Modal analysis of plates resting on elastic foundation based on the first-order shear deformation theory and finite element method

This paper investigates the free vibration characteristics of plate structures supported by a Pasternak elastic foundation, utilizing the first-order shear deformation theory (FSDT). FSDT simplifies the plate theory by considering only first-order shear deformation, enhancing formulation simplicity. Additionally, employing plate theory reduces computational complexity, as 2D models entail fewer degrees of freedom compared to their 3D counterparts. The finite element method (FEM) with 8-node quadrilateral element is employed for computational analysis, implemented using MATLAB. First, a comparison is made with some existing data to show the accuracy and reliability of the research. Numerical examples are then presented of the influence of the effects of thickness variation, foundation parameters and boundary conditions on frequency are investigated. The results show that the method converges very fast and reliability when compared to other research findings. The results of the research can be applied to many different engineering applications related to plates resting on elastic foundation.