Dynamic response of thin plates on time-varying elastic point supports

In this article, an analytical-numerical approach is presented in order to determine the dynamic response of thin plates resting on multiple elastic point supports with time-varying stiffness. The proposed method is essentially based on transforming a familiar governing partial differential equation into a new solvable system of linear ordinary differential equations. When dealing with time-invariant stiffness, the solution of this system of equations leads to a symmetric matrix, whose eigenvalues determine the natural frequencies of the point-supported plate. Moreover, this method proves to be applicable for any plate configuration with any type of boundary condition. The results, where possible, are verified upon comparison with available values in the literature, and excellent agreement is achieved.