Dynamic stability analysis of functionally graded plate with variable thickness
Email:
nguyenthaohoa@gmail.com
Từ khóa:
Dynamic stability, variable thickness, microplate, isogeometric method, functionally graded material, modified couple stress theory.
Tóm tắt
Understanding the dynamic stability behaviour of functionally graded microstructures is of great importance for the development of advanced micro-electromechanical systems, aerospace components, and high-performance smart structures. Accurate prediction of instability regions and vibration characteristics can significantly improve structural reliability, safety, and lightweight design efficiency in modern engineering applications. This study presents an analytical method for analysing the dynamic stability of FG variable thickness microplate based on Mindlin plate theory, modified couple stress theory and the Bolotin method. The microplate thickness is assumed to vary along the length and width with a non-linear variation. The isogeometric analysis method is used to derive the pulse frequency and dynamic stability region of the plate under different boundary conditions. The accuracy of the model and calculation method is verified through numerical comparison with reliable publications. A set of numerical results is collected to evaluate the influence of input parameters; these results are crucial for the optimal calculation and design of variable thickness structures in practice.Tài liệu tham khảo
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[17]. P. Phung-Van, M. Abdel-Wahab, K. M. Liew, S. P. A. Bordas, H. Nguyen-Xuan, Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory, Composite Structures, 123 (2015) 137-149. https://doi.org/10.1016/j.compstruct.2014.12.021
[18]. H. X. Nguyen, E. Atroshchenko, H. Nguyen-Xuan, T. P. Vo, Geometrically nonlinear isogeometric analysis of functionally graded microplates with the modified couple stress theory, Computers Structures, 193 (2017) 110-127. https://doi.org/10.1016/j.compstruc.2017.07.017
[19]. S. C. Han, W. T. Park, W. Y. Jung, A four-variable refined plate theory for dynamic stability analysis of S-FGM plates based on physical neutral surface, Composite Structures, 131 (2015) 1081-1089. https://doi.org/10.1016/j.compstruct.2015.06.025
[20]. T. T. Tran, V. K. Tran, Q. H. Pham, A. M. Zenkour, Extended four-unknown higher-order shear deformation nonlocal theory for bending, buckling and free vibration of functionally graded porous nanoshell resting on elastic foundation, Composite Structures, 264 (2021) 113737. https://doi.org/10.1016/j.compstruct.2021.113737
[2]. 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
[3]. 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
[4]. R. D. Mindlin, H. F. Tiersten, Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11 (1962) 415-448. https://doi.org/10.1007/BF00253946
[5]. 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
[6]. M. H. Shojaeefard, H. Saeidi Googarchin, M. Mahinzare, M. Ghadiri, Free vibration and critical angular velocity of a rotating variable thickness two-directional FG circular microplate, Microsystem Technologies, 24 (2018) 1525-1543. https://doi.org/10.1007/s00542-017-3557-8
[7]. 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
[8]. V. N. Anh, T. V. 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 (2026) 85-108. https://doi.org/10.1016/j.dt.2025.09.024
[9]. J. Lawongkerd, P. R. 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
[10]. 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
[11]. N. V. Hung, The effect of blast loading on the forced vibration of functionally graded plates with nonuniform thickness, Transport and Communications Science Journal, 76 (2025) 1049-1063. https://doi.org/10.47869/tcsj.76.8.2
[12]. T. H. N. Thi, V. K. Tran, P. H. Tu, P. H. Thao, Finite element method for transient response of viscoelastic multi-directional FGP skew-nanoplate resting on visco-Pasternak foundation taking into account surface effect using nonlocal strain gradient theory, Acta Mechanica Sinica, 42 (2026) 524824. https://doi.org/10.1007/s10409-025-24824-x
[13]. T. T. T. Thuy, N. T. Anh, D. N. Mai, T. Van-Ke, Oscillation control of bio-inspired helicoid laminated composite shell integrated piezoelectric surface layer with initial geometrical imperfection, International Journal of Mechanics and Materials in Design, 22 (2026) 25. https://doi.org/10.1007/s10999-025-09860-7
[14]. T. Banh-Thien, H. Dang-Trung, L. Le-Anh, V. Ho-Huu, T. Nguyen-Thoi, Buckling analysis of non-uniform thickness nanoplates in an elastic medium using the Isogeometric Analysis, Composite Structures, 162 (2017) 182-193. https://doi.org/10.1016/j.compstruct.2016.11.092
[15]. Q. H. Pham, V. K. Tran, T. T. Tran, P. C. Nguyen, P. Malekzadeh, Dynamic instability of magnetically embedded functionally graded porous nanobeams using the strain gradient theory, Alexandria Engineering Journal, 61 (2022) 10025-10044. https://doi.org/10.1016/j.aej.2022.03.007
[16]. V. V. Bolotin, Dynamic Stability of Structures, in Nonlinear Stability of Structures, A. N. Kounadis, W. B. Krätzig, Eds., International Centre for Mechanical Sciences, 342, Springer, Vienna, (1995) 3-72. https://doi.org/10.1007/978-3-7091-4346-9_1
[17]. P. Phung-Van, M. Abdel-Wahab, K. M. Liew, S. P. A. Bordas, H. Nguyen-Xuan, Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory, Composite Structures, 123 (2015) 137-149. https://doi.org/10.1016/j.compstruct.2014.12.021
[18]. H. X. Nguyen, E. Atroshchenko, H. Nguyen-Xuan, T. P. Vo, Geometrically nonlinear isogeometric analysis of functionally graded microplates with the modified couple stress theory, Computers Structures, 193 (2017) 110-127. https://doi.org/10.1016/j.compstruc.2017.07.017
[19]. S. C. Han, W. T. Park, W. Y. Jung, A four-variable refined plate theory for dynamic stability analysis of S-FGM plates based on physical neutral surface, Composite Structures, 131 (2015) 1081-1089. https://doi.org/10.1016/j.compstruct.2015.06.025
[20]. T. T. Tran, V. K. Tran, Q. H. Pham, A. M. Zenkour, Extended four-unknown higher-order shear deformation nonlocal theory for bending, buckling and free vibration of functionally graded porous nanoshell resting on elastic foundation, Composite Structures, 264 (2021) 113737. https://doi.org/10.1016/j.compstruct.2021.113737
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Kiểu trích dẫn
Nguyen Thao, H. (1778778000). Dynamic stability analysis of functionally graded plate with variable thickness. Tạp Chí Khoa Học Giao Thông Vận Tải, 77(4), 607-618. https://doi.org/10.47869/tcsj.77.4.20
