal of Mechanical Engineering 17: 127131.##[21] Choi K.B., Kim D.H., 2006, Monolithic parallel linear compliant mechanism for two axes ultraprecision linear motion, Review of Scientific Instruments 77(6): 065106.##[22] Tian Y., Shirinzadeh B., Zhang D., Zhong Y., 2010, Three ﬂexure hinges for compliant mechanism designs based on dimensionless graph analysis, Precision Engineering 34: 92–100.##[23] Baruh H., 1999, Analytical Dynamics, McGrawHill.##[24] Dwivedy S.K., Wberhard P., 2006, Dynamic analysis of flexible manipulators, a literature review, Mechanism and Machine Theory 41: 749777.##[25] Nayfeh A.H., 1981, Introduction to Perturbation Techniques, John Wiley & Sons, Inc.##[26] Benosman M., Vey G.L., 2004, Control of flexible manipulators: a survey, Robotica 22: 533545.##[27] Lee J.D., Geng Z., 1993, Dynamic model of a flexible Stewart platform, Computers and Structures 48: 367374.##[28] Zhou Z., Xi J., Mechefske C.K., 2006, Modeling of a fully flexible 3PRS manipulator for vibration analysis, Journal of Mechanical Design 128: 403412.##[29] Piras G., Cleghorn W.L., Mills J.K., 2005, Dynamic finiteelement analysis of planar high speed, highprecision parallel manipulator with flexible links, Mechanism and Machine Theory 40: 849862.##[30] Wang X., Mills J.K., 2005, FEM dynamic model for active vibration control of flexible linkages and its application to a planar parallel manipulator, Journal of Applied Acoustics 66: 11511161.## ##]
2DMagnetic Field and Biaxiall InPlane PreLoad Effects on the Vibration of Double Bonded Orthotropic Graphene Sheets
2
2
In this study, thermononlocal vibration of double bonded graphene sheet (DBGS) subjected to 2Dmagnetic field under biaxial inplane preload are presented. The elastic forces between layers of graphene sheet (GS) are taken into account by Pasternak foundation and the classical plate theory (CLPT) and continuum orthotropic elastic plate are used. The nonlocal theory of Eringen and Maxwell’s relations are employed to incorporate the smallscale effect and magnetic field effects, respectively, into the governing equations of the GSs. The differential quadrature method (DQM) is used to solve the governing differential equations for simply supported edges. The detailed parametric study is conducted, focusing on the remarkable effects of the angle and magnitude of magnetic field, different type of loading condition for couple system, tensile and compressive inplane preload, aspect ratio and nonlocal parameter on the vibration behavior of the GSs. The result of this study can be useful to design of micro electro mechanical systems and nano electro mechanical systems.
1

193
205


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


M.J
Maboudi
Faculty of Mechanical Engineering, University of Kashan, Kashan
Faculty of Mechanical Engineering, University
Iran


