2012
4
4
4
114
Theory of Generalized Piezoporo Thermoelasticity
2
2
In this paper, the basic constitutive equations and equations of motion are derived to describe the behavior of thermoelastic porous piezoelectric medium by using Biot’s theory and the theory of generalized thermoelasticity with on relaxation time (LordShulman). The electrical enthalpy density function is derived in the general coordinates. Also, clear definitions for the poroelastic modulus, electrical, thermal and additional mixed coefficients are embedded. The uniqueness of the solution for the complete system of equations is presented.
1

327
338


M
Jabbari
Postgraduate School of Engineering, South Tehran Branch, Islamic Azad University
Postgraduate School of Engineering, South
Iran
mohsen.jabbari@gmail.com


A
Yooshi
Postgraduate School of Engineering, South Tehran Branch, Islamic Azad University
Postgraduate School of Engineering, South
Iran
Porous piezo materials
Generalized thermoelasticity
Biot’s theory
Two phase
Electrodynamic Maxwell’s equation
[[1] Biot M.A., 1941, General theory of three –dimensional consolidation, Journal of Applied Physics12:155164.##[2] Biot M.A., 1955, Theory of elasticity and consolidation for a porous anisotropic solid, Journal of Applied Physics 26:182185.##[3] Biot M.A., Willis D.G., 1954, The elastic coefficients of the theory of consolidation, Journal of Applied Physics 24:594601.##[4] Vashishth A.K., Gupta V., 2009, Vibrations of porous piezoelectric ceramic plates, Journal of Sound and Vibration 325:781797.##[5] Biot M.A., 1962, Mechanics of deformation and acoustic propagation in porous media, Journal of Applied Physics 33:14821498.##[6] Mandl G., 1964, Change in skeletal volume of a fluidfilled porous body under stress, Journal of the Mechanics and Physics of Solids 12:299–315.##[7] Brown R.J.S, Korringa J., 1975, The dependence of the elastic properties of a porous rock on the compressibility of the pore fluid, Geophysics 40:608616.##[8] Zimmerman R.W., Somerton W.H., King M.S., 1986, Compressibility of porous rocks , Journal of Geophysical Reasearch 91:12765–12777.##[9] Zimmerman R.W., Myer L.R., Cook N.G.W., 1994, Grain and void compression in fractured and porous rock, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 31:179–184.##[10] Garg S. K., Nayfeh A. H., 1986, Compressional wave propagation in liquid and/or gas saturated elastic porous media, Journal of Applied Physics 60:30453055.##[11] Pride S.R., Gangi A.F., Morgan F.D., 1992, Deriving the equations of motion for porous isotropic media, Journal of the Acoustical Society of America 92:32783290.##[12] Thompson M., Willis J.R., 1991, A reformulation of the equations of anisotropic poroelasticity, Journal of Applied Mechanics 58:612–616.##[13] Albert D. G, 1993, A comparison between wave propagation in water‐saturated and air‐saturated porous materials, Journal of Applied Physics 73:2836.##[14] Cowin S., 1999, Bone poroelasticity, Journal of Biomechanics 32:217238.##[15] Tod S.R., 2003, An anisotropic fractured poroelastic effective medium theory, Geophysical Journal International 155:1006–1020.##[16] Wersing W., Lubitz K., Moliaupt J., 1986, Dielectric elastic and piezoelectric properties of porous PZT ceramics, Ferroelectrics 68:7797.##[17] Dunn H., Taya M., 1993, Electromechanical properties of porous piezoelectric ceramics, Journal of the American Ceramic Society 76:16971706.##[18] Kurashige M., 1989, A thermoelastic theory of fluidfilled porous materials, International Journal of Solids and Structures 25: 10391052.##[19] Ciarletta M., Scarpetta E., 1996, Some results on thermoelasticity for porous piezoelectric materials, Mechanics Research Communications 23:110.##[20] Ghassemi A., Diek A., 2002, Porothermoelasticity for swelling shales, Journal of Petroleum Science and Engineering 34:123 –135.##[21] Batifol C., Zielinski T. G., Galland M.A., Ichchou M. N., 2006, Hybrid piezoporoelastic sound package concept: numerical/experimental validations, Proceedings of International Symposium on Active Control of Sound and Vibration, Adelaide, Australia.##[22] Youssef H.M., 2007, Theory of generalized porothermoelasticity, International Journal of Rock Mechanics and Mining Sciences 44:222227.##[23] Nasedkin A., 2009, New model for piezoelectric porous medium with application to analysis of ultrasonic piezoelectric transducers, Proceedings of the 7th Euromech Solid Mechanics Conference, Lisbon, Portugal.##[24] Zielinski T.G., 2010, Fundamentals of multiphysics modelling of piezoporoelastic structures, Archives of Mechanics 62:343378.##[25] Sharma M.D., 2010, Piezoelectric effect on the velocities of waves in an anisotropic piezoporoelastic medium, Proceedings the Royal of Society A Mathematical Physical and Engineering sciences 466:19771992.##[26] Wang H.F., 2000, Theory of Linear Poroelasticity: with Application to Geomechanics and Hydrogeology, USA, Princeton University Press.##[27] Coussy O., 2004, Poromechanics, New York, Wiley, First edition.##[28] Coussy O., 2010, Mechanics and Physics of Porous Solids, New York, Wiley, First edition.##[29] Ikeda T., 1990, Fundamentals of Piezoelectricity, Oxford University Press.##[30] Hetnarski B., Eslami M.R., 2009, Thermal Stresses: Advanced Theory and Applications, USA, Springer, First edition.##[31] Kidner M. R. F., Hansen C. H., 2008, A comparison and review of theories of the acoustics of porous materials, International Journal Acoustics and Vibration 13:112119.##[32] Yang D., Zhang Z., 2002, Poroelastic wave equation including the Biot/squirt mechanism and the solid/fluid coupling anisotropy, Wave Motion 35:223–245.##[33] Kraus J.D., 1984, Electromagnetic, USA, McGrawHill Inc, Second edition.##[34] Deresiewicz H., Skalak R., 1963, On uniqueness in dynamic poroelasticity, Bulletin of the Seismological Society of America 53:783788. ##]
Analytical Solution for Electromechanical Behavior of Piezoelectric Rotating Shaft Reinforced by BNNTs Under Nonaxisymmetric Internal Pressure
2
2
In this study, twodimensional electromechanical analysis of a composite rotating shaft subjected to nonaxisymmetric internal pressure and applied voltage is investigated where hollow piezoelectric shaft reinforced by boron nitride nanotubes (BNNTs). Composite structure is modeled based on piezoelectric fiber reinforced composite (PFRC) theory and a representative volume element has been considered for predicting the elastic, piezoelectric and dielectric properties of the composite rotating shaft. Distribution of radial, circumferential, shear and effective stresses and electric displacement in composite rotating shaft are determined based on Fourier series. The detailed parametric study is conducted, focusing on the remarkable effects of angular velocity, electric potential, volume fraction and orientation angle of BNNTs on the distribution of stresses. The results show that properties of the piezoelectric shaft as matrix have significant influence on the electromechanical stresses where the PZT4 has less effective stresses against PVDF. Therefore, PZT4 could be considered for improving optimum design of rotating piezoelectric shaft under electric field and nonaxisymmetric mechanical loadings.
1

