Phase-field based free vibration analysis of cracked porous composite plates with parabolically varying thickness on elastic foundations
Email:
phamminhphuc@utc.edu.vn
Từ khóa:
Porous material, functionally graded plate, variable thickness, crack, Phase-field, elastic foundation.
Tóm tắt
Composite plates with cracks, variable thickness, and porous structures are increasingly used in modern engineering applications due to their superior performance under complex operating conditions. However, the combined effects of porosity, variable thickness, cracks, and elastic foundation on the free vibration behavior of such plates are still not fully understood. This study investigates the free vibration characteristics of a porous functionally graded plate with parabolically varying thickness along the x-axis. A crack is assumed to be located either at the center or at the edge of the plate. The material porosity is considered to be uniformly distributed through the plate thickness. The governing equations are established based on the first-order shear deformation theory in combination with the phase-field approach to simulate the crack behavior. The finite element method is employed to solve the resulting eigenvalue problem and obtain the natural frequencies of the plate. Parametric studies are carried out to examine the influences of crack length, crack position, porosity coefficient, thickness variation, and elastic foundation stiffness on the vibration response. The numerical results demonstrate that the crack length and crack location have a significant effect on the natural frequencies, while the presence of a stiff elastic foundation remarkably reduces the sensitivity of the vibration characteristics to cracking effects.Tài liệu tham khảo
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[21]. C. S. Huang, P. J. Yang, M. J. Chang, Three-dimensional vibration analyses of functionally graded material rectangular plates with through internal cracks, Composite Structures, 94 (2012) 2764–2776. https://doi.org/10.1016/j.compstruct.2012.03.012
[2]. N. V. Nguyen, D. H. Phan, Nonlinear free vibration of bi-directional functionally graded porous plates, Thin-Walled Structures, 192 (2023) 111198. https://doi.org/10.1016/j.tws.2023.111198
[3]. T. Assas, M. Zitouni, H. Bourada, Static, free vibration, and buckling analysis of functionally graded plates using the strain-based finite element formulation, Archive of Applied Mechanics, 94 (2024) 2243–2267. https://doi.org/10.1007/s00419-024-02635-0
[4]. E. Yıldırım, Effect of the porous structure on the hygrothermal vibration analysis of functional graded nanoplates, Acta Mechanica, 235 (2024) 5079–5106. https://doi.org/10.1007/s00707-024-03990-3
[5]. P.Kumar, R.Sharma, S.Singh, Thermoelectrical vibration and bending analysis of multidirectional functionally graded circular piezoelectric porous sigmoid plate, International Journal of Mechanical and Materials Design, (2025). https://doi.org/10.1007/s10999-025-09779-z
[6]. S. Jandaghi-Semnani, R. Attarnejad, R. Kazemi-Firouzjaei, Free vibration analysis of variable thickness thin plates by two-dimensional differential transform method, Acta Mechanica, (2013). https://doi.org/10.1007/s00707-013-0833-2
[7]. G. P. Sinha, B. Kumar, Frequency analysis of variable thickness Kirchhoff plates by isogeometric approach, Journal of The Institution of Engineers (India), Series C, 104 (2023) 271–280. https://doi.org/10.1007/s40032-023-00910-7
[8]. S. R. Farsani, Z. Saadat, R.-A. Jafari-Talookolaei, R. Tikani, S. Ziaei-Rad, Free vibrational analysis of variable thickness plate made of functionally graded porous materials using internal supports in contact with bounded fluid, Ocean Engineering, 263 (2022) 112335. https://doi.org/10.1016/j.oceaneng.2022.112335
[9]. R. Pilafkan, P. D. Folkow, Free vibration analysis of rectangular plates with variable thickness using a meshless method, Forces in Mechanics, 21 (2025) 100328. https://doi.org/10.1016/j.finmec.2025.100328
[10]. P. M. Phuc, Analysis free vibration of the functionally grade material cracked plates with varying thickness using the phase-field theory, Transport and Communications Science Journal, 70 (2019) 122–131. https://doi.org/10.25073/tcsj.70.2.35
[11]. P. M. Phuc, Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness, Transport and Communications Science Journal, 71 (2020) 853–867. https://doi.org/10.47869/tcsj.71.7.10
[12]. P. M. Phuc, D. T. Manh, N. D. Duc, Free vibration of cracked FG plates with variable thickness resting on elastic foundations, Thin-Walled Structures, 161 (2021) 107425. https://doi.org/10.1016/j.tws.2020.107425
[13]. P. M. Phuc, N. D. Duc, Free vibration of cracked MEE FG plates resting on elastic foundations using phase-field simulation, Journal of Engineering Mechanics, 149 (11) (2023) 04023103. https://doi.org/10.1061/JENMDT.EMENG-7088
[14]. B. K. Chandrakar, N. K. Jain, Ankur Gupta, Nonlinear vibration analysis of a cracked isotropic plate with varying thickness coupled with fluid, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2025. https://doi.org/10.1007/s40430-025-05616-8
[15]. L. Kurpa, R. Lewandowski, A. Żur, Free vibration analysis of porous functionally graded material plates with variable thickness on an elastic foundation, Mathematics and Computers in Simulation / Mathematics and Computational Applications, 29 (2024) 10. https://doi.org/10.3390/mca29010010
[16]. M. C. Srivastav, A. K. Barik, S. Chakraverty, Analysis of free vibration characteristics of porous FG skew plate using meshfree approach, Multiscale and Multidisciplinary Modeling, Experiments and Design, 7 (2024) 6245–6261. https://doi.org/10.1007/s41939-024-00576-3
[17]. M. Izadi, M. Abedi, P. S. Valvo, Free vibration analysis of a functionally graded porous triangular plate with arbitrary shape by isogeometric approach, Thin-Walled Structures, 205 (2024) 112422. https://doi.org/10.1016/j.tws.2024.112422
[18]. Y. Xue, C. Zhang, K. Shi, Y. Gao, Z. Gao, Free vibration analysis of functionally graded porous corrugated plates with porosity distributions in the thickness and width directions, Advances in Engineering Software, 212 (2026) 104066. https://doi.org/10.1016/j.advengsoft.2025.104066
[19]. A. S. Rezaei, A. R. Saidi, M. Abrishamdari, M. H. Pour Mohammadi, Natural frequencies of functionally graded plates with porosities via a simple four-variable plate theory: An analytical approach, Thin-Walled Structures, 120 (2017) 366–377. https://doi.org/10.1016/j.tws.2017.08.003
[20]. V. Kumar, S. J. Singh, V. H. Saran, S. P. Harsha, Vibration characteristics of porous FG plates with variable thickness resting on Pasternak’s foundation, European Journal of Mechanics – A/Solids, 85 (2021) 104124. https://doi.org/10.1016/j.euromechsol.2020.104124
[21]. C. S. Huang, P. J. Yang, M. J. Chang, Three-dimensional vibration analyses of functionally graded material rectangular plates with through internal cracks, Composite Structures, 94 (2012) 2764–2776. https://doi.org/10.1016/j.compstruct.2012.03.012
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Nhận bài
22/12/2025
Nhận bài sửa
17/04/2026
Chấp nhận đăng
10/05/2026
Xuất bản
15/05/2026
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Kiểu trích dẫn
Pham Minh, P. (1778778000). Phase-field based free vibration analysis of cracked porous composite plates with parabolically varying thickness on elastic foundations. Tạp Chí Khoa Học Giao Thông Vận Tải, 77(4), 342-356. https://doi.org/10.47869/tcsj.77.4.1
