ARTICLE
Dynamic instability analysis of porous sigmoid functionally graded truncated conical shells subjected to combined pressures
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1
School of Architecture and Transportation Engineering, Guilin University of Electronic Technology, Guilin, China
2
School of Physics and Telecommunication, Yulin Normal University, Yulin, China
Submission date: 2025-11-05
Final revision date: 2026-06-02
Acceptance date: 2026-06-13
Online publication date: 2026-06-22
Corresponding author
Wei WU
School of Physics and Telecommunication, Yulin Normal University, Yulin, China
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ABSTRACT
An improved model for assessing the material properties of porous sigmoid functionally graded (S-FGM) conical shells is introduced. Governing equations are derived within thin-shell theory, incorporating static hydraulic pressure, axial periodic loading, and a Winkler–Pasternak foundation. Critical frequencies and unstable regions are obtained via the Galerkin and Bolotin methods. Parametric studies show that the critical frequency decreases with higher porosity, half-vertex angle, or radius-thickness ratio, but increases with ceramic content or foundation stiffness. Porosity fraction and static axial loading notably affect instability regions, while hydraulic pressure has a negligible effect.
REFERENCES (24)
1.
Ali, A.Y., & Hasan, H.M. (2019). Nonlinear dynamic stability of an imperfect shear deformable orthotropic functionally graded material toroidal shell segments under the longitudinal constant velocity. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233 (19-20), 6827–6850.
https://doi.org/10.1177/095440....
2.
Allahkarami, F., Saryazdi, M.G., & Tohidi, H. (2020). Dynamic buckling analysis of bi-directional functionally graded porous truncated conical shell with different boundary conditions. Composite Structures, 252, Article 112680.
https://doi.org/10.1016/j.comp....
3.
Bich, D.H., & Ninh, D.G. (2016). Post-buckling of sigmoid-functionally graded material toroidal shell segment surrounded by an elastic foundation under thermo-mechanical loads. Composite Structures, 138, 253–263.
https://doi.org/10.1016/j.comp....
4.
Chi, S.-H., & Chung, Y.-L. (2006). Mechanical behavior of functionally graded material plates under transverse load—Part I: Analysis. International Journal of Solids and Structures, 43 (13), 3657–3674.
https://doi.org/10.1016/j.ijso....
5.
Duc, N.D., & Cong, P.H. (2015). Nonlinear dynamic response of imperfect symmetric thin sigmoid-functionally graded material plate with metal-ceramic-metal layers on elastic foundation. Journal of Vibration and Control, 21 (4), 637–646.
https://doi.org/10.1177/107754....
6.
Duc, N.D., Kim, S.E., & Chan, D.Q. (2018). Thermal buckling analysis of FGM sandwich truncated conical shells reinforced by FGM stiffeners resting on elastic foundations using FSDT. Journal of Thermal Stresses, 41 (3), 331–365.
https://doi.org/10.1080/014957....
7.
Fan, L.J., Sahmani, S., & Safaei, B. (2021). Couple stress-based dynamic stability analysis of functionally graded composite truncated conical microshells with magnetostrictive facesheets embedded within nonlinear viscoelastic foundations. Engineering with Computers, 37 (2), 1635–1655.
https://doi.org/10.1007/s00366....
8.
Foroutan, K., & Torabi, F. (2026). Nonlinear chaotic and periodic responses of obliquely stiffened sigmoid FG cylindrical shells under principal torsional parametric, subharmonic, and 1:2 internal resonances. Thin-Walled Structures, 221, Article 114463.
https://doi.org/10.1016/j.tws.....
9.
Fu, T.,Wu, X., Xiao, Z., & Chen, Z. (2021). Dynamic instability analysis of porous FGM conical shells subjected to parametric excitation in thermal environment within FSDT. Thin-Walled Structures, 158, Article 107202.
https://doi.org/10.1016/j.tws.....
10.