339
354


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


E
Haghparast
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran


S
Amir
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran
Composite rotating shaft
Microelectromechanical model
Nonaxisymmetric pressure
BNNTs fiber
[[1] Bayat M., Saleem M., Sahari B.B., Hamouda A.M.S., Mahdi E., 2009, Mechanical and thermal stresses in a functionally graded rotating disk with variable thickness due to radially symmetry loads, International Journal of Pressure Vessels and Piping 86: 357372.##[2] Hojjati M.H., Jafari S., 2009, Semiexact solution of nonuniform thickness and density rotating disks, Part II: Elastic strain hardening solution, International Journal of Pressure Vessels and Piping 86: 307318.##[3] Babaei M.H., Chen Z.T., 2008, Analytical solution for the electromechanical behavior of a rotating functionally graded piezoelectric hollow shaft, Archive of Applied Mechanics 78: 489500.##[4] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., 2011, Effect of material inhomogeneity on electrothermomechanical behaviors of functionally graded piezoelectric rotating shaft, Applied Mathematical Modelling 35: 2771–2789.##[5] Ghorbanpour Arani A., Shajari A.R., Amir S., Loghman A., 2013, Electrothermomechanical nonlinear nonlocal vibration and instability of embedded microtube reinforced by BNNT conveying fluid, Physica E 44: 424432.##[6] Akis T., Eraslan A.N., 2006, The stress response and onset of yield of rotating FGM hollow shafts, Acta Mechanica 187: 169187.##[7] Ghorbanpour Arani A., Bakhtiari R., Mohammadimehr M., Mozdianfard M.R., 2011, Electromagnetomechanical responses of a radially polarized rotating functionally graded piezoelectric shaft, Turkish Journal of Engineering and Environmental Sciences 35: 112.##[8] Atrian A., Jafari Fesharaki J., Majzoobi G.H., Sheidaee M., 2011, Effects of electric potential on thermomechanical behavior of functionally graded piezoelectric hollow cylinder under nonaxisymmetric loads, World Academy of Science, Engineering and Technology 59: 964967.##[9] Jafari Fesharaki J., Jafari Fesharaki V., Yazdipoor M., Razavian B., 2012, Twodimensional solution for electromechanical behavior of functionally graded piezoelectric hollow cylinder, Applied Mathematical Modelling 36: 55215533.##[10] Tan P., Tong L., 2001, Microelectromechanics models for piezoelectricﬁberreinforced composite materials, Composite Science Technology 61: 75969.##[11] Tan P., Tong L., 2001, Micromechanics models for nonlinear behavior of piezoelectric ﬁber reinforced composite materials, International Journal of Solids and Structures 38: 89999032.##[12] Ghorbanpour Arani A., Shajari A.R., Atabakhshian V., Amir S., Loghman A., 2013, Nonlinear dynamical response of embedded fluid conveyed microtube reinforced by BNNTs, Composites: Part B 44: 424432.## ##]
Analysis of Laminated Soft Core Sandwich Plate Having Interfacial Imperfections by an Efficient C0 FE Model
2
2
An efficient C0 continuous two dimensional (2D) finite element (FE) model is developed based on a refined higher order shear deformation theory (RHSDT) for the static analysis of soft core sandwich plate having imperfections at the layer interfaces. In this (RHSDT) theory, the inplane displacement field for the face sheets and the core is obtained by superposing a globally varying cubic displacement field on a zigzag linearly varying displacement field. The transverse displacement is assumed to have a quadratic variation within the core and it remains constant in the faces beyond the core. In this theory, the interfacial imperfection is represented by a liner springlayer model. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the sandwich plate. The nodal field variables are chosen in an efficient manner to circumvent the problem of C1 continuity requirement of the transverse displacements associated with the RHSDT. The proposed model is implemented to analyze the laminated composites and sandwich plates having interfacial imperfection. Many new results are also presented which should be useful for the future research.
1

