Wave based method for mid-frequency analysis of coupled vibro-acoustic problem

Conventional element based methods for modeling acoustic problems are limited to low-frequency applications. Recently, wave based method has been developed which is based on the indirect Trefftz approach. In contrast with the finite element method, in which the structural and acoustic domains are discretized into small elements and the dynamic equations are solved within each element using simple, approximate shape functions, the field variable distributions within the entire of the structural or acoustic domains are approximated in terms of wave functions, which are exact solutions of the homogeneous parts of the dynamic equations and particular solutions of the inhomogeneous dynamic equations are added. The contributions of the wave functions are determined by applying the boundary conditions in a weighted residual formulation or least-squares formulation. Then, direct differentiation of the expressions with respect to design variables leads to expressions of the sensitivities. A comparison with the element based method illustrates that the prediction method has a substantially higher convergence rate, which makes the method applicable for accurate coupled vibro-acoustic predictions up to mid-frequency.