Forced vibration analysis of variable thickness microplate
Email:
damvusonquyen@gmail.com
Từ khóa:
Dynamic response, variable thickness, functionally graded material, microplate, isogeometric analysis.
Tóm tắt
Nowadays, with the development of material science, nano- or microstructures are increasingly of interest in research because of their applications in micro-electromechanical technology, semiconductor chips, or sensors. In this study, the isogeometric approach (IGA) method combining the Mindlin plate hypothesis and the modified couple stress hypothesis is used to analyse the forced vibration of a micro-plate with variable thickness made of materials with variable mechanical characteristics subjected to the effect of different types of dynamic loads. The thickness change of the microplate is considered in two directions with a nonlinear law, while the material characteristics vary with the plate thickness. The model's and method's accuracy are validated by comparing it with results from published studies. Then, the paper surveys the impact of geometric and material coefficient on the transient responses of FG microplate. The research results provide important bases in the design and optimization calculation of micro-electromechanical systems serving the chip and sensor industries.Tài liệu tham khảo
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[2]. A. Witvrouw, A. Mehta, The Use of Functionally Graded Poly-SiGe Layers for MEMS Applications, Materials Science Forum, 492–493 (2005) 255–260. https://doi.org/10.4028/www.scientific.net/msf.492-493.255
[3]. Z. Lee, C. Ophus, L.M. Fischer, N. Nelson-Fitzpatrick, K.L. Westra, S. Evoy, V. Radmilovic, U. Dahmen, D. Mitlin, Metallic NEMS components fabricated from nanocomposite Al-Mo films, Nanotechnology, 17 (2006) 3063–3070. https://doi.org/10.1088/0957-4484/17/12/042
[4]. N.A. Fleck, G.M. Muller, M.F. Ashby, J.W. Hutchinson, Strain gradient plasticity: Theory and experiment, Acta Metallurgica Et Materialia, 42 (1994) 475–487. https://doi.org/10.1016/0956-7151(94)90502-9
[5] A.C. Eringen, Nonlocal polar elastic continua, International Journal of Engineering Science, 10 (1972) 1–16. https://doi.org/10.1016/0020-7225(72)90070-5
[6]. D.C.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, 51 (2003) 1477–1508. https://doi.org/10.1016/S0022-5096(03)00053-X
[7]. Tiersten H.F., R.D. Mindlin, Effects of couple-stresses in linear elasticity, Wear 6 (1963) 243. https://doi.org/10.1016/0043-1648(63)90083-8
[8]. F. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39 (2002) 2731–2743. https://doi.org/10.1016/S0020-7683(02)00152-X
[9]. Q.H. Pham, P.C. Nguyen, V.K. Tran, Effects of hygro-thermal environment on dynamic responses of variable thickness functionally graded porous microplates, Steel and Composite Structures, 50 (2024) 563–581. https://doi.org/10.12989/scs.2024.50.5.563
[10]. D.T.M. Cuong, T. V. Do, N.V. Dung, Effect of novel elastic foundations on the thermal buckling behavior of organic nanobeams, Mechanics Based Design of Structures and Machines, 54 (2026) 2556241. https://doi.org/10.1080/15397734.2025.2556241
[11]. T.D. Van, M.C. Van, V.M. Phung, V.N.D. Anh, Mechanical responses of nanoplates resting on viscoelastic foundations in multi-physical environments, European Journal of Mechanics - A/Solids, 106 (2024) 105309. https://doi.org/10.1016/j.euromechsol.2024.105309
[12] T.H.N. Thi, V.K. Tran, V.K. Trai, L. Hoai, An IGA approach for linear and nonlinear free vibration of tri-directional functionally graded porous microplate in nonlinear high-temperature environment with nonlinear variable thickness, Thin-Walled Structures, 217 (2025) 113784. https://doi.org/10.1016/j.tws.2025.113784.
[13]. V.N. Anh, T. Van Ke, N.T.T. Huong, N.T. Hue, P.H. Tu, Nonlinear Free Vibrations of Functionally Graded Graphene Origami-Enabled Auxetic Metamaterial Skew-microplates with Variable Thickness Using Isogeometric Analysis, Defence Technology, 57 (2025) 85-108. https://doi.org/10.1016/j.dt.2025.09.024.
[14] J. Lawongkerd, P. Roodgar Saffari, T. Jearsiripongkul, C. Thongchom, S.O. Ismail, P.R. Saffari, S. Keawsawasvong, Vibration characteristics of multilayer functionally graded microplates with variable thickness reinforced by graphene platelets resting on the viscoelastic medium under thermal effects, International Journal of Thermofluids, 22 (2024) 100611. https://doi.org/10.1016/j.ijft.2024.100611.
[15]. T. Nguyen Chi, H. Vu Van, H. Le Hong, H. Nguyen Huu, T. Pham Duc, T. Dao Minh, Study of static bending of functionally graded beams using analytical method, Transport and Communications Science Journal, 76 (2025) 928–938. https://doi.org/10.47869/tcsj.76.7.1.
[16]. N.T. Dung, L.M. Thai, T. Van Ke, T.T.H. Huyen, P. Van Minh, Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory, Comptes Rendus: Mécanique, 350 (2022) 121–141. https://doi.org/10.5802/crmeca.105.
[17]. Y.S. Li, E. Pan, Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory, International Journal of Engineering Science, 97 (2015) 40–59. https://doi.org/10.1016/j.ijengsci.2015.08.009.
[18]. P. Van Minh, T. Van Ke, A Comprehensive Study on Mechanical Responses of Non-uniform Thickness Piezoelectric Nanoplates Taking into Account the Flexoelectric Effect, Arabian Journal for Science and Engineering, 48 (2023) 11457–11482. https://doi.org/10.1007/s13369-022-07362-8.
[19]. H.M. Ma, X.L. Gao, J.N. Reddy, A non-classical Mindlin plate model based on a modified couple stress theory, Acta Mechanica, 220 (2011) 217–235. https://doi.org/10.1007/s00707-011-0480-4.
[20]. Q.H. Pham, P.C. Nguyen, V.K. Tran, Q.X. Lieu, T.T. Tran, Modified nonlocal couple stress isogeometric approach for bending and free vibration analysis of functionally graded nanoplates, Engineering with Computers, 39 (2023) 993–1018. https://doi.org/10.1007/s00366-022-01726-2.
[21]. T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, 194 (2005) 4135–4195. https://doi.org/10.1016/j.cma.2004.10.008.
[22]. P.H. Tu, T. Van Ke, V.K. Trai, L. Hoai, An isogeometric analysis approach for dynamic response of doubly-curved magneto electro elastic composite shallow shell subjected to blast loading, Defence Technology, 41 (2024) 159–180. https://doi.org/10.1016/j.dt.2024.06.005.
[23]. M. Song, S. Kitipornchai, J. Yang, Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets, Composite Structures, 159 (2017) 579–588. https://doi.org/10.1016/j.compstruct.2016.09.070.
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Nhận bài
29/11/2025
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30/12/2025
Chấp nhận đăng
14/01/2026
Xuất bản
15/05/2026
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Kiểu trích dẫn
Dam Vu Son, Q. (1778778000). Forced vibration analysis of variable thickness microplate. Tạp Chí Khoa Học Giao Thông Vận Tải, 77(4), 594-606. https://doi.org/10.47869/tcsj.77.4.19
