The Natural Frequency of Elastic Plates with Void by Ritz-Method

Abstract

To use a new computational method for the problem of the flexural vibration of thin, isotropic rectangular plates with arbitrarily positioned voids. In this paper we use static beam functions under point load as admissible functions and Rayleigh-Ritz method for analysis of discontinuous variation of rigidity of the plates. The voids of plate are expressed continuously by using extended Dirac function, which is defined as Dirac function existing continuously in prescribed region. The governing equation for a plate with voids composed of an isotropic material is formulated without modifying the rigidity of the plates, as done in the equivalent plate analogy. The natural frequencies of simply supported and clamped plates with voids are obtained from the governing equation by this energy method. The model is able to determine the frequency of plates with voids. It is shown that numerical results all converge very fast and are in excellent agreement with other researcher’s results. The numerical results obtained from the solution method used here show good agreement with results obtain form the previous equivalent plates analogy. Key Words: Plates with voids; Static beam function