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


S
Amir
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran
Nonlocal vibration
Thermononlocal
Couple system
2Dmagnetic field
Biaxial inplane preload
[[1] Pradhan S.C., Kumar A., 2010, Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method, Computational Materials Science 50: 239245.##[2] Murmu T., Adhikari S., 2011, Axial instability of doublenanobeamsystems, Physics Letters A 375: 601608.##[3] Murmu T., Adhikari S., 2011, Nonlocal vibration of bonded doublenanoplatesystems, Composites: Part B 42: 19011911.##[4] Singh J.P., Dey S.S., 1990, Transverse vibration of rectangular plates subjected to inplane forses by a difference based vibrational approach, International Journal of Mechanical Sciences 32: 591599.##[5] Zhang Y., Liu G., Han X., 2005, Transverse vibrations of doublewalled carbon nanotubes under compressive axial load, Physics Letters A 340: 258266.##[6] Mustapha K.B., Zhong Z.W., 2010, Free transverse vibration of an axially loaded nonprismatic singlewalled carbon nanotube embedded in a twoparameter elastic medium, Computational Materials Science 50: 742751.##[7] Karami Khorramabadi M., 2009, Free vibration of functionally graded beams with piezoelectric layers subjected to axial load, Journal of Solid Mechanics 1: 2228.##[8] Murmu T., Pradhan S.C., 2009, Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity, Journal of Applied Physics 106: 104301.##[9] Kiani K., 2012, Vibration analysis of elastically restrained doublewalled carbon nanotubes on elastic foundation subjected to axial load using nonlocal shear deformable beam theories, International Journal of Mechanical Sciences 68: 1634.##[10] Ajiki H., Ando T., 1993, Electronic states of carbon nanotubes, Journal of Physical Society of Japan 62: 12551266.##[11] Ajiki H., Ando T., 1994, Aharonovbohm effect in carbon nanotubes, Physica B 201: 252349.##[12] Ajiki H., Ando T., 1996, Energy bands of carbon nanotubes in magnetic fields, Journal of Physical Society of Japan 65: 505514.##[13] Saito R., Dresselhaus G., Dresselhaus M.S., 1998, Physical Properties of Carbon Nanotubes, Imperial College Press, London.##[14] O´connell M.J., 2006, Carbon Nanotubes: Properties and Applications, CRC Press, Boca Raton.##[15] Ghorbanpour Arani A., Amir S., 2011, Magnetothermoelastic stresses and perturbation of magnetic field vector in a thin functionally graded rotating disk, Journal of Solid Mechanics 3: 392407.##[16] Lu H., Gou J., Leng J., Du S., 2011, Magnetically aligned carbon nanotube in nanopaper enabled shapememory nanocomposite for high speed electrical actuation, Applied Physics Letters 98: 174105.##[17] Camponeschi E., Vance R., AlHaik M., Garmestani H., Tannenbaum R., 2007, Properties of carbon nanotube–polymer composites aligned in a magnetic field, Carbon 45: 20372046.##[18] Bubke K., Gnewuch H., Hempstead M., Hammer J., Green M.L.H., 1997, Optical anisotropy of dispersed carbon nanotubes induced by an electric field, Applied Physics Letters 71: 19061908.##[19] Liu T X., Spencer J.L., Kaiser A.B., Arnold W.M., 2004, Electricfield oriented carbon nanotubes in different dielectric solvents, Current Applied Physics 4: 125128.##[20] Kiani K., 2012, Transverse wave propagation in elastically conﬁned singlewalled carbon nanotubes subjected to longitudinal magnetic ﬁelds using nonlocal elasticity models, Physica E 45: 8696.##[21] Murmu T., McCarthy M.A., Adhikari S., 2013, Inplane magnetic ﬁeld affected transverse vibration of embedded singlelayer graphene sheets using equivalent nonlocal elasticity approach, Composite Structures 96: 5763.##[22] Timoshenko S., WoinowskyKrieger S., 1959, Theory of Plates and Shells, Second edition, MCGRAWHILL, London.##[23] Eringen A.C. 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 47034710.##[24] John, K.D., 1984, Electromagnetics, McGrawHil1, Moscow.##[25] Reddy J.N., 1997, Mechanics of Laminated Composite Plates, Theory and Analysis, Chemical Rubber Company, Boca Raton, FL.##[26] Sherbourne A.N., Pandey M.D., 1991, Differential quadrature method in the buckling analysis of beams and composite plates, Computers and Structures 40: 903913.##[27] Bert C.W., Malik M., 1996, Differential quadrature method in computational mechanics: a review, Applied Mechanics Reviews 49: 128.##[28] Chen W., Shu C., He W., Zhong T., 2000, The applications of special matrix products to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates, Computers and Structures 74: 6576.##[29] Lancaster P., Timenetsky M., 1985, The Theory of Matrices with Applications, second edition, Academic Press Orlando.##[30] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., Mozdianfard M.R., Node S.M., 2013, Elastic foundation effect on nonlinear thermovibration of embedded double layered orthotropic graphene sheets using differential quadrature method, Journal of Mechanical Engineering Science: Part C 227:862879.## ##]
Nonlocal Vibration of Embedded Coupled CNTs Conveying Fluid Under ThermoMagnetic Fields Via Ritz Method
2
2
In this work, nonlocal vibration of double of carbon nanotubes (CNTs) system conveying fluid coupled by viscoPasternak medium is carried out based on nonlocal elasticity theory where CNTs are placed in uniform temperature change and magnetic field. Considering EulerBernoulli beam (EBB) model and Knudsen number, the governing equations of motion are discretized and Ritz method is applied to obtain the frequency of coupled CNTs system. The detailed parametric study is conducted, focusing on the remarkable effects of the Knudsen number, aspect ratio, small scale, thermomagnetic fields, velocity of conveying fluid and viscoPasternak medium on the stability of coupled system. The results indicate that magnetic field has significant effect on stability of coupled system. Also, it is found that trend of figures have good agreement with the previous researches. Results of this investigation could be applied for optimum design of nano/micro mechanical devices for controlling stability of coupled systems conveying fluid under thermomagnetic fields.
1

