A Finite Element Approach to the Prediction of Sound Transmission through Panels with Acoustic Resonators

Previous research by the authors has shown that sound radiated by a vibrating panel can be reduced considerably by using tuned acoustic resonators. The length of the tube resonators determines the frequency range in which sound is reduced. The shape of the spectrum is determined by the ratio of the cross-sectional areas of the resonators to the area of the panel. Maximum sound reduction is achieved if the volume velocities at the surface of the vibrating panel and those at the entrance of the resonators are equal in magnitude but opposite in phase. Up to now, the effect of the resonators on the radiated sound has been studied with a one-dimensional analytical model. In this paper, a three-dimensional acousto-elastic model is developed using the finite element method. The purpose of this model is to study the influence of the flexibility and the boundaries of the panel, as well as the presence of rooms behind and in front of the panel on the sound transmission. Modelling the complete structure, including the resonators and the interaction with the air inside the resonators, is computationally expensive. Therefore, an alternative approach is developed. Because of the repetitive pattern of resonators in the panel, the structural part of the panel is modelled with superelements. To enable coupling between the structural part of the model and the air behind and in front of the panel, a new interface element is derived. The formulation of this interface element also includes the acoustic behaviour of the resonators. Sound transmission loss calculations are made for one configuration and the results are compared with the results obtained with a one-dimensional analytical model. INTRODUCTION Previously, the effect of tube resonators on the sound radiated by a vibrating panel was studied with a one-dimensional analytical model [2]. It was shown that the radiated sound can be M.H.C. Hannink, R.M.E.J. Spiering, Y.H. Wijnant and A. de Boer reduced considerably by tuning the length and the radius of these resonators. In this paper, an acousto-elastic model, based on the finite element method (FEM), is developed to study the effect in a three-dimensional setup. The model can be used to calculate the sound transmission loss of panels with resonators for different geometries and boundary conditions. Figure 1 shows a resonator panel for the situation studied in this paper. At the incident side, the panel is acoustically excited by applying a harmonic pressure perturbation on the panel. The sound is transmitted into a room with sound absorbing walls. Using a fully coupled FEM model of the complete structure, the air inside the resonators, and the room, is computationally expensive. Therefore, an alternative approach is developed.