Dynamics of an axially moving unidirectional plate partially immersed in fluid under two frequency parametric excitation

This paper analyzes characteristics of combination resonances and its stability for an axially moving plate partially immersed in fluid subjected to two frequency excitation. With a consideration to fluid-structure interaction, the equations of motion are established based on the classical thin plate theory. The Galerkin method is applied to discretize the vibration equations. Adopting multiple scales method to solve combination resonances, system's frequency-response equations under steady state motion are obtained. Based on Lyapunov's stability theory, judging conditions for the stability of equations are acquired. Through numerical example, this paper analyzes characteristics of combination resonances while the ratio of two excitation frequencies meet with 2:1, and further provides time history curves, frequency-response curves and phase trajectories in moving phase plane. Influences played on dynamic characteristics by parameters such as excitation amplitudes, axially moving speed, damping and detuning parameters are also discussed. Results reveal that, under two frequency excitation, system presents rich and interesting non-linear phenomena.