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

即使在今天，预测由具有高度异质微结构的材料制成的部件的声学行为也是一项非常苛刻和具有挑战性的任务。有几个原因使这个问题如此难以解决。一方面，只有在部署大量有限元的情况下，才能准确地解析微观结构。另一方面，需要考虑结构域和流体域之间的所有物理上相关的相互作用。如前所述，高度复杂结构的贴体离散化需要大量的有限元(自由度)，从而导致不可接受的计算时间。因此，需要其他方法，例如虚构的领域方法。在过去的几年里，虚拟区域方法，如有限元方法(FCM)，已经证明了它们的能力。为了考虑微结构材料的振动声学特性，这些方法需要扩展。因此，需要对时域的声波方程或频域的Helmholtz方程进行FCM离散化。此外，还需要设计适当的耦合策略，以导致弱耦合或强耦合。这里，虚拟区域方法的主要优点是能够考虑复杂的几何特征，同时能够直接叠加具有力学和流体性质的单元。因此，可以建立一种有效和稳健的策略来解决振动声学问题。尽管应用了非协调离散，但数值计算的工作量仍然相当大。因此，第二种想法使用基于均匀化技术的简化数值模型。为此，假设结构由均匀的介质组成，其中忽略微结构。尽管对模型进行了简化，但仍有望在具体应用中取得合理的结果。除了数值方法的发展外，第二个重点是全面的验证程序。在这方面，部署了不同的实验装置。为了检查结构的振动特性，使用了三维激光扫描测振仪。此外，利用简单的实验装置，如阻抗管，测量了声学参数随频率的变化，并将测量结果与数值结果进行了比较。作为最后一步，在消声室中使用麦克风阵列和远场麦克风测试声压辐射。所获得的数据是说明所提出方法的性能的基础。

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.