Analysis of vibration of clamped square plates by the Rayleigh-Ritz method with asymptotic solutions from a modified Bolotin method

Estimates of flexural frequencies of clamped square plates are initially obtained by the modified Bolotin's method. The mode shapes in “each direction” are then determined and the product functions of these mode shapes are used as admissible functions in the Rayleigh-Ritz method. The data for the first twenty eigenvalues in each of the three (four) symmetric groups obtained by the (i) Bolotin, (ii) Rayleigh and (iii) Rayleigh-Ritz methods are reported here. The Rayleigh estimates are found to be much closer to the true eigenvalues than the Bolotin estimates. The present product functions are found to be much superior to the conventional beam eigenmodes as admissible functions in the Rayleigh-Ritz method of analysis.