VALIDATION OF A DIRECT/INDIRECT HYBRIDFINITE ELEMENT - WAVE BASED METHOD FOR 3D STEADY-STATE ACOUSTIC ANALYSIS Bert Pluymers 1 , Bert Van Genechten 1 , Petra Silar 2 , Achim Hepberger 2 , Wim Desmet 1 1 K.U.Leuven, Department of Mechanical Engineering, division PMA, Celestijnenlaan 300B, B-3001 Leuven, Belgium 2 ACC Acoustic Competence Center G.m.b.H., Inffeldgasse 25, A-8010 Graz, Austria Email: bert.pluymers@mech.kuleuven.be SUMMARY: This paper discusses the use of wave based prediction methods for the analysis of steady-state inte- rior acoustic problems. Conventional element based prediction methods, such as the finite element method (FEM), are commonly used, but are restricted to low-frequency applications. The wave based method (WBM) is an alter- native deterministic technique which is based on the indirect Trefftz approach. The WBM is computationally very efficient, allowing the analysis of problems at higher frequencies. The efficiency of the WBM is most pronounced for problems of moderate geometrical complexity. For the analysis of problems with a more complex geometry, a hybrid finite element-wave based method is developed. This hybrid approach combines the strengths of the two methods, namely, the high computational efficiency of the WBM and the ability of the FEM to model problems of arbitrary geometrical complexity. This paper illustrates the enhanced efficiency of the WBM and its hybrid variant as compared to the conventional FEM by means of an experimental 3D interior cavity validation. KEYWORDS: vibro-acoustics, wave based method, hybrid method, Trefftz method, cavity analysis 1. INTRODUCTION The finite element method (FEM) [1] is most commonly used for the analysis of interior acoustic problems. The FEM makes use of a fine element discretization of the problem domain and applies simple polynomial shape functions to represent the dynamic response field within each element. Due to the approximating nature of the applied shape functions, element sizes need to decrease with raising frequency in order to maintain a reasonable prediction accuracy [2]. As a result, numerical model sizes grow with frequency and become prohibitively large at high frequencies [3]. However, due to the discretization into small elements, the FEM is able to model problems of arbitrary geometry. The wave based method (WBM) [4] is an alternative deterministic prediction technique which is based on an indirect Trefftz approach [5]. The method makes use of wave functions which are exact solutions of the governing differential equation to represent the dynamic response field. The resulting numerical Trefftz models are much smaller than the element based models and exhibit enhanced convergence behaviour [6]. These two features make the WBM applicable for the analysis of steady-state acoustic problems in a higher frequency range [7, 8]. However, in order to fully exploit the computational efficiency of the WBM, the problem geometry should be of moderate complexity. Recently, a family of hybrid methods has been developed. These hybrid finite element - wave based (FE-WB) methods [9, 10] combine the strength of the FEM, namely the ability to model problems of arbitrary geometry, with the enhanced computational efficiency of the WBM, and, as a result, are able to tackle arbitrarily shaped problems at higher frequencies [11, 12]. This paper discusses the application of both the WBM and the hybrid FE-WB method for the analysis of interior acoustic problems. The performance of both methods is illustrated by means of an experimental validation case. 2. PROBLEM DEFINITION Consider a steady-state interior acoustic problem, as shown in figure 1. A closed boundary surrounds a bounded fluid domain V , which is characterized by its speed of sound c and its ambient fluid density ρ 0 . The fluid domain is excited by an acoustic volume velocity point source q at circular frequency ω. The time-harmonic pressure response is given by p(r,t)= p(r,ω)e jωt with r =[xyz] T the position vector, T the transpose operator, j 1