An improved state-space method for coupled fluid–structure interaction analysis

Abstract

This paper presents an improved state-space method for incorporating fluid–structure interaction into structural acoustic analyses. Giordano and Koopmann [J. A. Giordano and G. H. Koopmann, “State-space boundary element-finite element coupling for fluid–structure interaction analysis,” J. Acoust. Soc. Am. 98, 363–372 (1995)] introduced a state-space approach for the coupled analysis of fluid-loaded structures. Giordano’s method employed a third-order interpolation of the fluid impedance, coupled with state-space formalism, permitting the direct eigenvalue analysis of the coupled system, and thereby yielding the fluid-loaded modes and natural frequencies. This is in contrast to the common technique of sweeping through a range of frequencies so as to identify the natural frequencies and mode shapes. The original state-space approach yielded system matrices of order 4N, where N is the number of degrees of freedom in the underlying model. Where Giordano’s method employed an interpolation based on surface velocity, the work presented in this paper uses an interpolation based on surface displacement. This simple modification to the method yields a system order of 3N, with concomitant reduction in the required computational effort, storage, etc. We further present a method to assess the validity of the resonances obtained through this approximation technique. The method is demonstrated here for an infinite 1-D panel in a baffle, using the surface variational principle and the method of assumed modes to develop the coupled fluid–structure problem. This structure and the analysis methods are not fundamental to the state-space development, and are used solely as vehicles to demonstrate the new formulation.