Nonlinear Dynamics of an Axially Moving Plate Submerged in Fluid with Parametric and Forced Excitation

In this study, analytical and numerical methods are applied to investigate the dynamic response of an axially moving plate subjected to parametric and forced excitation. Based on the classical thin plate theory, the governing equation of the plate coupled with fluid is established and further discretized through the Galerkin method. These equations are solved using the method of multiple scales to obtain amplitude-frequency curves and phase-frequency curves. The stability of steady-state response is examined using Lyapunov’s stability theory. In addition, numerical analysis is employed to validate the results of analytical solutions based on the Runge–Kutta method. The multi-value and stability of periodic solutions are verified through stable periodic orbits. Detailed parametric studies show that proper selection of system parameters enables the system to stay in primary resonance or simultaneous resonance, and the state of the system can switch among different periodic motions, contributing to the optimization of fluid–structure interaction system.