Hoa, L.K., Phi, B.G., Chan, D.Q., & Hieu, D.V. (2022). Buckling analysis of FG porous truncated conical shells resting on elastic foundations in the framework of the shear deformation theory. Advances in Applied Mathematics and Mechanics, 14 (1), 218–247.
https://doi.org/10.4208/aamm.O....
11.
Mallek, H., Mellouli, H., Ben Said, L., Wali, M., Dammak, F., & Alhadri, M. (2025). Porosity effects on nonlinear static performances of functionally graded shells considering thickness stretching. Facta Universitatis, Series: Mechanical Engineering, 23 (4), 827–860.
https://doi.org/10.22190/FUME2....
12.
Naj, R., Sabzikar Boroujerdy, M., & Eslami, M.R. (2008). Thermal and mechanical instability of functionally graded truncated conical shells. Thin-Walled Structures, 46 (1), 65–78.
https://doi.org/10.1016/j.tws.....
13.
Nemati, A.R., & Mahmoodabadi, M.J. (2020). Effect of micromechanical models on stability of functionally graded conical panels resting on Winkler–Pasternak foundation in various thermal environments. Archive of Applied Mechanics, 90 (5), 883–915.
https://doi.org/10.1007/s00419....
14.
Ng, T.Y., Lam, K.Y., Liew, K.M., & Reddy, J.N. (2001). Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading. International Journal of Solids and Structures, 38 (8), 1295–1309.
https://doi.org/10.1016/S0020-....
15.
Pal, S., Rout, M., Deb Singha, T., & Karmakar, A. (2025). Thermoelastic free vibration of rotating pretwisted porous p-FGM, e-FGM, and s-FGM conical shells in nonlinear temperature distribution. Journal of Vibration and Control, 31 (7–8), 1258–1277.
https://doi.org/10.1177/107754....
16.
Sofiyev, A.H. (2009). The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure. Composite Structures, 89 (3), 356–366.
https://doi.org/10.1016/j.comp....
17.
Sofiyev, A.H. (2010). The buckling of FGM truncated conical shells subjected to combined axial tension and hydrostatic pressure. Composite Structures, 92 (2), 488–498.
https://doi.org/10.1016/j.comp....
18.
Sofiyev, A.H. (2016). Parametric vibration of FGM conical shells under periodic lateral pressure within the shear deformation theory. Composites Part B: Engineering, 89, 282–294.
https://doi.org/10.1016/j.comp....
19.
Sofiyev, A.H., Alizada, A.N., Akin, Ö., Valiyev, A., Avcar, M., & Adiguzel, S. (2012). On the stability of FGM shells subjected to combined loads with different edge conditions and resting on elastic foundations. Acta Mechanics, 223 (1), 189–204.
https://doi.org/10.1007/s00707....
20.
Sofiyev, A.H., & Schnack, E. (2012). The vibration analysis of FGM truncated conical shells resting on two-parameter elastic foundations. Mechanics of Advanced Materials and Structures, 19 (4), 241–249.
https://doi.org/10.1080/153764....
21.
Wu, H., Yang, J., & Kitipornchai, S. (2020). Mechanical analysis of functionally graded porous structures: A review. International Journal of Structural Stability and Dynamics, 20 (13), Article 2041015.
https://doi.org/10.1142/S02194....
22.
Yuan, Y., Zhao, X., Zhao, Y., Sahmani, S., & Safaei, B. (2021). Dynamic stability of nonlocal strain gradient FGM truncated conical microshells integrated with magnetostrictive facesheets resting on a nonlinear viscoelastic foundation. Thin-Walled Structures, 159, Article 107249.
https://doi.org/10.1016/j.tws.....
23.
Zhang, J., & Li, S. (2010). Dynamic buckling of FGM truncated conical shells subjected to non-uniform normal impact load. Composite Structures, 92 (12), 2979–2983.
https://doi.org/10.1016/j.comp....
24.
Zhu, J., Lai, Z., Yin, Z., Jeon, J., & Lee, S. (2001). Fabrication of ZrO2–NiCr functionally graded material by powder metallurgy. Materials Chemistry and Physics, 68 (1-3), 130–135.
https://doi.org/10.1016/S0254-....