An efficient method for vibration and stability analysis of rectangular plates axially moving in fluid

An efficient method is developed to investigate the vibration and stability of moving plates immersed in fluid by applying the Kirchhoff plate theory and finite element method. The fluid is considered as an ideal fluid and is described with Bernoulli’s equation and the linear potential flow theory. Hamilton’s principle is used to acquire the dynamic equations of the immersed moving plate. The mass matrix, stiffness matrix, and gyroscopic inertia matrix are determined by the exact analytical integration. The numerical results show that the fundamental natural frequency of the submersed moving plates gradually decreases to zero with an increase in the axial speed, and consequently, the coupling phenomenon occurs between the first- and second-order modes. It is also found that the natural frequency of the submersed moving plates reduces with an increase in the fluid density or the immersion level. Moreover, the natural frequency will drop obviously if the plate is located near the rigid wall. In addition, the developed method has been verified in comparison with available results for special cases.