Analytical method for studying free vibrations of round plates on a non-homogeneous elastic foundation

Free axisymmetric vibrations of a circular plate resting on an inhomogeneous, continuous elastic Winkler foundation are investigated. The foundation inhomogeneity is represented by a spatially varying subgrade modulus, which may be described by an arbitrary continuous function. For this class of structures, an analytical modal analysis method based on an exact solution of the governing partial differential equation is proposed. Numerical results for a circular plate are presented in tabulated form. To validate the proposed approach, the results are compared with those obtained from finite element analysis using the LIRA-FEM software package.