Forced Vibration Analysis of Isotropic Thin Circular Plate Resting on Nonlinear Viscoelastic Foundation

In this work, forced vibration analysis of isotropic thin circular plate resting on nonlinear viscoelastic foundation is investigated. The dynamic analogue of the Von Kármán equations is used to establish the governing equations. The system coupled nonlinear partial differential equations are transformed to system of nonlinear ordinary differential equation using Galerkin decomposition method. Consequently, the analytical solutions are provided using differential transformation method with Padè Laplace after treatment technique. The developed solutions are verified using the existing results in the literature, and good agreement is observed. Subsequently, the analytical solutions are used to investigate the effects of various parameters on the dynamic response of the plate. From the results, it is observed that nonlinear frequency ratio of vibrating circular plate increases with increased linear elastic foundation and tensile force. Nevertheless, it is established that the nonlinear frequency ratio of the plate decreases as nonlinear Winkler foundation and compressive force increase. Also, the results revealed that clamped edge and simply supported edge condition recorded the same softening nonlinearity. However, axisymmetric case of vibration gives lower nonlinear frequency ratio compared to symmetric case. Also, maximum deflection occurs when excitation force is zero; likewise attenuation deflection is observed due to the presence of viscoelastic foundation. It is expected that the findings from this research will enhance the design of structures subjected to vibration under where circular plates are used.