Waveguide Finite Element Method

1 EXECUTIVE SUMMARY In a low frequency analysis of vibration in a built-up structure, the eigen frequencies and the corresponding eigenmodes help the understanding of how and why the structure behaves as it does. These eigen solutions are also useful in calculations of forced response by modal super-position procedures. However, as frequency increases there are more and more modes with increasingly complex forms and the relative information content in each of them decreases. The level and distribution of damping also becomes increasingly important. For such high frequency motion it is therefore beneficial to change view point and describe the motion in terms of damped waves, in particular so if the structure is relatively long in one direction. If, moreover, it has constant geometrical and material properties along this direction, wave solutions can be found with a versatile and numerically efficient method—the waveguide finite element method (FEM). As an alternative deterministic method to vibro-acoustic problems, waveguide FEM improves the efficiency especially for structure who has a waveguide like property. In addition, it provides insightful information on wave solutions, which in turn is used to evaluate parameters , e.g. group velocity, modal density, for statistical energy analysis (SEA) use. Both of these two characteristics make waveguide FEM a preferable method to bridge the gap between low and high frequencies, which satisfies the requirements of MID-FREQUENCY project to develop effective and efficient vibration and acoustic analysis, modeling and design methods. In this chapter, the concept and formulation of waveguide FEM is firstly introduced in section 3. In this section, two derivative methods are also described, spectral super element method (SSEM) and waveguide FEM with Rayleigh-Ritz's procedure. The derivative techniques complements waveguide FEM in finite length structure and further enhances the efficiency. Subsequently, the performance of waveguide FEM and its derivative methods are demonstrated in section 4. The applications are shown in four different aspects: dispersion curves, finite plate response, curved structure and sound transmission through built-up panels excited by a diffuse sound field. These benchmark illustrations show wide versatility and a good performance; the waveguide FEM should be useful in industrial practices.