Application of the time dependent finite difference theory to the study of sound and vibration interactions in ducts

The time dependent finite difference theory is extended to the solution of the acoustic wave equation in rectangular ducts when acoustic/structural interactions are allowed at a duct wall. The treatment of the boundary condition which describes the coupling is examined, and the stability of the procedure is studied and found to depend on the nature of this coupling. The convergence of solutions is discussed as a function of the discretization of the solution domain, particularly at frequencies approaching resonance.