Nonlinear Vibration of Function Graded Magneto-electro-elastic Microplates using Nonlocal Stress Theory
Main Article Content
Abstract
This work presents an analysis of nonlinear vibration in Function Graded Magneto-Electro-Elastic (FG-MEE) plates subjected to mechanical, electrical, and magnetic loads using the nonlocal stress theory approach. In this study two types of MEE plates, namely BaTiO3 and CoFe2O4 were considered. The basic equations are derived using classical plate theory with nonlocal stress theory and are solved using the Galerkin method and Runge-Kutta method. We investigated the effects of nonlocal parameters, materials, and geometrical characteristics on the natural frequencies and nonlinear vibration of the FG-MEE microplates.
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Keywords:
FGM; MEE; Vibration; Nonlocal stress theory.
References
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[4] C. Hsu, C. Hwu, Coupled Stretching-Bending Boundary Element Analysis for Unsymmetric Magneto-Electro-Elastic Laminates with Multiple Holes, Cracks and Inclusions, Engineering Analysis with Boundary Elements, Vol. 139, 2022, pp. 137-151, https://doi.org/10.1016/j.enganabound.2022.03.018.
[5] H. Kuo, Y. Wang, Wave Motion of Magneto-Electro-Elastic Laminated Plates Withmembrane-Type Interfacial Imperfections, Composite Structures, Vol. 293, 2022, pp. 115661, https://doi.org/10.1016/j.compstruct.2022.115661.
[6] X. Zhang, Q. Xu, X. Zhao, Y. Li, J. Yang, Nonlinear Analyses of Magneto-Electro-Elastic Laminated Beams in Thermal Environments, Composite Structures, Vol. 234, 2020, pp. 111524, https://doi.org/10.1016/j.compstruct.2019.111524.
[7] M. Vinyas, K. Sunny, D. Harursampath, N. T. Trung, M. Loja, Influence of Interphase on the Multi-Physics Coupled Frequency of Three-Phase Smart Magneto-Electro-Elastic Composite Plates, Composite Structures,
Vol. 226, 2019, pp. 111254, https://doi.org/10.1016/j.compstruct.2019.111254.
[8] L. Zhou, M. Li, Y. Cai, H. Zhao, E. Zhao, The Multi-Physic Cell-Based Smoothed Finite Element Method for Dynamic Characterization of Magneto-Electro-Elastic Structuresu Thermal Conditions, Composite Structures,
Vol. 240, 2020, pp. 112045, https://doi.org/10.1016/j.compstruct.2020.112045.
[9] J. Chen, H. Chen, E. Pan, P. R. Heyliger, Modal Analysis of Magneto-Electro-Elastic Plates using the State-Vector Approach, Journal of Sound and Vibration, Vol. 304, 2007, pp. 722-34, https://doi.org/10.1016/j.jsv.2007.03.021.
[10] N. D. Dat, T. Q. Quan, M. Vinyas, N. D. Duc, Analytical Solutions for Nonlinear Magneto-Electro-Elastic Vibration of Smart Sandwich Plate with Carbon Nanotube Reinforced Nanocomposite Core in Hygrothermal Environment, International Journal of Mechanical Sciences, Vol. 186, 2020, pp. 105906, https://doi.org/10.1016/j.ijmecsci.2020.105906.
[11] N. D. Dat, T. Q. Quan, N. D. Duc, Vibration Analysis of Auxetic Laminated Plate with Magneto-Electro-Elastic Face Sheets Subjected to Blast Loading, Composite Structures, Vol. 280, 2022, pp. 114925, http://dx.doi.org/10.1016/j.compstruct.2021.114925.
[12] H. T. Liu, Y. H. Qie, Y. G. Zhou, Investigation of Non-Local Theory Solution to A Three-Dimensional Rectangular Permeable Crack in Magneto-Electro-Elastic Materials, International Journal of Mechanical Sciences, Vol. 134, 2017, pp. 460-78, https://doi.org/10.1016/j.ijmecsci.2017.10.039.
[13] L. L. Zhang, J. X. Liu, X. Q. Fang, G. Q. Nie, Effects of Surface Piezoelectricity and Nonlocal Scale on Wave Propagation in Piezoelectric Nanoplates, European Journal of Mechanics A/Solids, Vol. 46, 2014, pp. 22-29, http://dx.doi.org/10.1016/j.euromechsol.2014.01.005.
[14] J. Y. Chen, J. H. Guo, E. N. Pan, Reflection and Transmission of Plane Wave in Multilayered Nonlocal Magneto-Electro-Elastic Plates Immersed in Liquid, Composite Structures, Vol. 162, 2017, pp. 401-410, http://dx.doi.org/10.1016/j.compstruct.2016.11.004.
[15] S. Sahmani, M. M. Aghdam, T. Rabczuk, Nonlocal Strain Gradient Plate Model for Nonlinear Large-Amplitude Vibrations of Functionally Graded Porous Micro/Nano-Plates Reinforced with GPLs, Composite structures,
Vol. 198, 2018, pp. 51-62, https://doi.org/10.1016/j.compstruct.2018.05.031.
[16] G. Monaco, N. Fantuzzi, F. Fabbrocino, R. Luciano, Critical Temperatures for Vibrations and Buckling of Magneto-Electro-Elastic Nonlocal Strain Gradient Plates, Nanomaterials, Vol. 11, No. 1, 2021, pp. 1-18, https://doi.org/10.3390/nano11010087.
[17] F. Ramirez, P. Heyliger, E. Pan, Discrete Layer Solution to Free Vibrations of Functionally Graded Magneto-Electro-Elastic Plates, Mechanics of Advanced Materials and Structures, Vol. 13, No. 3, 2006, pp. 249-66, http://dx.doi.org/10.1080/15376490600582750.
[18] E. Ismail, O. Ramazan, Thermal Vibration and Buckling of Magneto-Electro-Elastic Functionally Graded Porous Nanoplates using Nonlocal Strain Gradient Elasticity, Composite structures, Vol. 296, 2022, pp. 115878, https://doi.org/10.1016/j.compstruct.2022.115878.