تاثیر دقت پارامتر مقیاس طول بر فرکانس های طبیعی میکرو ورق مستطیلی متخلخل مرتعش

[1] A.C. Eringen, Nonlocal polar elastic continua, International journal of engineering science, 10(1) (1972) 1-16.

[2] K. Khorshidi, A. Fallah, A. Siahpush, Free vibrations analaysis of functionally graded composite rectangular na-noplate based on nonlocal exponential shear deformation theory in thermal environment,  (2017).

[3] K. Khorshidi, A. Siahpush, A. Fallah, Electro-Mechanical free vibrations analysis of composite rectangular piezoelectric nanoplate using modified shear deformation theories, Journal of Science and Technology of Composites, 4(2) (2017) 151-160.

[4] D.C. Lam, F. Yang, A. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, 51(8) (2003) 1477-1508.

[5] R.A. Toupin, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, 11(1) (1962) 385-414.

[6] R. Mindlin, H. Tiersten, Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and analysis, 11(1) (1962) 415-448.

[7] F. Yang, A. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39(10) (2002) 2731-2743.

[8] S. Park, X. Gao, Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering, 16(11) (2006) 2355.

[9] M.A. Khorshidi, The material length scale parameter used in couple stress theories is not a material constant, International Journal of Engineering Science, 133 (2018) 15-25.

[10] Z. Li, Y. He, J. Lei, S. Guo, D. Liu, L. Wang, A standard experimental method for determining the material length scale based on modified couple stress theory, International Journal of Mechanical Sciences, 141 (2018) 198-205.

[11] M. Kahrobaiyan, M. Asghari, M. Ahmadian, Strain gradient beam element, Finite Elements in Analysis and Design, 68 (2013) 63-75.

[12] C. Liebold, W.H. Müller, Comparison of gradient elasticity models for the bending of micromaterials, Computational Materials Science, 116 (2016) 52-61.

[13] L. He, J. Lou, E. Zhang, Y. Wang, Y. Bai, A size-dependent four variable refined plate model for functionally graded microplates based on modified couple stress theory, Composite Structures, 130 (2015) 107-115.

[14] J. Reddy, J. Kim, A nonlinear modified couple stress-based third-order theory of functionally graded plates, Composite Structures, 94(3) (2012) 1128-1143.

[15] H.-T. Thai, S.-E. Kim, A size-dependent functionally graded Reddy plate model based on a modified couple stress theory, Composites Part B: Engineering, 45(1) (2013) 1636-1645.

[16] M. Şimşek, J. Reddy, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory, International Journal of Engineering Science, 64 (2013) 37-53.

[17] A. Bakhsheshy, K. Khorshidi, Free vibration of functionally graded rectangular nanoplates in thermal environment based on the modified couple stress theory, Modares Mechanical Engineering, 14(15) (2015) 323-330.

[18] K. Khorshidi, A. Fallah, Free vibration analysis of size-dependent, functionally graded, rectangular nano/micro-plates based on modified nonlinear couple stress shear deformation plate theories, Mechanics of Advanced Composite Structures‎, 4(2) (2017) 127-137.

[19] A. Bakhsheshy, H. Mahbadi, The effect of multidimensional temperature distribution on the vibrational characteristics of a size-dependent thick bi-directional functionally graded microplate, Noise & Vibration Worldwide,  (2019) 0957456519883265.

[20] A. Bakhsheshy, H. Mahbadi, The effect of fluid surface waves on free vibration of functionally graded microplates in interaction with bounded fluid, Ocean Engineering, 194 (2019) 106646.

[21] K. Al-Basyouni, A. Tounsi, S. Mahmoud, Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position, Composite Structures, 125 (2015) 621-630.

[22] R. Aghazadeh, E. Cigeroglu, S. Dag, Static and free vibration analyses of small-scale functionally graded beams possessing a variable length scale parameter using different beam theories, European Journal of Mechanics-A/Solids, 46 (2014) 1-11.

