Christopher Jelich, M.Sc.

Assessing the vibroacoustic behavior of thin-walled lightweight structures is an important aspect of designing quiet machines and vehicles. The advances in numerical modeling techniques allow accurate predictions of vibroacoustic quantities such as radiated sound power and transmission loss ahead of manufacturing. Including them in design optimization and uncertainty analyses has become a common engineering practice in recent decades. However, repeatedly evaluating vibroacoustic quantities for different parameters and various frequencies poses a significant computational challenge. This especially holds for the popular choice of the combined approach of finite element method (FEM) and boundary element method (BEM) for the analysis of structures in the low frequency range.

The research project targets to develop an efficient scheme for solving fully coupled FEM-BEM structural acoustic problems at predefined parameter and frequency points. The key challenge lies in the consideration of implicit parameter dependence, i.e. non-affine parameterized systems. We address this by parametric model order reduction and propose a greedy reduced basis scheme. The scheme approximates the solution at the predefined points by linear combination of a reduced basis. It iteratively expands the basis by adding the response at the parameter and frequency point that is currently worst approximated. Our greedy reduced basis scheme finds the solution at all predefined parameter and frequency points based on the evaluation of a few high-fidelity solutions. The convergence of the solution is visualized in Figure 1 for an academic example with two parameters: Young’s modulus and frequency.

Jelich, C., Baydoun, S. K., Voigt, M., Marburg, S. (2021): A greedy reduced basis algorithm for structural acoustic systems with parameter and implicit frequency dependence, submitted to International Journal of Numerical Methods in Engineering.