A general approximate solution of the problem of free vibrations of annular plates of stepped thickness

An approximate solution to the title problem is proposed for the case in which the inner boundary of the circular plate is free and the outer edge is elastically restrained against rotation. The displacement amplitude is approximated by means of a superposition of simple polynomial co-ordinate functions, which satisfy identically the boundary conditions at the outer edge only and which yield excellent accuracy in the case of simply connected circular plates. The optimized Rayleigh-Ritz method is then used to generate the frequency determinant minimizing the eigenvalues with respect to an exponential parameter contained in each polynomial cc-ordinate function. A comparison with eigenvalues obtained using a finite element solution is also presented and good agreement is shown to exist. (C) 1996 Academic Press Limited