Extension of fictitious domain methods for vibroacoustic problems – Analysis of heterogeneous, foamed damping materials

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Even today, the prediction of the acoustical behaviour of components made of materials exhibiting a highly heterogeneous microstructure is a very demanding and challenging task. There are several reasons that make this problem so difficult to solve. On the one hand, the microstructure can only be accurately resolved if a large number of finite elements are deployed. On the other hand, all physically relevant interactions between the structural and fluid domain need to be taken into account. As mentioned before the body-fitted discretization of highly complex structures demands a large number of finite elements (degrees of freedom) and thus results in inacceptable computational times. Consequently, alternative methods, such as fictitious domain approaches, are required. Over the last years fictitious domain methods, such as the finite cell method (FCM), have proven their capabilities. To account for the vibroacoustic properties of microstructured materials these methods need to be extended. Therefore, the acoustic wave equation in the time domain or the Helmholtz equation in the frequency domain need to discretized by means of the FCM. Moreover, suitable coupling strategies that result in a weak or strong coupling need to be devised. Here, the main advantage of fictitious domain methods is the ability to take complex geometrical features into account while being able to straightforwardly superimpose cells with mechanical and fluidic properties. Thus, an efficient and robust strategy for vibroacoustic problems can be set up. Despite the application of nonconforming discretizations the numerical effort is still considerably large. Therefore, a second idea uses simplified numerical models based on homogenization techniques. To this end, the structure is assumed to consist of a homogeneous medium where the microstructure is neglected. In spite of this model simplification it is still expected to achieve reasonable results for specific applications. Besides the development of numerical methods a second focus is put on a comprehensive validation procedure. In this context, different experimental set-ups are deployed. To check the vibrational behavior of the structure under investigation a 3D laserscanning- vibrometer is used. In addition, the frequency-dependent acoustic parameters are measured by means of simple experimental set-ups such as an impedance tube and the results are compared to the numerically obtained values. As a last step the sound pressure radiation is tested in an anechoic room using microphone arrays and far field microphones. The acquired data are the foundation for illustrating the performance of the proposed methods.