SOLUTION OF COUPLED ACOUSTIC PROBLEMS: A PARTIALLY OPENED CAVITY COUPLED WITH A MEMBRANE AND A SEMI-INFINITE EXTERIOR FIELD

There have been many attempts to understand the coupling phenomena between a solid structure and the surrounding fluid. However, the studies were restricted to interaction only between a structure and a finite cavity or a structure and acoustic field of infinite size. The system that we have studied has a structure that faces both a cavity of finite size and an external field of semi-infinite size. We also allow a hole, which can directly interact with the cavity as well as the external field. This configuration, therefore, provides two different interactions, or communication means. One is the finite structure and the other is the hole of finite size. This paper studies as to how these two components interact with the other two systems: the finite cavity covered by the structure and the hole, and the semi-infinite fluid. For simplicity, a two-dimensional and partially opened cavity coupled with a membrane and an exterior field was selected. The solution has to be found by solving a boundary value problem, but this case has to do with the boundaries that have two different conditions: one is the membrane and the other is the hole. The solution has been found in terms of the modal functions that satisfy the boundary conditions of finite cavity, membrane and hole. Non-dimensional coupling coefficients are obtained from the solution. The results exhibit that the coupling effect gives additional peaks and troughs in the averaged pressure of the cavity. These peaks and troughs are symmetrically arranged with respect to Helmholtz frequency of the cavity. The strong coupling occurs at the trough frequencies where the membrane interacts actively with the cavity and the exterior field.