Vibration and buckling analysis of nanoplates resting on variable elastic foundations
Email:
doandv@lqdtu.edu.vn
Keywords:
natural oscillation, buckling, elastic foundation, finite element method
Abstract
Nanostructures are widely used in electronic circuits, sensors, and military equipment. Therefore, analyzing mechanical response of nanoscale structures is a scientific foundation to help engineers in designing and manufacturing these structures in technical practice. This paper investigates the natural oscillation response and buckling of a nanoplate supported by a modified elastic foundation, utilizing a four-node plate element where each node possesses six degrees of freedom. The equilibrium equation for the nanoplate is derived using the third-order shear deformation theory, and the finite element method has been employed to solve this equation and determine the natural oscillation frequency and critical buckling load of the nanoplate. In this paper, we have established the reliability and convergence of the calculation theory by comparing analytical results with those obtained from the published finite element method. Consequently, we examined the impact of various material parameters, geometry, boundary conditions, and elastic foundation on the frequency response, natural oscillation modes, and critical buckling load of the nanoplateReferences
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[3]. N. C. Tho, N. T. Thanh, T. D. Tho, P. V. Minh, L. K. Hoa, Modelling of the flexoelectric effect on rotating nanobeams with geometrical imperfection, J Braz. Soc. Mech. Sci. Eng., 43 (2021) 510. https://doi.org/10.1007/s40430-021-03189-w
[4]. T.V. Ke, D.V. Thom, N.T. Dung, N.V. Chinh, P.V. Minh, Galerkin-Vlasov approach for bending analysis of flexoelectric doubly-curved sandwich nanoshells with piezoelectric/FGP/piezoelectric layers using the nonlocal strain theory, Acta Mech. Sin, 41 (2025) 123543. https://doi.org/10.1007/s10409-024-23543-x
[5]. T.V. Ke, P.V. Minh, N.T. Dung, L.M. Thai, D.V. Thom, Flexoelectric effect on bending and free vibration behaviors of piezoelectric sandwich FGP nanoplates via nonlocal strain gradient theory, J. Vib. Eng. Technol., 12 (2024) 6567-6596. https://doi.org/10.1007/s42417-023-01270-3
[6]. N. Zhang, S. Zheng, D. Chen, Size-dependent static bending, free vibration and buckling analysis of curved flexomagnetic nanobeams, Meccanica, 57 (2022) 1505–1518. https://doi.org/10.1007/s11012-022-01506-8
[7]. D. M. Tien, D. V. Thom, P.V. Minh, N.C. Tho, T.N. Doan, D.N. Mai, The application of the nonlocal theory and various shear strain theories for bending and free vibration analysis of organic nanoplates, Mech. Based Des. Struct. Mach., 52 (2024) 588-610. https://doi.org/10.1080/15397734.2023.2186893
[8]. R. P. Shimpi, Refined plate theory and its variants, AIAA J, 40 (2002) 137–146. https://doi.org/10.2514/3.15006
[9]. A. S. Sayyad, Y. M. Ghugal, Effects of nonlinear hygrothermomechanical loading on bending of FGM rectangular plates resting on two-parameter elastic foundation using four-unknown plate theory, J. Ther. Stress, 42 (2019) 213–232. https://doi.org/10.1080/01495739.2018.1469962
[10]. D.M. Tien, D.V. Thom, P.V. Minh, N.C. Tho, T.N. Doan, D.N. Mai, The application of the nonlocal theory and various shear strain theories for bending and free vibration analysis of organic nanoplates, Mech. Based Des. Struct. Mach, (2023). https://doi.org/10.1080/15397734.2023.2186893
[11]. R. Aghababaei, J. N. Reddy, Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates, J. Sound Vib, 326 (2009) 277–289. https://doi/10.1016/j.jsv.2009.04.044
[12]. H. Akhavan, S.H. Hashemi, H.R.D. Taher, A. Alibeigloo, S.Vahabi, Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part I: Buckling analysis, Comp. Mat. Sci, 44 (2009) 968–978.
[13]. K.Y.Lam, C. M. Wang, X.Q He, Canonical exact solutions for Levy-plates on two-parameter foundation using Green's functions, Eng. Structures, 22 (2000). https://doi.org/10.1016/S0141-0296(98)00116-3.
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Received
19/10/2024
Revised
16/11/2024
Accepted
10/12/2024
Published
15/12/2024
Type
Research Article
How to Cite
Thân Văn, T., Trương Thị Hương, H., & Đào Văn, Đoan. (1734195600). Vibration and buckling analysis of nanoplates resting on variable elastic foundations . Transport and Communications Science Journal, 75(9), 2238-2251. https://doi.org/10.47869/tcsj.75.9.1
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