Dynamic response of thin plate with damping subjected to in-plane compressive harmonic excitation

Abstract

The dynamics of a rectangular plate with initial deflection excited by an external force comprising two components, a constant and periodically varying term, were analyzed by the authors of the paper. It was noted that the plate’s initial deflection was perpendicular to its surface, resulting in asymmetry. The partial differential equation governing the plate’s behavior was simplified to the one-degree-of-freedom Mathieu equation. The three methods have been used to analyze the system’s dynamics: the FEM, the sampled-based method and path-following. The equivalence of the full model with the reduced one was confirmed by the researchers. It was found that the Mathieu equation was suitable for investigating the dynamics of the rectangular plate across various parameters and for studying the sensitivity to initial conditions. It is shown that the reduced model is very efficient for detecting ranges of multistability and bifurcations sequence. A good agreement is also observed for values of stress obtained from full and reduced models.