Free vibration analysis of rectangular plates with internal point supports.

Abstract

Interest in the free vibration frequencies and associated mode shapes of rectangular plates resting on internal point supports has arisen in connection with the design of electronic circuit boards, solar panels and other industrial problems. An analytical solution is presented for the free vibration analysis of rectangular plates with multiple internal point supports. The solution is also shown to be easily modified to account for the effects of attached masses. The basic solution for each case consists of the Levy type solution for a plate with one discrete point support. N similar solutions for N discrete point supports are then superimposed to create an eigenvalue matrix from which the plate's natural frequencies and associated mode shapes can be determined. Due to the nature of the Levy type solution, only plates with two opposite edges simply supported are considered. The remaining edges are either simply supported, clamped or free. There are therefore six possible combinations of plate boundary conditions. The objective of this thesis is to give a concise and clear description of the mathematical procedure employed and to present the results of some representative frequency and mode shape studies.