Free vibrations of rectangular plates with interior point supports

Abstract

A new approach for the representation of point supports in the vibration analysis of plates was presented in earlier work [1–3]. The approach was based on simulating a point support on a free edge as a zero of a flexibility function, representing a fictitious elastic restraint distribution over the free edge. The application of this approach, to a variety of problems, concerning rectangular plates with point supports located on the free edges, was demonstrated in subsequent studies [4,5]. The present study provides an extension of the flexibility function approach to the problem of rectangular plates with interior point supports. In the analysis, a rectangular plate is considered with two opposite edges simply supported and classical boundary conditions on the other two edges, with one or more interior point supports along the line perpendicular to the simply supported edges. Extensive numerical results for a range of problem parameters have been obtained. The results show the versatility of the flexibility function approach in the vibration analysis of rectangular plates with arbitrarily located interior point supports.