Theoretical analysis of vibration characteristics of rectangular thin plate fully immersed in fluid with finite dimension

In this paper, a theoretical method is developed to investigate the effect of a finite flow field on free vibration of a rectangular thin plate fully immersed in an incompressible and inviscid liquid. Rayleigh–Ritz method is applied to obtaining resonant frequencies and mode shapes of the wet plate, and different boundary conditions of a rectangular plate are discussed in this study, including fully clamped, free, and cantilever plates. The Galerkin method is utilized to deal with continuity conditions on the interface between plate and fluid and the beam method is applied to constructing mode shapes of a rectangular plate. Numerical results of the finite element method (FEM) are used to compare with the theoretical analysis on resonant frequencies and mode shapes and it shows the high accuracy of the proposed solution. In order to provide a convenient and accurate method to deal with the vibration characteristics of an immersed plate, the convergence of the Galerkin method is discussed and a modified computation method is presented. Finally, the effect of fluid's boundary on the resonating plate and the relation between the flow field and plate are investigated.