Analytical 3-D p-element for quadrilateral plates—Part 1: Thick isotropic plate structures

An analytical three-dimensional (3-D) p-version element for the vibration analysis of arbitrary quadrilateral thick plates is presented. With the additional hierarchical shape functions and analytically integrated element matrices, the computed accuracy is considerably improved. The computed natural frequencies of cantilever and simply supported square plates show that the convergence rate of the present element is very fast with respect to the number of hierarchical terms and it can predict very accurate modes. The element is applicable to the free vibration analysis of quadrilateral, polygonal plates as well as 3-D space structures. The continuous wavelet transform (CWT) is applied for the identification of damping ratios. Based on the Rayleigh damping model, the damped vibration response is obtained. A simple experiment is performed to verify the predicted vibration responses. The results show that the proposed element is also efficient for the vibration response analysis of plates.