On the coupled vibration of an ideal fluid with a linear elastic structure

Abstract

The purpose of this paper is to analyse theoretically and numerically the coupled vibration of an ideal fluid with a linear elastic structure. It is proved in the paper that the natural frequencies of the coupled vibration do exist and are all real positive. The paper presents an efficient method to transform a coupled fluid-structure system to the structure with added mass and the vibrational analysis of the former is replaced by the latter in vacuum only. Numerical solution is outlined for the transformed problem and a compact frequency equation is derived in which fluid variables do not appear. This simplifies the analysis significantly. A convergent proof has been given to guarantee the reliability of the solution. The paper also offers a general algorithm bombined with Ritz method, boundary element method, and finite element method to analyse the transformed problem. Based on this algorithm, one can apply a known structural analysing program, with a little modification, to solve many different kinds of fluid-structure coupling problems. Some numerical results are given to show the efficiency of the algorithm.