The wave-based method （WBM） has been applied for the prediction of mid-frequency vibrations of fiat plates. The scaling factors, Gauss point selection rule and truncation rule are introduced to insure the wave model to converge. Numerical results show that the prediction tech- nique based on WBM is with higher accuracy and smaller computational effort than the one on FEM, which implies that this new technique on WBM can be applied to higher-frequency range.
A wave number method （WNM） is proposed to deal with the two-dimensional coupled structural-acoustic problem. Based on an indirect Trefftz approach, the displacement and the pressure response are approximated respectively by a set of wave functions, which exactly satisfy the governing equations and are independent of the size of the coupled system. The wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions, which arise from the external excitation. The weighting coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions and it is performed by applying the weighted residual formulation. The example is computed by the WNM and the BEM. The results show that, the WNM can attain the same accuracy and convergence as the BEM with less degrees of freedom.
Conventional element based methods for modeling acoustic problems are limited to low-frequency applications due to the huge computational efforts. For high-frequency applications, probabilistic techniques, such as statistical energy analysis （SEA）, are used. For mid-frequency range, currently no adequate and mature simulation methods exist. Recently, wave based method has been developed which is based on the indirect TREFFTZ approach and has shown to be able to tackle problems in the mid-frequency range. In contrast with the element based methods, no discretization is required. A sufficient, but not necessary, condition for convergence of this method is that the acoustic problem domain is convex. Non-convex domains have to be partitioned into a number of （convex） subdomains. At the interfaces between subdomains, specific coupling conditions have to be imposed. The considered two-dimensional coupled vibro-acoustic problem illustrates the beneficial convergence rate of the proposed wave based prediction technique with high accuracy. The results show the new technique can be applied up to much higher frequencies.
