Vibration and stability analysis on the water entry process of a thin plate

In this study, the stability and vibration characteristics of a thin plate in the water entry process are investigated. In the water entry process, the mass, damping and stiffness of the system change continuously with time to make the stability of the fluid-structure system exhibit the time-varying characteristics. Based on the nonlinear plate theory and the linear potential flow theory, the equation of motion of the plate interacting with external airflow and water flow is established. For the linear equation, the changes of the natural frequencies of the plate entering the water are researched by applying the generalized eigenvalue method, from which the stability of the system is analyzed. For the nonlinear equation, the displacement time responses and phase portraits of the plate subjected to harmonic excitation are discussed by numerical simulations. When the plate enters the water, the stability of the plate becomes worse. The range of the external excitation frequency makes significant effects on the vibration characteristics of the plate. The plate falls into instability with the entry velocity increasing. Finally, the effects of the fluid density, the aspect ratios and the length-to-thickness ratios of the plate on the stability and vibration characteristics of the plate are discussed.