ARTICLE
Analysis of vibration characteristics of porous functionally graded conical shell in thermal environments
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1
School of Advanced Manufacturing, Nanchang University, Nanchang, China
2
School of Aeronautical Manufacturing and Mechanical Engineering, Nanchang Hangkong University, Nanchang, China
Submission date: 2025-12-29
Final revision date: 2026-06-15
Acceptance date: 2026-07-16
Online publication date: 2026-08-17
Corresponding author
Runhao WAN
School of Advanced Manufacturing, Nanchang University, China
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ABSTRACT
This study investigates the free vibration modal frequencies of a metal-ceramic functionally graded porous conical shell under thermal loading. Temperature-dependent material properties and two porosity distribution patterns, namely uniform and non-uniform porosity distributions,
are considered. Based on the Sanders shell theory and the Rayleigh–Ritz method with Chebyshev polynomials, the model is verified by FEM within 5.04% error. Parametric analysis shows that temperature dominates at low wave numbers, while porosity governs at high wave numbers. Increasing the S-shaped volume fraction exponent raises frequencies and weakens thermal effects, providing a theoretical basis for high-temperature engineering applications.
REFERENCES (24)
1.
Asemi, K., & Jedari Salami, S. (2015). A study on low velocity impact response of FGM rectangular plates with 3D elasticity based graded finite element modeling. Journal of Theoretical and Applied Mechanics, 53 (4), 859–872.
https://doi.org/10.15632/jtam-....
2.
Chen, Y.G., Wang, Q.S., Zhong, R., Shi, X.J., & Qin, B. (2023). Fiber orientation and boundary stiffness optimization of laminated cylindrical shells with elastic boundary for maximum the fundamental frequency by an improved sparrow search algorithm. Thin-Walled Structures, 193, Article 111299.
https://doi.org/10.1016/j.tws.....
3.
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....
4.
Chumanov, I.V., Anikeev, A.N., & Chumanov, V.I. (2015). Fabrication of functionally graded materials by introducing wolframium carbide dispersed particles during centrifugal casting and examination of FGM’s structure. Procedia Engineering, 129, 816–820.
https://doi.org/10.1016/j.proe....
5.
Ding, S.H., & Li, X. (2008). An anti-plane shear crack in bonded functionally graded piezoelectric materials under electromechanical loading. Computational Materials Science, 43 (2), 337–344.
https://doi.org/10.1016/j.comm....
6.
Feng, J.B., & Hu, Y.D. (2026). Three-dimensional magneto-thermoelastic coupling resonance of spinning functionally graded cylindrical shells with porosity. Thin-Walled Structures, 219 (Part A), Article 114175.
https://doi.org/10.1016/j.tws.....
7.
Huang, X.-L., & Shen, H.-S. (2004). Nonlinear vibration and dynamic response of functionally graded plates in thermal environments. International Journal of Solids and Structures, 41 (9–10), 2403–2427.
https://doi.org/10.1016/j.ijso....
8.
Kalali, A.T., Hassani, B., & Hadidi-Moud, S. (2016). Elastic-plastic analysis of pressure vessels and rotating disks made of functionally graded materials using the isogeometric approach. Journal of Theoretical and Applied Mechanics, 54 (1), 113–125.
https://doi.org/10.15632/jtam-....
9.
Kołakowski, Z., & Teter, A. (2016). Some aspects of dynamic coupled response of functionally graded thin-walled columns with square cross-sections under in-plane pulse compression. Journal of Theoretical and Applied Mechanics, 54 (2), 449–462.
https://doi.org/10.15632/jtam-....
10.
Li, H.C., Pang, F.Z., Ren, Y., Miao, X.H., & Ye, K.F. (2019). Free vibration characteristics of functionally graded porous spherical shell with general boundary conditions by using first-order shear deformation theory. Thin-Walled Structures, 144, Article 106331.
https://doi.org/10.1016/j.tws.....
11.
Liu, W.G., Shu, B., Guo, L.Q., & He, H.L. (2017). Impacts of thermal environment on modal frequency of FGM shells (in Chinese). Journal of Vibration and Shock, 36 (4), 127–131.
https://doi.org/10.13465/j.cnk....
12.
Loy, C.T., & Lam, K.Y. (1997). Vibration of cylindrical shells with ring support. International Journal of Mechanical Sciences, 39 (4), 455–471.
https://doi.org/10.1016/S0020-....
13.
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....
14.
Matsunaga, H. (2009). Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory. Composite Structures, 88 (4), 519–531.
https://doi.org/10.1016/j.comp....
15.
Pillai, A.U., & Rahaman, M.M. (2026). A novel phase-field model for fatigue failure in functionally graded materials under thermo-mechanical loading. Composite Structures, 379, Article 120003.
https://doi.org/10.1016/j.comp....
16.
Reddy, J.N. (2000). Analysis of functionally graded plates. International Journal for Numerical Methods in Engineering, 47 (1–3), 663–684.
https://doi.org/10.1002/(SICI)...
17.
Shen, H.-S. (2012). Nonlinear vibration of shear deformable FGM cylindrical shells surrounded by an elastic medium. Composite Structures, 94 (3), 1144–1154.
https://doi.org/10.1016/j.comp....
18.
Wan, R.H., Liu, W.G., Chen, L., & Pang, L. (2025a). Analysis of traveling wave vibration of GNPs-reinforced bi-directional functionally graded rotating joined cylindrical-conical-cylindrical shells. Acta Mechanica, 236 (5), 3035–3053.
https://doi.org/10.1007/s00707....
19.
Wan, R.H., Liu, W.G., Cheng, L., & Pang, L. (2025b). Traveling wave vibration analysis of rotating reinforced functionally graded conical shells. Journal of Mechanical Science and Technology, 39 (5), 2417–2429.
https://doi.org/10.1007/s12206....
20.
Wang, Y.Q., Ye, C., & Zu, J.W. (2018). Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities. Applied Mathematics and Mechanics, 39 (11), 1587–1604.
https://doi.org/10.1007/s10483....
21.
Wang, Y.W., & Wu, D.F. (2017). Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory. Aerospace Science and Technology, 66, 83–91.
https://doi.org/10.1016/j.ast.....
22.
Wu, L. (2004). Thermal buckling of a simply supported moderately thick rectangular FGM plate. Composite Structures, 64 (2), 211–218.
https://doi.org/10.1016/j.comp....
23.
Xu, H.D., Wang, Y., Xu, Z.Q., & Yu, X.G. (2024). Gegenbauer-Ritz method for free vibration analysis of rotating functionally graded graphene reinforced porous composite stepped cylindrical shells with arbitrary boundary conditions. Engineering Structures, 303, Article 117555.
https://doi.org/10.1016/j.engs....
24.
Xue, Y.Q., Jin, G.Y., Zhang, C.Y., Han, X.H., & Chen, J. (2023). Free vibration analysis of functionally graded porous cylindrical panels and shells with porosity distributions along the thickness and length directions. Thin-Walled Structures, 184, Article 110448.
https://doi.org/10.1016/j.tws.....