[23] K. Magnucki, P. Stasiewicz, Elastic buckling of a porous beam, Journal of Theoretical and Applied Mechanics, 42(4) (2004) 859-868.

[24] E. Farzaneh Joubaneh, A. Mojahedin, A. Khorshidvand, M. Jabbari, Thermal buckling analysis of porous circular plate with piezoelectric sensor-actuator layers under uniform thermal load, Journal of Sandwich Structures & Materials, 17(1) (2015) 3-25.

[25] M. Jabbari, A. Mojahedin, A. Khorshidvand, M. Eslami, Buckling analysis of a functionally graded thin circular plate made of saturated porous materials, Journal of Engineering Mechanics, 140(2) (2013) 287-295.

[26] P. Stasiewicz, K. Magnucki, Elastic buckling of a Pours beam, Theoretical and Applied Mechanics, 140 (2008) 287-298.

[27] M. Rezaei, A. Mojahedin, M.R. Eslami, Mechanical Buckling of FG Saturated Porous Rectangular Plate under Temperature Field, Iranian Journal of Mechanical Engineering Transactions of the ISME, 17(1) (2016) 61-78.

[28] A.R.Y.N. Yadegari Naeini, A. Ghasemi, Analysis of Bending and Buckling of Circular Porous Plate Using First-Order Shear Deformation Theory, Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 6(4) (2014) 55-62.

[29] Ş.D. Akbaş, Vibration and static analysis of functionally graded porous plates, Journal of Applied and Computational Mechanics, 3(3) (2017) 199-207.

[30] P. Leclaire, K.V. Horoshenkov, M.J. Swift, D.C. Hothersall, THE VIBRATIONAL RESPONSE OF A CLAMPED RECTANGULAR POROUS PLATE, Journal of Sound and Vibration, 247(1) (2001) 19-31.

[31] P. Leclaire, K. Horoshenkov, A. Cummings, Transverse vibrations of a thin rectangular porous plate saturated by a fluid, Journal of Sound and Vibration, 247(1) (2001) 1-18.

[32] E. Arshid, A. Khorshidvand, Flexural Vibrations Analysis of Saturated Porous Circular Plates Using Differential Quadrature Method, Modares Mechanical Engineering, 19(1) (2017) 78-100.

[33] A.K. Vashishth, V. Gupta, Vibrations of porous piezoelectric ceramic plates, Journal of Sound and Vibration, 325(4) (2009) 781-797.

[34] G. Altintas, Natural vibration behaviors of heterogeneous porous materials in micro scale, Journal of Vibration and Control, 20(13) (2014) 1999-2005.

[35] C. Della, D.W. Shu, Vibration of porous beams with embedded piezoelectric sensors and actuators,  (2015).

[36] I. Mechab, B. Mechab, S. Benaissa, B. Serier, B.B. Bouiadjra, Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38(8) (2016) 2193-2211.

[37] N. Shafiei, S.S. Mirjavadi, B. MohaselAfshari, S. Rabby, M. Kazemi, Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams, Computer Methods in Applied Mechanics and Engineering, 322 (2017) 615-632.

[38] M. Şimşek, M. Aydın, Size-dependent forced vibration of an imperfect functionally graded (FG) microplate with porosities subjected to a moving load using the modified couple stress theory, Composite Structures, 160 (2017) 408-421.

[39] J. Zhao, Q. Wang, X. Deng, K. Choe, R. Zhong, C. Shuai, Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions, Composites Part B: Engineering, 168 (2019) 106-120.

[40] K. Khorshidi, A. Bakhsheshy, Free Vibration analysis of Functionally Graded Rectangular plates in contact with bounded fluid, Modares Mechanical Engineering, 14(8) (2014) 165-173.

[41] L. Yin, Q. Qian, L. Wang, W. Xia, Vibration analysis of microscale plates based on modified couple stress theory, Acta Mechanica Solida Sinica, 23(5) (2010) 386-393.