355
371


R.P
Khandelwal
Department of Civil Engineering, Indian Institute of Technology
Department of Civil Engineering, Indian Institute
Iran
ravi.iitdelhi@gmail.com


A
Chakrabarti
Department of Civil Engineering, Indian Institute of Technology
Department of Civil Engineering, Indian Institute
Iran


P
Bhargava
Department of Civil Engineering, Indian Institute of Technology
Department of Civil Engineering, Indian Institute
Iran
Composites
Finite element methods
Interfacial imperfection
Sandwich plate
Soft core
[[1] Reissner E., 1944, On the theory of bending of elastic plates, Journal of Mathematical Physics 23:184–191.##[2] Mindlin R.D., 1951, Influence of rotary inertia and shear deformation on flexural motions of isotropic elastic plates, Journal of Applied Mechanics 18:31–38.##[3] Yang P.C., Norris C.H., Stavsky Y., 1966, Elastic wave propagation in heterogeneous plates, International Journal of Solids and Structures 2: 665–684.##[4] Reddy J.N., 1984, A simple higher–order theory for laminated composite plates, Journal of Applied Mechanics ASME 45: 745–752.##[5] Srinivas S., 1973, A refined analysis of composite laminates, Journal of Sound and Vibration 30: 495–507.##[6] Toledano A., Murakami H., 1987, A composite plate theory for arbitrary laminate configuration, Journal of Applied Mechanics ASME 54: 81–189.##[7] Li X., Liu D., 1995, Zigzag theory for composite laminates, Journal of American Institute of Aeronautics and Astronautics 33(6): 1163–1165.##[8] Lu X., Liu D., 1992, An interlaminar shear stress continuity theory for both thin and thick composite laminates, Journal of Applied Mechanics ASME 59: 502–509.##[9] Lu X., Liu D., 1992, An interlaminar shear stress continuity theory for both thin and thick composite laminates, Journal of Applied Mechanics ASME 59: 502–509.##[10] Di Scuiva M., 1984, A refined transverse shear deformation theory for multilayered anisotropic plates, Atti Academia delle Scienze di Torino 118: 279–295.##[11] Murakami H., 1986, Laminated composite plate theory with improved in–plane responses, Journal of Applied Mechanics ASME 53: 661–666.##[12] Liu D., Li X., 1996, An overall view of laminate theories based on displacement hypothesis, Journal of Composite Material 30: 1539–1560.##[13] Bhaskar K., Varadan T.K., 1989, Refinement of higher order laminated plate theories, Journal of American Institute of Aeronautics and Astronautics 27: 1830–1831.##[14] Di Sciuva M., 1992, Multilayered anisotropic plate models with continuous interlaminar stress, Computers and Structures 22(3):149–167.##[15] Lee C.Y., Liu D., 1991, Interlaminar shear stress continuity theory for laminated composite plates, Journal of American Institute of Aeronautics and Astronautics 29: 2010–2012.##[16] Cho M., Parmerter R.R., 1993, Efficient higher order composite plate theory for general lamination configurations, Journal of American Institute of Aeronautics and Astronautics 31(7): 1299–1306.##[17] Carrera E., 2003, Historical reviews of zigzag theories for multilayered plates and shells, Applied Mechanics Reviews 38: 342352.##[18] Frosting Y., 2003, Classical and high order computational models in the analysis of modern sandwich panels, Composites: Part B 34: 83–100.##[19] Givil H.S., Rabinovitch O. Frostig Y., 2007, Highorder nonlinear contact effects in the dynamic behavior of delaminated sandwich panel with a flexible core, International Journal of Solids and Structures 44: 77–99.##[20] Brischetto S., Carrera E., Demasi L., 2009, Improved response of unsymmetrically laminated sandwich plates by using zigzag functions, Journal of sandwich structures and materials 11: 257267.##[21] Plantema F.J., 1966, Sandwich Construction, Wiley, New York.##[22] Allen H.G., 1969, Analysis and Design of Structural Sandwich Panels, Pergamon Press, Oxford.##[23] Liaw B., Little R.W., 1967, Theory of bending multilayer sandwich plates, Journal of American Institute of Aeronautics and Astronautics 5(2): 301–304.##[24] Azar J.J., 1968, Bending theory for multilayer orthotropic sandwich plates, Journal of American Institute of Aeronautics and Astronautics 6(10): 2166–2169.##[25] Foile G.M., 1970, Bending of clamped orthotropic sandwich plates, ASCE Journal Engineering Mechanics 96: 243–261.##[26] Whitney J.M., 1972, Stress analysis of thick laminated composite and sandwich plates, Journal of Composite Material 6: 525–538.##[27] Khatua T.P., Cheung Y.K., 1973, Bending and vibration of multilayer sandwich beams and plates, International Journal of Numerical Methods Engineering 6: 11–24.##[28] Monforton G.R., Ibrahim I.M., 1975, Analysis of sandwich plates with unbalanced cross ply faces, International Journal of Mechanical Science 17: 227–238.##[29] Pandya B.N., Kant T., 1988, Higher–order shear deformable theories for flexure of sandwich platesfinite element evaluations, International Journal of Solids and Structures 24(12): 1267–1286.##[30] Pagano N.J., 1970, Exact solution of rectangular bidirectional composites and sandwich plates, Journal of Composite Material 4: 20–34.##[31] Pagano N.J., 1969, Exact solution of composite laminates in cylindrical bending, Journal of Composite Material 3: 398–411.##[32] O'Connor D.J., 1987, A finite element package for the analysis of sandwich construction, Composite Structures 8: 143–161.