A modal method for coupled fluid-structure interaction analysis

A modal method is developed for solving, analyzing, and controlling vibration and sound radiation of coupled fluid-structure systems. The method recasts the coupled equation of a coupled fluid-structure system in the classical matrix structural dynamic equation by modeling the acoustic load vector as direct linear function of the acceleration, velocity, and displacement vector. With the Rayleigh damping assumption of the coupled fluid-structure system the resulting equation can be uncoupled via a transformation to modal coordinates and analyzed by solving independent equations of single degree of freedom system. The modal radiation efficiencies, effect of modal interaction on sound radiation, mode shapes, and modal control of the coupled fluid-structure system are presented and discussed. Numerical example of the vibration and sound radiation of a fluid-loaded stiffened plate is presented solely as a vehicle to demonstrate the method. The comparisons in terms of computed sound power of the present method with the standard coupling method and available published results show a very good agreement. The mode shapes and the self- and mutual-radiation efficiencies of modes of the fluid-loaded stiffened plate are given and discussed. The study of the effect of modal interaction on sound power shows that the power radiated by a single mode is to increase total radiated power and the interaction of modes may lead to an increase or a decrease or no change in the total radiated power. Numerical results also show that the modal control achieves a fluid-loaded stiffened plate.