Free Vibration Analysis of Orthotropic Thin Rectangular SSSS Plate Using Polynomial Series Function

Free vibration analysis of material orthotropic rectangular thin plate simply supported on all edges (SSSS) plate using Taylor’s series function in Ritz method was carried out. A Taylor’s series truncated at the 5th terms was used to develop the polynomial shape function which satisfied the boundary condition of the plate. This was substituted into the potential energy functional of Ritz and minimized the resulting functional to get the free vibration equation. Three sets of the flexural rigidity ratios for x, y and xy were used. The values of the flexural rigidities for the three sets are 1.0; 1.0; 1.0 and 1.0; 0.5; 1.0 and 1.0; 0.5; 0.5 respectively. The fundamental frequencies were obtained for various aspect ratio ranging from 0.1 to 2 at increments of 0.1. Fundamental natural frequency of the plate for aspect ratio of 1.0 for the three sets of flexural rigidity ratios are respectively 19.75, 17.10 and 15.61. The corresponding values from the works of Pilkey are respectively 19.74, 17.10 and 15.61. The closeness between the valus from the present study and those of Pilkey indicates that the approach of the present study is satisfactory and reliable