Analytical and experimental investigation on vibrating circular plates with stepped thickness over a concentric circular region

Transverse vibrations of the structural elements described in the title are studied for the case where the edges are elastically restrained against translation and rotation. Since finding an exact solution is a difficult task, it was considered convenient to approximate the response of the plate in the case of free, axisymmetric vibrations by means of a summation of simple polynomial coordinate functions that satisfy the governing boundary conditions. The Ritz method is used in order to generate the frequency equation. The natural frequency coefficients are optimized by minimizing each eigenvalue with respect to an undetermined exponential parameter included in each coordinate function.