Wave propagation analysis of porous functionally graded piezoelectric nanoplates with a visco-Pasternak foundation

doi:10.1007/s10483-023-2953-7

Abstract

Abstract: This study investigates the size-dependent wave propagation behaviors under the thermoelectric loads of porous functionally graded piezoelectric (FGP) nanoplates deposited in a viscoelastic foundation. It is assumed that (i) the material parameters of the nanoplates obey a power-law variation in thickness and (ii) the uniform porosity exists in the nanoplates. The combined effects of viscoelasticity and shear deformation are considered by using the Kelvin-Voigt viscoelastic model and the refined higher-order shear deformation theory. The scale effects of the nanoplates are captured by employing nonlocal strain gradient theory (NSGT). The motion equations are calculated in accordance with Hamilton’s principle. Finally, the dispersion characteristics of the nanoplates are numerically determined by using a harmonic solution. The results indicate that the nonlocal parameters (NLPs) and length scale parameters (LSPs) have exactly the opposite effects on the wave frequency. In addition, it is found that the effect of porosity volume fractions (PVFs) on the wave frequency depends on the gradient indices and damping coefficients. When these two values are small, the wave frequency increases with the volume fraction. By contrast, at larger gradient index and damping coefficient values, the wave frequency decreases as the volume fraction increases.

Key words: scale effect, functionally graded material (FGM), dispersion characteristic, piezoelectric nanoplate, viscoelastic foundation

2010 MSC Number:

74K10

Zhaonian LI, Juan LIU, Biao HU, Yuxing WANG, Huoming SHEN. Wave propagation analysis of porous functionally graded piezoelectric nanoplates with a visco-Pasternak foundation. Applied Mathematics and Mechanics (English Edition), 2023, 44(1): 35-52.

