DSC-element method for free vibration analysis of rectangular Mindlin plates

Abstract

A novel DSC-element method is proposed to investigate the free vibration of moderately thick plates based on the well-known Mindlin first-order shear deformation plate theory. The development of the present approach not only employs the concept of finite element method, but also implements the discrete singular convolution (DSC) delta type wavelet kernel for the transverse vibration analysis. This numerical algorithm is allowed dividing the domain of Mindlin plates into a number of small discrete rectangular elements. As compared with the global numerical techniques i.e. the DSC–Ritz method, the flexibility is increased to treat complex boundary constraints. For validation, a series of numerical experiments for different meshes of Mindlin plates with assorted combinations of edge supports, plate thickness and aspect ratios is carried out. The established natural frequencies are directly compared and discussed with those reported by using the finite element and other numerical and analytical methods from the open literature.