Nonlinear free oscillation of imperfect FG porous stiffened open conical panels resting on an elastic foundation under thermal conditions

Document Type : Research Article

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Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

Abstract

This research investigates the nonlinear free oscillation analysis of imperfect, functionally graded, porous, stiffened, open conical panels resting on an elastic foundation under thermal conditions. To establish the governing nonlinear dynamic equations, the classical shell theory, the nonlinear von Kármán assumptions, and Hamilton’s principle are employed. Due to the use of the multiple scales method (MSM), the equations of motion must be rewritten in dimensionless form; therefore, the dimensionless parameters are introduced. The Galerkin approach is utilized to discretize the dimensionless partial differential equations (PDEs). By neglecting in-plane inertias and solving the resulting algebraic relations, the discretized system reduces to a nonlinear ordinary differential equation. Based on this final nonlinear ODE, the linear frequencies are extracted, and the numerical results are validated with previous studies for different geometries. Furthermore, the MSM is employed to determine the nonlinear frequency relationship. Finally, the effects of geometrical variations, material properties, imperfections, and foundation effects are investigated. The reported outcomes highlight the importance of imperfect FG-porous stiffened conical panels to multiple parameters, providing valuable insights into their vibration behavior under simply supported conditions.

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AUT Journal of Mechanical Engineering
Volume 10, Issue 3
July 2026
Pages 389-416

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