Abstract

In many practical engineering applications there is the interaction of distinct domains, where coupling effects are important in assessing the structural response. A particular case is given by the interaction between a vibrating structure and a reservoir, with the latter conveniently simplified to an acoustic model. This paper presents a closed form analytical solution to the dynamic interaction problem of a framed structure and a two dimensional acoustic cavity system. Initially, eigenvalues and eigenmodes are obtained accurately and then individual contributions of each mode are combined to build the structural dynamic response. A fourth order Runge‐Kutta numerical integration routine is applied on the evaluation of relative displacements. Finally, practical applications are given, where the proposed method is employed effectively in the solution of sine and seismic excitations. These results are compared to finite element models, with an excellent agreement achieved by the proposed procedure. It is also verified that the fundamental mode shape governs the dynamic response, enabling the use of simplified expressions for the generalized parameters. Immediate results include validation of numerical solutions as well as parametric studies of the involved variables. The proposed procedure can be extended for different sets of boundary conditions.