Some observations on the application of the Rayleigh–Ritz method

This paper deals with the applicability of the Rayleigh–Ritz method for the determination of frequency coefficients of beams and plates with elastically restrained edges. Natural frequencies of beams elastically restrained against rotation and translation at both ends and of rectangular isotropic plates with elastic edge restraints are studied by using the Rayleigh–Ritz method along with orthogonal polynomials as co-ordinate functions. It is shown that the approximate satisfaction of boundary conditions introduces additional constraints into the formulation that bring unexpected values in the results. On the other hand, it is shown that there are defects in the approximations when the natural boundary conditions in beams are taken into account. The adequate procedure for constructing the co-ordinate functions to avoid numerical errors is presented.