##[33] Lee L.J., Fan Y.J., 1996, Bending and vibration analysis of composite sandwich plates, Computers and Structures 60(1): 103–112.##[34] Oskooei S., Hansen J.S., 2000, Higher order finite element for sandwich plates, Journal of American Institute of Aeronautics and Astronautics 38(3): 525–533.##[35] Frostig Y., Baruch M., Vinley O., Sheinman I., 1992, Highorder theory for sandwich beam behaviour with transversely flexible core, Journal of Engineering Mechanics ASCE 118(5): 1026–1043.##[36] Thomsen O.T., 1993, Analysis of local bending effects in sandwich plates with orthotropic face layers subjected to localised loads, Composite Structures 25: 511–520.##[37] Kant T., Swaminathan K., 2002, Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory, Composite Structures 56: 329–344.##[38] Carrera E., Ciuffreda A., 2005, Bending of composites and sandwich plates subjected to localized lateral loadings: a comparison of various theories, Composite Structures 68: 185202.##[39] Carrera E., Brischetto S., 2009, A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates, Applied Mechanics Reviews 62: 117.##[40] Pandit M.K., Sheikh A.H., Singh B.N., 2008, An improved higher order zigzag theory for the static analysis of laminated sandwich plate with softcore, Finite Element in Analysis and Design 44: 602–10.##[41] Pandit M.K., Sheikh A.H., Singh B.N., 2010, Stochastic perturbation based finite element for deflection statistics of soft core sandwich plate with random material properties, International Journal of Mechanical Science 51(5): 14–23.##[42] Mantari J.L., Oktem A.S., Soares C.G., 2012, A new higher order shear deformation theory for sandwich and composite laminated plates, Composites: Part B 45: 1489–1499.##[43] Khandelwal R.P., Chakrabarti A., Bhargava P., 2012, Accurate calculation of transverse stresses for soft core sandwich laminates, Proceedings of Third Asian Conference on Mechanics of Functional Materials and Structures (ACMFMS) 58 December, IIT Delhi, India.##[44] Chen T.C., Jang H.I., 1995, Thermal stresses in a multilayered anisotropic medium with interfacethermal resistance, Journal of Applied Mechanics ASME 62: 810–811.##[45] Lai Y.S., Wang C.Y., Tien Y.M., 1997, Micromechanical analysis of imperfectly bonded layered media, Journal of Engineering Mechanics ASCE 123: 986–995.##[46] Di Sciuva M., Gherlone M., 2003a, A global/local thirdorder Hermitian displacement field with damaged interfaces and transverse extensibility: analytical formulation, Composite Structures 59: 419431.##[47] Di Sciuva M., Gherlone M., 2003b, A global/local thirdorder Hermitian displacement field with damaged interfaces and transverse extensibility: FEM formulation, Composite Structures 59: 433444.##[48] Cheng Z., Jemah A.K., Williams F.W., 1996a, Theory of multilayered anisotropic plates with weakend interfaces, Journal of Applied Mechanics ASME 63: 1019–1026.##[49] Di Sciuva M., 1997, A geometrically nonlinear theory of multilayered plates with interlayer slips, Journal of American Institute of Aeronautics and Astronautics 35(11): 1753–1759.##[50] Chakrabarti A., Sheikh A.H., 2004, Behavior of laminated sandwich plates having interfacial imperfections by a new refined element, Computational Mechanics 34: 87–89.##[51] Cheng Z., Howson W.P., Williams F.W., 1997, Modelling of weakly bonded laminated composite plates at large deflections, International Journal of Solids and Structures 34(27): 35833599.##[52] Cheng Z., Kennedy D., Williams F.W., 1996b, Effect of interfacial imperfection on buckling and bending of composite laminates, Journal of American Institute of Aeronautics and Astronautics 34(12): 25902595.##[53] Cheng Z., Kitipornchai S., 2000, Prestressed composite laminates featuring interlaminar imperfection, International Journal of Mechanical Science 42: 425443.## ##]
Closedform Solution of Dynamic Displacement for SLGS Under Moving the Nanoparticle on ViscoPasternak Foundation
2
2
In this paper, forced vibration analysis of a singlelayered graphene sheet (SLGS) under moving a nanoparticle is carried out using the nonlocal elasticity theory of orthotropic plate. The SLGS under moving the nanoparticle is placed in the elastic and viscoelastic foundation which are simulated as a Pasternak and ViscoPasternak medium, respectively. Movement of the nanoparticle is considered as a linear movement with constant velocity from an edge to another edge of graphene sheet. Using the nonlinear Von Kármán straindisplacement relations and Hamilton’s principle, the governing differential equations of motion are derived. The differential equation of motion for all edges simply supported boundary condition is solved by an analytical method and therefore, the dynamic displacement of SLGS is presented as a closedform solution of that. The influences of medium stiffness (Winkler, Pasternak and damper modulus parameter), nonlocal parameter, aspect ratio, mechanical properties of graphene sheet, time and velocity parameter on dimensionless displacement (dynamic displacement to static displacement of SLGS) are studied. The results indicate that, as the values of stiffness modulus parameter increase, the maximum dynamic displacement of SLGS decreases. Therefore, the results are in good agreement with the previous researches.
1