206
215


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


S
Amir
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran
Vibration
Coupled system
Conveying fluid
Knudsen Number
magnetic field
ViscoPasternak medium
[[1] Iijima S., 1991, Helical micro tubes of graphitic carbon, Nature 354: 5658.##[2] Yan Z., Jiang L.Y., 2011, The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects, Nanotechnology 22(24): 2457032457010.##[3] Ghorbanpour Arani A., Zarei M.S., Mohammadimehr M., Arefmanesh A., Mozdianfard M.R., 2011, The thermal effect on buckling analysis of a DWCNT embedded on the pasternak foundation, Physica E 43: 16421648.##[4] Ghorbanpour Arani A., Mohammadimehr M., Arefmanesh A., Ghasemi A., 2009, Transverse vibration of short carbon nanotube using cylindrical shell and beam models, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224: 745756.##[5] Zhen Y., Fang B., Tang Y., 2011, Thermalmechanical vibration and instability analysis of fluidconveying double walled carbon nanotubes embedded in viscoelastic medium, Physica E 44: 379385.##[6] Kuang Y.D., He X.Q., Chen C.Y., Li G.Q., 2009, Analysis of nonlinear vibrations of doublewalled carbon nanotubes conveying fluid, Computation Materials Science 45: 875880.##[7] Wang L., 2010, Vibration analysis of fluidconveying nanotubes with consideration of surface effects, Physica E 43: 437439.##[8] Khosravian N., RafiiTabar H., 2007, Computational modelling of the flow of viscous fluids in carbon nanotubes, Journal of Physics D: Applied Physics 40: 70467052.##[9] Wang L., Ni Q., Li M., Qian Q., 2008, The thermal effect on vibration and instability of carbon nanotubes conveying fluid, Physica E 40: 31793182.##[10] Murmu T., McCarthy M.A., Adhikari S., 2012, Vibration response of doublewalled carbon nanotubes subjected to an externally applied longitudinal magnetic field: a nonlocal elasticity approach, Journal of Sound and Vibration 331: 50695086.##[11] Murmu T., Pradhan S.C., 2009, Thermomechanical vibration of a singlewalled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory, Computation Materials Science 46: 854859.##[12] Murmu T., Adhikari S., 2011, Nonlocal buckling behavior of bonded doublenanoplatesystems, Journal of Applied Physics 108(8): 084316084319.##[13] Khodami Maraghi Z., Ghorbanpour Arani A., Kolahchi R., Amir S., Bagheri M.R., 2013, Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid, Composites Part B Engineering 45(1): 423432.##[14] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 47034710.##[15] Ghavanloo E., Fazelzadeh S.A., 2011, Flowthermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid, Physica E 44(1): 1724.##[16] Karniadakis G., Beskok A., Aluru N., 2005, Microflows and Nanoflows: Fundamentals and Simulation, Springer.##[17] Mirramezani M., Mirdamadi H.R., 2012, The effects of knudsendependent flow velocity on vibrations of a nanopipe conveying fluid, Archive of applied mechanics 82(7): 879890.##[18] Ghorbanpour Arani A., Shajari A.R., Atabakhshian V., Amir S., Loghman A., 2013, Nonlinear dynamical response of embedded fluidconveyed microtube reinforced by BNNTs, Composites Part B Engineering 44(1): 424432.##[19] Amabili M., 2008, Nonlinear Vibrations and Stability of Shells and Plates, Italy, Cambridge University Press.##[20] Yang J., Ke L.L., Kitipornchai S., 2010, Nonlinear free vibration of singlewalled carbon nanotubes using nonlocal Timoshenko beam theory, Physica E 42(5): 17271735.##[21] Mohammadimehr M., Saidi A.R., Ghorbanpour Arani A., Arefmanesh A., Han Q., 2010, Torsional buckling of a DWCNT embedded on winkler and pasternak foundations using nonlocal theory, Journal of Mechanical Science and Technology 24(6): 1289–1299.## ##]