Modal analysis of circular plates resting on an inhomogeneous elastic Winkler foundation

Free axisymmetric circular plate vibrations resting on an inhomogeneous continuous elastic Winkler foundation are considered. The inhomogeneity of the foundation is characterized by a variable subgrade modulus, which generally can be described by any continuous function. For this type of structures, analytical formulas of modal analysis predicated on the exact solution of the corresponding partial differential equation are presented. Calculation results for a circular plate are tabulated in the illustrative example. Comparison of the obtained results is presented with those of finite element analysis performed using LIRA-FEM software package.