372
385


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


A
Shiravand
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran


S
Amir
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran
Graphene sheet
ViscoPasternak medium
, Moving nanoparticle
Closedform solution
Nonlocal elasticity theory
[[1] Sellers K., Mackay C., Bergeson L.L., Clough S.R., Hoyt M., Chen J., Henry K., Hamblen J., 2008, Nanotechnology and the Environment, CRC Press.##[2] Reddy J.N., 2003, Mechanics of laminated composite plates and shells, CRC press LLC, New York.##[3] Timoshenko S., 1959, Theory Of plates and shells, McGrawHill, Secound Edition.##[4] Vinson J.R., 2005, Plate and Panel Structures of Isotropic, Composite and Piezoelectric Materials, Including Sandwich Construction, Springer, Netherlands.##[5] Eringen A.C., 1972, Nonlocal polar elastic continua, International Journal of Engineering Science 10: 116.##[6] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 4703–4710.##[7] Eringen A.C., 2002, Nonlocal Continuum Field Theories, SpringerVerlag, New York.##[8] Eringen A.C., Edelen D.G.B., On nonlocal elasticity, International Journa ofl Engineering Science 10: 233–248.##[9] Pradhan S.C., Phadikar J.K., 2009, Nonlocal elasticity theory for vibration of nanoplates, Journal of Sound and Vibration 325: 206223.##[10] Murmu T., Adhikari S., 2011, Nonlocal vibration of bonded doublenanoplatesystems, Composites Part B: Engineering 42: 19011911.##[11] Murmu T., Adhikari S., 2011, Axial instability of doublenanobeamsystems, Physics Letters A 375: 601608.##[12] 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.##[13] Ghorbanpour Arani A., Shiravand A., Rahi M., Kolahchi R., 2012, Nonlocal vibration of coupled DLGS systems embedded on ViscoPasternak foundation, Physica B: Condensed Matter 407: 41234131.##[14] Shu C., 1999, Diffrential Quadrature and its Application in Eengineering, springer.##[15] Zong Z., Zhang Y., 2009, Advanced Diffrential Quadrature Methods, CRC Press, New York.##[16] Kiani K., 2010, Longitudinal and transverse vibration of a singlewalled carbon nanotube subjected to a moving nanoparticle accounting for both nonlocal and inertial effects, Physica E: Lowdimensional Systems and Nanostructures 42: 23912401.##[17] Kiani K., 2011, Smallscale effect on the vibration of thin nanoplates subjected to a moving nanoparticle via nonlocal continuum theory, Journal of Sound and Vibration 330: 48964914.##[18] Kiani K., 2011, Nonlocal continuumbased modeling of a nanoplate subjected to a moving nanoparticle. Part I: Theoretical formulations, Physica E: Lowdimensional Systems and Nanostructures 44: 229248.##[19] Kiani K., 2011, Nonlocal continuumbased modeling of a nanoplate subjected to a moving nanoparticle. Part II: Parametric studies, Physica E: Lowdimensional Systems and Nanostructures 44: 249269.##[20] Şimşek M., 2011, Nonlocal effects in the forced vibration of an elastically connected doublecarbon nanotube system under a moving nanoparticle, Computational Materials Science 50: 21122123.##[21] Ghorbanpour Arani A., Roudbari M.A., Amir S., 2012, Nonlocal vibration of SWBNNT embedded in bundle of CNTs under a moving nanoparticle, Physica B: Condensed Matter 407: 36463653.##[22] Pradhan S.C., Kumar A., 2011, Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method, Composite Structures 93: 774779.## ##]
Thermoelastic Damping in a Capacitive Microbeam Resonator Considering Hyperbolic Heat Conduction Model and Modified Couple Stress Theory
2
2
In this paper, the quality factor of thermoelastic damping in an electrostatically deflected microbeam resonator has been investigated. The thermoelastic coupled equations for the deflected microbeam have been derived using variational and Hamilton principles based on modified couple stress theory and hyperbolic heat conduction model. The thermoelastic damping has been obtained discretizing the governing equations over spatial domain and applying complex frequency approach. The effects of the applied bias DC voltage, playing simultaneously role of an external force and softening parameter, on the quality factor have been studied. The obtained results of the modified couple stress and classic theories are compared and the effects of the material internal lengthscale parameter on the differences between results of two theories have been discussed. In addition, the effects of different parameters such as beam length and ambient temperature on the quality factor have been studied.
1

386
401


M
Najafi
Mechanical Engineering Department, Urmia University
Mechanical Engineering Department, Urmia
Iran


G
Rezazadeh
Mechanical Engineering Department, Urmia University
Mechanical Engineering Department, Urmia
Iran
g.rezazadeh@urmia.ac.ir


