Approximate solution for free vibrations of thin orthotropic rectangular plates

In this paper the problem of approximate evaluation of the frequencies of orthotropic plates is investigated. Starting from a general approximate formula for the frequency, proposed by Hearmon, it is shown how to calculate the fundamental mode of an orthotropic rectangular plate with different restraint conditions using the proper coefficient values already available in the scientific literature. For the higher modal frequencies, a particular form of the Rayleigh 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 to the real one. In order to test the accuracy of the proposed method an extensive finite element investigation was carried out. The numerical results obtained show that the average difference between the values computed with the approximate new method and the finite element values is less than 0.74%. (c) 2005 Elsevier Ltd. All rights reserved.