Theoretical Analysis of Free Vibration and Transient Response of Rectangular Plate–Cavity System Under Impact Loading

This paper presents a theoretical method to solve the free vibration and transient responses of a rectangular plate–cavity system. The spectral collocation method was used to solve the resonant frequencies and corresponding mode shapes of rectangular plates based on Kirchhoff thin plate and Mindlin–Reissner thick plate theories. A linear velocity potential function was employed to model the fluid pressure applied to the plate surface. Unlike in previous studies, it was not assumed that the wet-mode shapes were the same as the dry-mode ones. Rather, the wet modes were assumed to be the superposition of the dry modes; then, the resonant frequencies and corresponding mode shapes of the wet modes could be obtained by solving the equations of the coupled system by exploiting the orthogonality of dry modes. Using dry modes’ orthogonality and superposition of the wet modes, the transient responses of the rectangular plate–cavity system under impact loading can be solved. A method for estimating the resonant frequencies of the coupled system is proposed based on parametric studies to determine the influence of the fluid properties and plate materials on resonant frequencies. As a result, the resonant frequencies and transient responses obtained from the proposed theoretical methods are in excellent agreement with those obtained from finite element analysis.