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References

[1] MARUANI, J., BRUANT, I., PABLO, F., and GALLIMARD, L. Active vibration control of a smart functionally graded piezoelectric material plate using an adaptive fuzzy controller strategy. Journal of Intelligent Material Systems and Structures, 30, 2065–2078(2019)
[2] RAHIMI, G. H., AREFI, M., and KHOSHGOFTAR, M. J. Application and analysis of functionally graded piezoelectrical rotating cylinder as mechanical sensor subjected to pressure and thermal loads. Applied Mathematics and Mechanics (English Edition), 32, 997–1008(2011) https://doi.org/10.1007/s10483-011-1475-6
[3] BIRMAN, V. Modeling and analysis of functionally graded materials and structures. Applied Mechanics Reviews, 60, 195–216(2007)
[4] EBRAHIMI, F. and BARATI, M. R. Dynamic modeling of preloaded size-dependent nanocrystalline nano-structures. Applied Mathematics and Mechanics (English Edition), 38, 1753–1772(2017) https://doi.org/10.1007/s10483-017-2291-8
[5] ALIZADA, A. N. and SOFIYEV, A. H. Modified Young’s moduli of nano-materials taking into account the scale effects and vacancies. Meccanica, 46, 915–920(2010)
[6] YANG, F., CHONG, A., LAM, D., and TONG, P. Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures, 39, 2731–2743(2002)
[7] MINDLIN, R. D. Second gradient of strain and surface-tension in linear elasticity. International Journal of Solids and Structures, 1, 417–438(1965)
[8] MA, L. H., KE, L. L., WANG, Y. Z., and WANG, Y. S. Wave propagation analysis of piezoelectric nanoplates based on the nonlocal theory. International Journal of Structural Stability and Dynamics, 18, 1850060(2018)
[9] FLECK, N. A. and HUTCHINSON, J. W. A phenomenological theory for strain gradient effects in plasticity. Journal of the Mechanics Physics of Solids, 41, 1825–1857(1993)
[10] LAM, D. C. C., YANG, F., CHONG, A. C. M., WANG, J., and TONG, P. Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids, 51, 1477–1508(2003)
[11] LIM, C. W., ZHANG, G., and REDDY, J. N. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. Journal of the Mechanics and Physics of Solids, 78, 298–313(2015)
[12] LI, L., HU, Y., and LING, L. Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory. Physica E: Lowdimensional Systems and Nanostructures, 75, 118–124(2016)
[13] LI, L., TANG, H., and HU, Y. The effect of thickness on the mechanics of nanobeams. International Journal of Engineering Science, 123, 81–91(2018)
[14] SAHMANI, S. and AGHDAM, M. M. Nonlinear vibrations of pre- and post-buckled lipid supramolecular micro/nano-tubules via nonlocal strain gradient elasticity theory. Journal of Biomechanics, 65, 49–60(2017)
[15] FARAJPOUR, A., YAZDI, M. R. H., RASTGOO, A., and MOHAMMADI, M. A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment. Acta Mechanica, 227, 1849–1867(2016)
[16] EBRAHIMI, F., BARATI, M. R., and DABBAGH, A. A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates. International Journal of Engineering Science, 107, 169–182(2016)
[17] EBRAHIMI, F. and DABBAGH, A. On flexural wave propagation responses of smart FG magnetoelectro-elastic nanoplates via nonlocal strain gradient theory. Composite Structures, 162, 281–293(2017)
[18] EBRAHIMI, F. and DABBAGH, A. Wave propagation analysis of embedded nanoplates based on a nonlocal strain gradient-based surface piezoelectricity theory. European Physical Journal Plus, 132, 449(2017)
[19] ABAZID, M. A. The nonlocal strain gradient theory for hygrothermo-electromagnetic effects on buckling, vibration and wave propagation in piezoelectromagnetic nanoplates. International Journal of Applied Mechanics, 11, 1950067(2019)
[20] SUN, L. H. Current research and development trend of functionally gradient materials. Advances in Material Science, 3, 10–13(2019)
[21] JADHAV, P. A. and BAJORIA, K. M. Free and forced vibration control of piezoelectric FGM plate subjected to electro-mechanical loading. Smart Materials and Structures, 22, 065021(2013)
[22] JANDAGHIAN, A. A. and RAHMANI, O. Vibration analysis of functionally graded piezoelectric nanoscale plates by nonlocal elasticity theory: an analytical solution. Superlattices and Microstructures, 100, 57–75(2016)
[23] JANDAGHIAN, A. A. and RAHMANI, O. Size-dependent free vibration analysis of functionally graded piezoelectric plate subjected to thermo-electro-mechanical loading. Journal of Intelligent Material Systems and Structures, 28, 3039–3053(2017)
[24] SHARIFI, Z., KHORDAD, R., GHARAATI, A., and FOROZANI, G. An analytical study of vibration in functionally graded piezoelectric nanoplates: nonlocal strain gradient theory. Applied Mathematics and Mechanics (English Edition), 40, 1723–1740(2019) https://doi.org/10.1007/s10483-019-2545-8
[25] DEHSARAJI, M. L., AREFI, M., and LOGHMAN, A. Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect. Defence Technology, 17, 119–134(2021)
[26] LI, H. N., LI, C., SHEN, J. P., and YAO, L. Q. Vibration analysis of rotating functionally graded piezoelectric nanobeams based on the nonlocal elasticity theory. Journal of Vibration Engineering & Technologies, 9, 1155–1173(2021)
[27] JOUBANEH, E. F., MOJAHEDIN, A., KHORSHIDVAND, A. R., and JABBARI, M. Thermal buckling analysis of porous circular plate with piezoelectric sensor-actuator layers under uniform thermal load. Journal of Sandwich Structures & Materials, 17, 3–25(2015)
[28] BARATI, M. R., SHAHVERDI, H., and ZENKOUR, A. M. Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory. Mechanics of Advanced Materials and Structures, 24, 987–998(2016)
[29] BARATI, M. R. and ZENKOUR, A. M. Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions. Journal of Vibration and Control, 24, 1910–1926(2016)
[30] WANG, Y. Q. and ZU, J. W. Porosity-dependent nonlinear forced vibration analysis of functionally graded piezoelectric smart material plates. Smart Materials and Structures, 26, 105014(2017)
[31] NGUYEN, L. B., THAI, C. H., ZENKOUR, A. M., and NGUYEN-XUAN, H. An isogeometric Bézier finite element method for vibration analysis of functionally graded piezoelectric material porous plates. International Journal of Mechanical Sciences, 157, 165–183(2019)
[32] EBRAHIMI, F. and BARATI, M. R. Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory. Composite Structures, 159, 433–444(2017)
[33] EBRAHIMI, F. and BARATI, M. R. Damping vibration analysis of smart piezoelectric polymeric nanoplates on viscoelastic substrate based on nonlocal strain gradient theory. Smart Materials and Structures, 26, 065018(2017)
[34] AREFI, M. and ZENKOUR, A. M. Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin-Voigt viscoelastic nanoplate and two piezoelectric layers. Acta Mechanica, 228, 475–493(2016)
[35] LIU, H., LIU, H., and YANG, J. L. Vibration of FG magneto-electro-viscoelastic porous nanobeams on visco-Pasternak foundation. Composites Part B: Engineering, 155, 244–256(2018)
[36] ZENKOUR, A. M. and SOBHY, M. Nonlocal piezo-hygrothermal analysis for vibration characteristics of a piezoelectric Kelvin-Voigt viscoelastic nanoplate embedded in a viscoelastic medium. Acta Mechanica, 229, 3–19(2017)
[37] ARANI, A. G., JAMALI, M., GHORBANPOUR-ARANI, A. H., KOLAHCHI, R., and MOSAYYEBI, M. Electro-magneto wave propagation analysis of viscoelastic sandwich nanoplates considering surface effects. Journal of Mechanical Engineering Science, 231, 387–403(2016)