Free vibration analysis of rectangular plates with variable thickness using a meshless method

Abstract

This paper presents a comprehensive study on the free vibration analysis of rectangular plates with variable thickness, utilizing three-dimensional elasticity theory and a meshless method. Traditional plate theories, such as classical and shear deformation theories, often fail to provide accurate results for thick plates or those with complex geometries. To overcome these limitations, the study adopts the three-dimensional elasticity approach, which considers the full material behavior and the entire plate structure. The meshless method, specifically the Radial Point Interpolation Method (RPIM) with multi-quadrics radial basis functions, is employed to solve the vibration problem. This method offers advantages over traditional finite element methods by using scattered nodes and higher-order shape functions, thus eliminating issues related to meshing and re-meshing. The plates’ thickness is assumed to vary linearly and nonlinearly in one or both directions in the plate plane, and the study investigates the impact of different thickness ratios, aspect ratios, and boundary conditions on the natural frequencies of the plate. The results show that the meshless method provides a high degree of accuracy and fast convergence for both thin and thick plates with variable thickness, making it a reliable and efficient tool for free vibration analysis. This work thus contributes with valuable insights to the dynamic behavior of variable-thickness plates, with applications in many engineering fields where weight reduction and structural performance are critical. The work also provides eigenfrequency results on several plate structures with varying thickness, which may serve as a reference using 3D theory.