Free vibration of an elastically restrained circular plate coupled with fluid

摘要

This paper presents an analytical method for the hydroelastic vibration of an elastically restrained circular plate in contact with bounded fluid. The fluid is inviscid and incompressible while the circular plate satisfies Kirchhoff's thin plate theory. The plate displacements are expanded in series of mode shapes of the same plate in vacuo, and the fluid motion is described by velocity potential function, which satisfies the fluid boundary conditions and compatibility requirement on the coupled surface. On basis of the equilibrium equation of plate, the eigenvalue equation of the system is established by using orthogonality of dry mode shapes. The results are in excellent agreement with the ones calculated by finite element method. Furthermore, effects of the spring stiffness and fluid depth on free vibration characteristics of the circular plate are investigated.