DYNAMIC ANALYSIS OF COMPLEX STRUCTURE BY EQUIVALENT METHODS: APPLICATIONS TO ISOTROPIC AND ORTHOTROPIC PLATES

Abstract

This paper intends to provide an equivalent method for the evaluation of natural frequency of isotropic and orthotropic thin rectangular plates with different restraint conditions. Starting from a simple and a general approximate formula for the frequency, which is the extension of Hearmon’s expressions presented for the fundamental mode; it is shown how to calculate the fundamental mode of isotropic and orthotropic rectangular plates using the proper coefficient values already available in the scientific literature. For the higher modal frequencies, a particular form of Rayleigh’s method is proposed, leading to a simple procedure to calculate the fundamental frequency. In fact the frequency calculation is reduced to the evaluation of the fundamental frequency of a special plate associated with the real one. An extensive finite element investigation was carried out to test the accuracy of this analytical short cut method. In addition a comparative study has shown good agreement between the frequencies responses obtained from both analytical (equivalent method) and finite element solution using ANSYS program. This method allows us to both avoid huge calculations, and produce a fast and simple approximate calculus of free vibration frequencies. This in turn is a necessary part of the preliminary design phase and the general and immediate verification of a construction project to its completion.