Hydroelastic vibration of two annular plates coupled with a bounded compressible fluid

A theoretical study on a linear hydroelastic vibration of two annular plates coupled with a bounded fluid is presented. The proposed method, based on the Rayleigh-Ritz method and the finite Hankel transform, is verified through a finite element analysis by using a commercial computer code, with an excellent accuracy. It is assumed that plates with an unequal thickness and with an unequal inner radius are clamped along their edges and an inviscid compressible fluid fills the space between the annular plates and the outer rigid vessel. When the two annular plates are identical, distinct in-phase and out-of-phase modes are observed. By increasing the difference in the plate thickness, the symmetric in-phase and out-of-phase modes with respect to the middle plane of the system are gradually shifted to pseudo in-phase and out-of-phase modes, and eventually they are changed to mixed modes. It is found that the natural frequencies decrease with an increase of the fluid compressibility, and additional modes due to a fluid concentration are observed when the plates are coupled with a compressible fluid. The fluid compressibility effect on the natural frequency is dominant in the out-of-phase modes and the higher modes. Also, the effects of the fluid thickness or the distance between the plates and the inner radius of the plates on the natural frequencies of the wet modes are investigated. (c) 2006 Elsevier Ltd. All rights reserved.