MATHEMATICAL MODELING OF DYNAMIC INSTABILITY REGIONS OF A REINFORCED COMPOSITE PLATE
Received: 2026-05-30
Published: 2026-06-06
Abstract
The paper is devoted to mathematical modeling of dynamic instability regions of a reinforced anisotropic composite plate (fiberglass) subjected to transverse parametric loading. Based on the refined Timoshenko theory and the hereditary theory of viscoelasticity, the mathematical model is formulated as a system of nonlinear integro-differential partial differential equations with weakly singular relaxation kernels. Using the Bubnov-Galerkin method, the problem is reduced to a system of nonlinear ordinary integro-differential equations and solved numerically using quadrature formulas after regularization of the weakly singular kernels. A universal procedure for determining dynamic instability regions of thin-walled structures under parametric loads is proposed, and the influence of physical and geometric parameters of the reinforced composite plate is demonstrated.
Keywords
List of references
-
Bolotin, V.V. (1964). The Dynamic Stability of Elastic Systems. Holden Day, San Francisco.
-
Bolotin, V.V. (1963). Nonconservative Problems of the Theory of Elastic Stability. MacMillan, New York.
-
Fayaz, D., Patel, S. N., Kumar, R., Watts, G. (2024). Nonlinear dynamic instability of laminated composite stiffened plates subjected to in-plane pulsating loading. Mechanics of Advanced Materials and Structures, 31(22), 5486–5517. https://doi.org/10.1080/15376494.2023.2216692.
-
Dai, Z., Tang, H., Wu, S., Habibi, M., Moradi, Z., Ali, H.E. (2023). Nonlinear consecutive dynamic instabilities of thermally shocked composite circular plates on the softening elastic foundation. Thin-Walled Structures, 186, 110645. https://doi.org/10.1016/j.tws.2023.110645.
-
Samadani, F. (2025). A semi-analytical methodology for predicting the vibroacoustic response of functionally graded nanoplates under thermal loads. Mechanics Based Design of Structures and Machines, 53(4), 2452–2486. https://doi.org/10.1080/15397734.2024.2407419.
-
Krysko, A.V., Kalutsky, L.A., Zakharova, A.A., Krysko, V.A. (2024). Mathematical modeling of functionally graded porous geometrically nonlinear micro/nano cylindrical panels. Bulletin of the Tomsk Polytechnic University. Geo Assets Engineering, 335(3), 216–229. https://doi.org/10.18799/24131830/2024/3/4505.
-
Eshmatov, B.Kh., Abdikarimov, R., Amabili, M., Vatin, N. (2023). Nonlinear vibrations and dynamic stability of viscoelastic anisotropic fiber reinforced plates. Magazine of Civil Engineering, 118, 11811. https://doi.org/10.34910/MCE.118.11.
-
Eshmatov, B.Kh., Mirsaidov, M.M., Abdikarimov, R.A., Vatin, N.I. (2024). Buckling of a viscoelastic anisotropic fiber reinforced plate under rapidly increasing shear load. Magazine of Civil Engineering, 117(5). https://doi.org/10.34910/MCE.129.10.
-
Badalov, F., Eshmatov, Kh., Yusupov, M. (1987). On certain methods of solving systems of integrodifferential equations encountered in viscoelasticity problems. Journal of Applied Mathematics and Mechanics, 51, 683–686. https://doi.org/10.1016/0021-8928(87)90025-6.
-
Verlan, A.F., Abdikarimov R.A., Eshmatov, Kh. (2010). Numerical modeling of nonlinear problems of the dynamics of viscoelastic systems with variable rigidity. Electronic Modeling, 32(2), 3–14.
About the Authors
License
This work is licensed under a Creative Commons Attribution 4.0 International License.