Solution of the Dynamic Interaction Problem between a Framed Structure and an Acoustic Cavity Using Imposed Deformation Functions at the Interface

This article presents an analytical procedure for solution of the dynamic interaction problem of a vibrating framed structure connected to a bidimensional cavity, containing an acoustic fluid. Initially the pressure solution for the fluid domain is developed, using the separation of variables technique. In a next step, this solution is applied to an entirely open cavity and to a closed cavity in the transversal direction, both containing a vibrating boundary with an arbitrary deformation. The generalized parameters of the structure (mass, rigidity, and force) are obtained by means of the virtual work principle, with the generalized force represented by the dynamic pressures acting on the interface. The dynamic equilibrium equation of the system is established for an imposed deformation, making a parametric study of the involved variables possible. Finally, it is demonstrated that this procedure can be generalized, allowing the construction of practical abacuses for other boundary conditions of both the structure and the cavity, and that these results allow a reasonable interpretation of the coupling regions, including the prediction of added mass and added stiffness effects, as well as corresponding frequencies and mode shapes of the coupled problem.