R
Shabani
Mechanical Engineering Department, Urmia University
Mechanical Engineering Department, Urmia
Iran
Modified couple stress theory
Thermoelastic damping
Lengthscale parameter
Electrostatic force
[[1] Tilmans H.A., Legtenberg R., 1994, Electrostatically driven vacuumencapsulated polysilicon resonators, Part II, Theory and performance, Sensors and Actuators A 45: 6784.##[2] Rezazadeh G., Khatami F., Tahmasebi A., 2007, Investigation of the torsion and bending effects on static stability of electrostatic torsional micromirrors, Microsystem Technologies 13: 715722.##[3] Ruhan M., Shen J., Wheeler C.B., 2001, latching micro electromagnetic relays, Sensors and Actuators A 91: 346350.##[4] Chen J.Y., Hsu Y.C., Lee S.S., Mukherjee T., Fedder G.K., 2008, Modeling and simulation of a condenser microphone, Sensors and Actuators A 145–146: 224230.##[5] Liu J., Martinn D.T., Kardirvel K., Nishida T., Cattafesta L., Sheplak M., Mann B., 2008, Nonlinear model and system identification of a capacitive dualbackplate MEMS microphone, Journal of Sound and Vibration 309: 276292.##[6] Saif M.T.A., Alaca B.E., Sehitoglu H., 1999, Analytical modeling of electrostatic membrane actuator micro pumps, Journal of Microelectromechanical Systems 8: 335–345.##[7] Zener C., 1937, Internal friction in solids. I. Theory of internal friction in reeds, Physical Review 52 (3): 230235.##[8] Zener C., 1938, Internal friction in solids. II. General theory of thermoelastic internal friction, Physical Review 53: 90–99.##[9] Rozshart R.V., 1990, The effect of thermoelastic internal friction on the Q of the micromachined silicon resonators, IEEE Solid State Sensor and Actuator Workshop, HiltonHead Island, SC, 13–16.##[10] Landau L.D., Lifshitz E.M., 1959, Theory of Elasticity, Pergamon Press, Oxford.##[11] Evoy S., Oikhovets A., Sekaric L., Parpia J.M., Craighead H.G., Carr D.W., 2000, Temperaturedependent internal friction in silicon nanoelectromechanical systems, Applied Physics 77(15): 23972399.##[12] Duwel A., Gorman J., Weinstein M., Borenstein J., Warp P., 2003, Experimental study of thermoelastic damping in MEMS 350 gyros, Sensors and Actuators A 103: 7075.##[13] Lifshitz R., Roukes M.L., 2000, Thermoelastic damping in micro and nano mechanical systems, Physical Review B 61: 56005609.##[14] Guo F.L., Rogerson G.A., 2003, Thermoelastic coupling effect on a micromachined beam resonator, Mechanics Research Communications 30: 513518.##[15] Sun Y., Fang D., Soh A.K., 2006, Thermoelastic damping in microbeam resonators, International Journal of Solids and Structures 43: 32133229.##[16] Nayfeh H., Younis M.I, 2004, Modeling and simulations of thermoelastic damping in microplates, Journal of Micromechanics Microengineering 14: 17111717.##[17] Sun Y., Saka M., 2008, Vibrations of microscale circular plates induced by ultrafast lasers, International Journal of Mechanical Sciences 50: 13651371.##[18] Sun Y., Tohmyoh H., 2009, Thermoelastic damping of the axisymmetric vibration of circular plate resonators. Journal of Sound and Vibration 319: 392405.##[19] Sun Y., Saka M., 2010, Thermoelastic damping in microscale circular plate resonators, Journal of Sound and Vibration 329: 328337.##[20] Sharma J.N., Sharma R., 2011, Damping in microscale generalized thermoelastic circular plate resonators, Ultrasonics 51(3): 352358.##[21] Rezazadeh G., Vahdat A.S, Pesteii S.M., Farzi B., 2009, Study of thermoelastic damping in capacitive microbeam resonators using hyperbolic heat conduction model, Sensors and Transducers Journal 108(9): 5472.##[22] Vahdat A.S., Rezazadeh G., 2011, Effects of axial and residual stresses on thermoelastic damping in capacitive microbeam resonator, Journal of the Franklin Institute 348: 622639.##[23] Shengli K., Shenjie Zh., Zhifeng N., Kai W., 2009, Static and dynamic analysis of microbeams based on strain gradient elasticity theory, International Journal of Engineering Science 47:487498.##[24] Wang B., Zhao J., Zhou S., 2010, A microscale timoshenko beam model based on strain gradient elasticity theory, European Journal of MechanicsA/Solids 29: 591599.##[25] Mindlin R.D., Tiersten H.F., 1962, Effects of couplestresses in linear elasticity, Archive for Rational Mechanics and Analysis 11: 415–448.##[26] Mindlin R.D., 1963, Influence of couplestresses on stressconcentrations, Experimental Mechanics3: 17.##[27] Toupin R.A., 1962, Elastic materials with couplestresses, Archive for Rational Mechanics and Analysis 11(1): 385414.##[28] Yang F., Chong A.C.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory of elasticity, International Journal of Solidsand Structures39: 27312743.##[29] Rezazadeh G., Vahdat A.S., Tayefehrezaei S., CetinkayaCe., 2012, Thermoelastic damping in a microbeam resonator using modified couple stress theory, Acta Mechanica 223(6): 11371152.##[30] Cao Y., Nankivil D.D., Allameh S., Soboyejo W., 2007, Mechanical properties of Au films on silicon substrates, Materials and Manufacturing processes 22: 187194.##[31] Shrotriya P., Allameh S.M., Lou J., Buchheit T., Soboyejo W.O., 2003, On the measurement of the plasticity lengthscale parameter in LIGA nickel foils, Mechanics of Materials 35: 233243.##[32] Rezazadeh G., Tahmasebi A., Zubstov M., 2006, Application of piezoelectric layers in electrostatic MEM actuators: controlling of pullin voltage, Microsystem Technologies 12: 11631170.##[33] Sad M.H, 2009, Elasticity Theory Application and Numerics, Elsevier Inc.##[34] Kong S., Zhou S., Nie Z., Wang K., 2008, The sizedependent natural frequency of Bernoulli–Euler microbeams, International Journal of Engineering Science 46: 42737.##[35] Park S.K., Gao X.L., 2006, Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics Microengineering 16: 23552359.##[36] Khisaeva Z.F., Ostojastarzewski M., 2006, Thermoelastic damping in nano mechanical resonators with finite wave speeds, Journal of Thermal stresses 29(3): 201216.##[37] Osterberg P.M., Senturia S.D., 1997, A test chip for MEMS material property measurement using electrostatically actuated tests tructures, Journal of Microelectromechanical Systems 6: 107188.## ##]
Torsional Waves in Prestressed Fiber Reinforced Medium Subjected to Magnetic Field
2
2
The propagation of torsional waves in a prestressed fiberreinforced halfspace under the effect of magnetic field and gravity has been discussed. The problem has been solved analytically using Whittaker function to obtain the exact solution frequency equations. Numerical results for stress, gravity and magnetic field are given and illustrated graphically. Comparisons are made with the results predicted by the boundary value condition for rigid boundary and for traction free boundary in the presence and in the absence of the effect of a magnetic field, gravity and stress. It is found that the reinforcement, gravity and magnetic field have great effects on the distribution.
1

