Free Vibration with Mindlin Plate Finite Element Based on the Strain Approach

Abstract

This paper presents the development of a quadrilateral plate bending finite element for the computation of natural frequencies of plates with arbitrary geometry. This element is based on the Reissner–Mindlin plate theory using assumed strains rather than displacements and contains only the three physical degrees of freedom at each of the four corner nodes. Tests of convergence are first established for square plates with both simply supported and clamped on their edges where it is shown that a good rate of convergence is obtained using few elements. Other tests are then applied to rectangular, circular, skew and stepped plates, in addition to a rectangular plate with a central cutout as well. The numerical results obtained show that the present element has successfully passed patch tests and its results of the natural frequencies and the associated modes of vibration are in excellent agreement when compared with analytical and other available numerical solutions.