Efficient deterministic and stochastic simulations of large-scale vibroacoustic models

Numerical finite element simulations have become an indispensable part of early product development. In preliminary interior noise assessments of aircraft cabins, for example, these simulations help in reducing development costs and aid in increasing passenger comfort. In order to obtain a meaningful noise assessment, models need to have a high-fidelity. With recent advances in modeling techniques the complexity of models with which such a noise assessment can be conducted is ever increasing. The problem with such complex and often times large-scale models is the computational efficiency. Interior noise simulations require substantial amounts of computational resources, which can lead to prohibitive computation times. In an early design stage, exact values of many important parameters are not known, highlighting the need for stochastic methods, which often demand multiple evaluations of similar models. Multiple evaluations of a computationally intensive model lead to even higher computational effort. In order to still conduct noise assessments and vibroacoustic simulations, more efficient methods to evaluate interior noise problems are needed. Therefore, the following thesis investigates several ways of increasing the computational efficiency for deterministic and stochastic vibroacoustic problems. In order to test novel methods not only on academic but also on increased fidelity models, the efficient methods are tested for three models, namely a benchmark plate cavity model, a stiffened airframe with cavity model and lastly, a high-fidelity aircraft segment model. Since the finite element method yields a sparse linear system of equations, the first part of this thesis concerns itself with efficiently solving this underlying system. Therefore, several direct and iterative solving techniques are examined and applied to the different models. It is shown that the special characteristics of the vibroacoustic problem, such as ill-conditioning, lead to inefficiency when it comes to applying even preconditioned iterative solving techniques and show that direct solvers perform strongly on vibroacoustic models. The restructuring of sparsity patterns of the system matrices is also examined and can lead to increased computational efficiency. For an aircraft cabin noise assessment, the turbulent boundary layer is an important source of excitation. However, it contains some inherent uncertainties, which leads to a stochastic system, which has to be evaluated multiple times for different excitations. In this thesis, an efficient method that combines low-rank approximations of covariance matrices and model order reduction is developed to efficiently predict the first two moments of the distribution of the solution vector due to uncertain loads. The method shows promising results for the considered models and can lead to a significant reduction in computational cost. Lastly, the inclusion of uncertain material parameters is examined. Here it is shown that low-rank approximations of covariance matrices can be interpolated via subspace interpolation. The interpolation leads to reduced computational effort for obtaining covariance matrices and therefore an important part of the output distribution. However, this thesis also shows the limits of the presented methods and discusses that the bad conditioning of the vibroacoustic system can lead to an increased methodological error for different frequencies. Nonetheless, this thesis introduces valuable methods that can be extended in the future to yield more efficient and robust vibroacoustic simulations.