Effects of Couple-stress Resultants on Thermo-electro-mechanical Behavior of Vibrating Piezoelectric Micro-plates Resting on Orthotropic Foundation

[1] C.K. Lee, Theory of laminated piezoelectric plates for the design of distributed sensors/actuators, Part I: Governing equations and reciprocal relationships, J. Acoust. Soc. Am., 87(3) (1990) 1144-1158.
[2] P.J.C. Branco, J.A. Dente, On the electromechanics of a piezoelectric transducer using a bimorph cantilever undergoing asymmetric sensing and actuation, Smart Mater. Struct., 13(4) (2004) 631-642.
[3] W.M. Zhang, G. Meng, D.I. Chen, Stability, Nonlinearity and reliability of electrostatically actuated MEMS devices, Sensors, 7(5) (2007) 760-796.
[4] J.M. Dietl, A.M. Wickenheiser, E. Garcia, A Timoshenko beam model for cantilevered pie-zoelectric energy harvesters, Smart Mater. Struct., 19(5) (2010) 055018.
[5] A.C. Eringen, D.G.B. Edelen, On nonlocal elasticity, Int. J. Eng. Sci., 10(3) (1972) 233-248.
[6] A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislo-cation and surface waves, J. Appl. phys., 54(9) (1983) 4703-4710.
[7] A.C. Eringen, Nonlocal Continuum Field Theories, Springer-Verlog New York Publisher, (2002).
[8] E.C. Aifantis, Strain gradient interpretation of size effects, Int. J. Fract., 95 (1/4) (1999) 299-314.
[9] R.A. Toupin, Elastic materials with couplestresses, Archi. Rational Mech. Anal., 11(1) (1962) 385-414.
[10] K. Khorshidi, T. Asgari, A. Fallah, Free vibrations analysis of functionally graded rectangular nanoplates based on nonlocal exponential shear deformation theory, Mech. Advanced Compos. Struct., 2(2) (2015) 79-93.
[11] C. Liu, L.L. Ke, Y.S. Wang, J. Yang, S. Kitipornchai, Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory, Compos. Struct., 106 (2013) 167-174.
[12] Y.S. Li, Z.Y. Cai, S.Y. Shi, Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory, Compos. Struct., 111 (2014) 522-529.
[13] N.A. Fleck, J.W. Hutchinson, A phenomenological theory for strain gradient effects in plasticity, J. Mech. Phys. Solids, 41(12) (1993) 1825-1857.
[14] R. Ansari, R. Gholami, S. Sahmani, Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory, Compos. Struct., 94(1) (2011) 221-228.
[15] R.D. Mindlin, H.F. Tiersten, Effects of couplestresses in linear elasticity, Arch. Rational Mech. Anal., 11(1) (1962) 415-448.
[16] F. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct., 39(10) (2002) 2731-2743.
[17] J. Lei, Y. He, B. Zhang, D. Liu, L. Shen, S. Guo, A size-dependent FG micro-plate model incorporating higher-order shear and normal deformation effects based on a modified couple stress theory, Int. J. Mech. Sci., 104 (2015) 8-23.
[18] M.H. Shojaeefard, H.S. Googarchin, M. Ghadiri, M. Mahinzare, Micro temperature-dependent FG porous plate: free vibration and thermal buckling analysis using modified couple stress theory with CPT and FSDT, Appl. Math. Modell., 50 (2017) 633-655.
[19] A. Farzam, B. Hassani, Thermal and mechanical buckling analysis of FG carbon nanotube reinforced composite plates using modified couple stress theory and isogeometric approach, Compos. Struct., 206 (2018) 774-790.
[20] J. Kim, K.K. Źur, J.N. Reddy, Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates, Compos. Struct., 209 (2019) 879-888.
[21] M. Aydogdu, Comparison of various shear deformation theories for bending, buckling, and vibration of rectangular symmetric cross-ply plate with simply supported edges, J. Compos. Mater., 40(23) (2006) 2143-2155.
[22] K.P. Soldatos, A transverse shear deformation theory for homogeneous monoclinic plates, Acta Mech., 94(3-4) (1992) 195-220.
[23] V. Panc, Theories of Elastic Plates, Springer Netherlands, (1975).
[24] S. Hosseini-Hashemi, K. Khorshidi, M. Amabili, Exact solution for linear buckling of rec-tangular Mindlin plates, J. Sound Vib., 315(1-2) (2008) 318-342.
[25] A. Hassani, M. Gholami, Analytical and numerical bending solutions for thermoelastic functionally graded rotating disks with nonuniform thickness based on mindlin’s theory, J. Stress Anal., 2(1) (2017) 35-49.
[26] H.T. Thai, D.H. Choi, A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates, Compos. Struct., 101 (2013) 332-340.
[27] K. Khorshidi, A. Fallah, Buckling analysis of functionally graded rectangular nano-plate based on nonlocal exponential shear deformation theory, Int. J. Mech. Sci., 113 (2016) 94-104.
[28] K. Khorshidi, A. Fallah, Effect of exponential stress resultant on buckling response of functionally graded rectangular plates, J. Stress Anal., 2(1) (2017) 27-33.
[29] P. Shi, C. Dong, F. Sun, W. Liu, Q. Hu, A new higher order shear deformation theory for static, vibration and buckling responses of laminated plates with the isogeometric analysis, Compos. Struct., 204 (2018) 342-358.
[30] H. Tanzadeh, H. Amoushahi, Buckling and free vibration analysis of piezoelectric laminated composite plates using various plate deformation theories, European J. Mech. Solids, 74 (2019) 242-256.
[31] P.L. Pasternak, On a New Method of an Elastic Foundation by Means of Two Foundation Constants, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstuvei Arkhitekture, (1954).
[32] A. Kutlu, M.H. Omurtag, Large deflection bending analysis of elliptic plates on orthotropic elastic foundation with mixed finite element method, Int. J. Mech. Sci., 65(1) (2012) 64-74.
[33] A.S. Sayyad, Y.M. Ghugal, Bending and free vibration analysis of thick isotropic plates by using exponential shear deformation theory, Appl. Comput. Mech., 6(1) (2012) 65-82.
[34] Y.M. Ghugal, A.S. Sayyad, Free vibration of thick orthotropic plates using trigonometric shear deformation theory, Lat. Am. J. Solids Struct., 8(3) (2011) 229-243.
[35] M. Karama, K.S. Afaq, S. Mistou, A new theory for laminated composite plates, Proceedings of the Institution of Mechanical Engineers, Part L: J. Mater. Des. Appl., 223(2) (2009) 53-62.
[36] E. Reissner, On transverse bending of plates, Including the effect of transverse shear deformation, Int. J. Solids Struct., 11(5) (1974) 567-573.
[37] L.L. Ke, C. Liu, Y.S. Wang, Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions, Physica E, 66 (2015) 93-106.
[38] K. Khorshidi, M. Karimi, Analytical modeling for vibrating piezoelectric nanoplates in interaction with inviscid fluid using various modified plate theories, Ocean Eng., 181 (2019) 267-280.
[39] M. Bahreman, H. Darijani, A.B. Fard, The sizedependent analysis of microplates via a newly developed shear deformation theory, Acta Mech., 230(1) (2019) 49-65.