On the use of a hybrid wave based-statistical energy ap- proach for the analysis of vibro-acoustic systems in the mid-frequency range K. Vergote, D. Vandepitte, W. Desmet K.U.Leuven, Department of Mechanical Engineering, Celestijnenlaan 300 B, B-3001, Heverlee, Belgium e-mail: karel.vergote@mech.kuleuven.be Abstract Most of the currently available numerical prediction techniques for the analysis of steady-state dynamic vibro-acoustic problems can be classified as being either deterministic or statistical approaches. The Finite Element Method (FEM), the most popular deterministic technique, is limited to the low-frequency range due to its sensitivity to interpolation and pollution errors. The statistical methods, of which the Statistical Energy Analysis (SEA) is most know, are limited to the high-frequency range due to their underlying assumptions. Between the low- and high-frequency ranges there is a relatively wide mid-frequency-range, in which some of the structural subsystems fulfill the requirements for the statistical approach and some others do not (yet). Recently, a hybrid deterministic-statistical framework which combines FE and SEA models has been developed by Shorter and Langley. However, the computational load associated with the FE models still limits the use of this method. In this paper, a hybrid framework is proposed which couples Trefftz-based deterministic models with statistical SEA models. The framework is used to couple SEA models with the recently developed Wave Based Method (WBM) of which the computational efficiency can be exploited to reduce the computational load as compared to the hybrid FE-SEA. 1 Introduction Most of the current numerical prediction techniques for steady-state dynamic analysis of vibro-acoustic systems can be classified as either deterministic or statistical approaches. The use of deterministic methods, like the standard Finite Element Method (FEM) [1], is limited to the so- called low-frequency range. The reason for this is twofold. On the one hand, the computational effort of the deterministic techniques typically increases exponentially with frequency, due to an increase in the spatial variation of the dynamic field variables [2]. On the other hand, the response of a system becomes more and more sensitive to small perturbations of its geometrical and material properties as the frequency increases, which introduces a significant level of scatter on the response of nominally identical systems [3]. The statistical methods, like the Statistical Energy Analysis (SEA) [4] are based on energy considerations. They are typically used for the prediction of the mean and variance of the dynamical response of an ensemble of nominally identical systems. However, the underlying assumptions, e.g. a high modal overlap and modal density, limit their use to high-frequency applications. In-between the low- and the high-frequency ranges there is a relative wide mid-frequency gap, for which currently no mature simulation techniques are available. Recently, an alternative deterministic modeling approach, the so-called Wave Based Method (WBM) [5], has been proposed. This indirect Trefftz method uses wave functions, which are exact solutions of the governing differential equations to describe the dynamic 2437