402
415


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


S
Kakar
Faculty of Electrical Engineering, SBBSIET Padhiana Jalandhar
Faculty of Electrical Engineering, SBBSIET
Iran
Magnetoelastic
Torsional waves
Initial stress
Fiber reinforced medium
Whittaker function
[[1] Bromwich T.J., 1898, On the influence of gravity on elastic waves and in particular on the vibrations of an elastic globe, Proceedings London Mathematical Society 30: 98120.##[2] Sezawa K., 1927, Dispersion of elastic waves propagated on the surface of stratified bodies and on curved surfaces, Bulletin of the Earthquake Research Institute 3: 118.##[3] Das N.C., Bhattacharya S.K., 1978, Axisymmetric vibrations of orthotropic shells in a magnetic field, Indian Journal of Pure and Applied Mathematics 45(1): 4054.##[4] Andreou E., Dassios G., 1997, Dissipation of energy for magnetoelastic waves in conductive medium, Quarterly of Applied Mathematics 55: 2339.##[5] Biot M.A., 1956, Theory of elastic waves in fluidsaturated porous solid, Journal of the Acoustical Society of America 2:168178.##[6] Suhubi E.S., 1965, Small torsional oscillations of a circular cylinder with finite electrical conductivity in a constant axial magnetic field, International Journal of Engineering Science 2: 441.##[7] Abdalla A.N., 1994, Torsional wave propagation in an orthotropic magnetoelastic hollow circular cylinder, Applied Mathematics and Computation 63: 281293.##[8] Datta B.K., 1985, On the stresses in the problem of magnetoelastic interaction on an infinite orthotropic medium with cylindrical hole, International Journal of Theoretical Physics 33(4): 177186.##[9] Acharya D.P., Roy I., Sengupta S., 2009, Effect of magnetic field and initial stress on the propagation of interface waves in transversely isotropic perfectly conducting media, Acta Mechanica 202: 3545.##[10] Belfield, Rogers, Spencer A., 1983, Stress in elastic plates reinforced by fibres lying in concentric circles, Journal of the Mechanics and Physics of Solids 31: 25.##[11] Rayleigh L., 1945, The Theory of Sound, Dover Publications 1 and 2.##[12] Bazer J.A., 1984, Survey of linear and nonlinear waves in a perfect magnetoelastic medium in the mechanical behavior of electromagnetic solid continua, Elsevier Science Publishers.##[13] Love A.E.H., 1977, 1926, Some Problems of Geodynamics, Cambridge University Press.##[14] Gupta S., Chattopadhyay A., Kundu S.K., Gupta A.K., 2009, Propagation of torsional surface waves in gravitating anisotropic porous halfspace with rigid boundary, International Journal of Applied Mathematics and Mechanics 6(9): 7689.##[15] Green A.E., 1954, Theoretical Elasticity, Oxford University Press.##[16] Love A.E.H., 1944, Mathematical Theory of Elasticity, Dover Publications, Forth Edition.##[17] Timoshenko S., 1951, Theory of Elasticity, McGrawHill Book Company, Second Edition.##[18] Westergaard H.M., 1952, Theory of Elasticity and Plasticity,Dover Publications.##[19] Thidé B., 1997, Electromagnetic Field Theory,Dover Publications.## ##]
Frequency Response Analysis of a Capacitive Microbeam Resonator Considering Residual and Axial Stresses and Temperature Changes Effects
2
2
This paper presents a study on the frequency response of a capacitive microbeam resonator under various applied stresses. The governing equation whose solution holds the answer to all our questions about the mechanical behavior is the nonlinear electrostatic equation. Due to the nonlinearity and complexity of the derived equation analytical solution are not generally available; therefore, the obtained differential equation has been solved by using a step by step linearization scheme and a Galerkin based reduced order model. The obtained static pullin voltages have been validated by previous reports and a good agreement has been achieved. The dynamic behavior of the beam under residual, axial and thermal stresses has been investigated. It has been shown that applying the positive residual stress and negative temperature changes shifts right the frequency response and decrease the vibration amplitude and vice versa. Also, it has been shown that applying the bias DC voltage beside the exciting AC voltage decreases the stiffness of the system and so, shifts left the frequency response and increases the vibration amplitude.
1

416
425


S
Valilou
Department of Mechanical Engineering, Khoy Branch, Islamic Azad University
Department of Mechanical Engineering, Khoy
Iran
svalilou@iaukhoy.ac.ir


