Free vibration and stability analyses of functionally graded plates resting on elastic foundations based on 2D and quasi-3D shear deformation theories using the finite strip method

This paper explores the elastic buckling and free vibration behavior of thick functionally graded material (FGM) plates placed on elastic foundations, using two-dimensional (2D) and quasi-three-dimensional (quasi-3D) shear deformation theories. The material properties of the FGM plates are assumed to vary continuously through the thickness based on a power-law distribution. By minimizing the total potential energy and solving the associated eigenvalue problem, the classical finite strip method is applied to determine the critical buckling loads and natural frequencies of the FGM plates. A key novelty of this work lies in the development of a quasi-3D shear deformation theory, which incorporates thickness stretching effects, providing a more accurate distribution of transverse shear strains across the plate thickness. Additionally, the FSM is utilized to efficiently discretize the inplane geometry, offering a computationally cost-effective solution for analyzing free vibration and mechanical buckling characteristics. The elastic foundation is modeled using Winkler and two-parameter Pasternak models. The complexity of the governing equations is reduced by decomposing the transverse displacement into bending, shear, and thickness stretching components. Numerical results for FGM plates with various boundary conditions are validated by comparing them with analytical solutions from existing literature. Additionally, the effects of parameters such as plate thickness-to-length ratio, length-to-width ratio, boundary conditions, and the powerlaw index are analyzed and discussed.