Eigenfrequencies of line supported rectangular plates
The problem of the free vibration of line-supported elastic plates of uniform thickness which are continuous in two directions is analysed by the Rayleigh-Ritz method. The admissible functions are a combination of the free vibrating beam functions and polynomials. The beam eigenfunctions which satisfy the boundary conditions for the plate are selected as the main part of the admissible functions, and the polynomials with undetermined coefficients are added as the modified part of the admissible functions in order to satisfy the zero deflection conditions at intermediate line supports. The coefficients of the polynomials are determined using the boundary conditions and the conditions at the intermediate line supports of the plate. The integrations of products of beam eigenfunctions with polynomials may be performed numerically or analytically in recurrent form without any approximate calculation. This presents a significant advantage over many other methods when the complexity and computation cost often increase substantially with increasing number of spans. In several cases, comparisons are made with values available in the literature, and in all cases close agreement may be achieved. As seen from the presented results, the convergence is very fast and the accuracy is generally better than in other methods.
scientific article; zbMATH DE number 527583