M
Jalilpour
Department of Mechanical Engineering, Khoy Branch, Islamic Azad University
Department of Mechanical Engineering, Khoy
Iran
MEMS
Resonator
Residual stress
Axial stress
Temperature Changes
Frequency Response
[[1] Basso M., Giarre L., Dahleh M., Mezic I., 1998,Numerical analysis of complex dynamics in atomic force microscopes, Proceedings of the IEEE International Conference on Control Applications 2:1026–1030.##[2] Fritz J., Baller M.K., Lang H.P., Rothuizen H., Vettiger P., Meyer E., Gntherodt H.J., Gerber C., Gimzewski J.K., 2001,Translating biomolecular recognition into nanomechanics , Science 288:316–318.##[3] Sidles JA., 1991, Noninductive detection of single protonmagnetic resonance, Applied Physics Letters 58:28542856.##[4] Nabian A., Rezazadeh G., Haddadderafshi M., Tahmasebi A., 2008, Mechanical behavior of a circular micro plate subjected to uniform hydrostatic and nonuniform electrostatic pressure, Microsyst Technol 14:235–240.##[5] Fathalilou M., Motallebi A., Rezazadeh G., Yagubizade H., Shirazi K., Alizadeh Y., 2009, Mechanical Behavior of an ElectrostaticallyActuated Microbeam under Mechanical Shock, Journal of Solid Mechanics 1: 4557.##[6] Senturia SD., 2001, Microsystem Design, Norwell, MA: Kluwer.##[7] Zhang Y., Zhao Y., 2006, Numerical and analytical study on the pullin instability of micro structure under electrostatic loading, Sensors and Actuators A: Physical 127: 366367.##[8] Rezazadeh G., Sadeghian H., Abbaspour E., 2008, A comprehensive model to study nonlinear behaviour of multilayered micro beam switches, Microsyst Technol 14: 143.##[9] Sadeghian H., Rezazadeh G., 2007, Application of the Generalized Differential Quadrature Method to the Study of PullIn Phenomena of MEMS Switches, Journal of Microelectromechanical Systems 16(6):13341340.##[10] Osterberg P.M., Senturia S.D., 1997, MTEST a test chip for MEMS material property measurement using electrostatically actuated test structures, Journal of Microelectromechanical Systems 6(2):107118.##[11] Senturia SD., Aluru N, White J., 1997, Simulating the behavior of MEMS devices, IEEE Computing in Science and Engineering 4(1): 30–43.##[12] AbdelRahman E.M., Younis M.I., Nayfeh A.H., 2002, Characterization of the mechanical behavior of an electrically actuated microbeam , Journal of Micromechanics and Microengineering 12:759–766.##[13] Rezazadeh G., Tahmasebi A., Zubtsov M., 2006, Application of Piezoelectric Layers in Electrostatic MEM Actuators: Controlling of Pullin Voltage, Microsyst Technol 12 : 11631170.##[14] Mukherjee T., Fedder G.K., White J., 2000, Emerging simulation approaches for micromachined devices, IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems 19: 1572–1589.##[15] Senturia SD., 1998, CAD challenges for microsensors, microactuators, and Microsystems, Proceedings of the IEEE 86: 1611–1626.##[16] Talebian S., Rezazadeh G., Fathalilou M., Yagubizade H., 2010, Effect of Temperature on Pullin Voltage and Natural Frequency of an Electrostatically Actuated Microplate, Mechatronics 20(6):666673.## ##]
Analysis of Five Parameter Viscoelastic Model Under Dynamic Loading
2
2
The purpose of this paper is to analysis the viscoelastic models under dynamic loading. A fiveparameter model is chosen for study exhibits elastic, viscous, and retarded elastic response to shearing stress. The viscoelastic specimen is chosen which closely approximates the actual behavior of a polymer. The module of elasticity and viscosity coefficients are assumed to be space dependent i.e. functions of in nonhomogeneous case and stressstrain are harmonic functions of time The expression for relaxation time for five parameter viscoelastic model is obtained by using constitutive equation. The dispersion equation is obtained by using Ray techniques. The model is justified with the help of cyclic loading for maxima or minima.
1

426
440


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


K
Kaur
Faculty of Science, BMSCTE, Muktsar
Faculty of Science, BMSCTE, Muktsar
Iran


K.C
Gupta
Faculty of Science, BMSCTE, Muktsar
Faculty of Science, BMSCTE, Muktsar
Iran
Shear waves
Viscoelastic media
Asymptotic method
dynamic loading
[[1] Alfrey T., 1944, Nonhomogeneous stress in viscoelastic media, Quarterly of Applied Mathematics 2:113.##[2] Barberan J., Herrera J., 1966, Uniqueness theorems and speed of propagation of signals in viscoelastic materials, Archive for Rational Mechanics and Analysis 23: 173.##[3] Achenbach J. D., Reddy D. P., 1967, Note on the wavepropagation in linear viscoelastic media, ZAMP 18: 141143.##[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):57–62.##[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 (ASME) 36: 908909.##[7] AbdAlla A. M., Ahmed S. M., 1996, Rayleigh waves in an orthotropic thermoelastic medium under gravity field and initial stress, Earth Moon and Planets 75: 185197.##[8] Batra R. C., 1998, Linear constitutive relations in isotropic finite elasticity, Journal of Elasticity 51: 243245.##[9] Murayama S., Shibata T., 1961, Rheological properties of clays, 5th International Conference of Soil Mechanics and Foundation Engineering 1: 269273.##[10] 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 273 – 303.##[11] Anagnostopoulos S.A., 1988, Pounding of buildings in series during earthquakes, Earthquake Engineering & Structural Dynamics 16(3): 443456.##[12] Jankowski R., Wilde K., Fujino Y., 1998, Pounding of superstructure segments in isolated elevated bridge during earthquakes, Earthquake Engineering & Structural Dynamics 27:487502.##[13] Muthukumar S., Desroches R., 2006, A Hertz contact model with nonlinear damping for pounding simulation, Earthquake Engineering & Structural Dynamics 35: 811828.##[14] Westermo B.D., 1989, The dynamics of interstructural connection to prevent pounding, Earthquake Engineering & Structural Dynamics 18: 687–699.##[15] Jankowski R., 2005, Nonlinear viscoelastic modelling of earthquakeinduced structural pounding, Earthquake Engineering & Structural Dynamics 34(6): 595611.##[16] Lakes R.S., 1998, Viscoelastic solids, CRC Press, New York.## ##]