The fully coupled vibroacoustic interaction of sandwich panels is studied using the finite and the boundary element methods. The extent of radiation damping is quantified for various configurations based on both harmonic response analyses and modal analyses. The underlying nonlinear eigenvalue problem is solved using a projection method based on contour integration yielding the shifted (wet) eigenfrequencies, modal radiation loss factors, and air-loaded structural modes. The numerical results clearly illustrate the relevance of air-loading when studying the vibration of sandwich structures. Further, the numerically obtained estimates for radiation damping are compared to both theoretical expressions and experimental results found in the literature. Although good agreement is observed in general, the comparison indicates the limited applicability of commonly used theoretical expressions when coincidence occurs in a frequency range where the modes are still well separated. Moreover, possible sources of error when experimentally determining radiation damping are discussed in detail. The results presented in this paper provide deep insights into the phenomenon of acoustic radiation damping and help to estimate its relevance in future research.

Summary The solution of frequency dependent linear systems arising from the discretization of vibro‐acoustic problems requires a significant computational effort in the case of rapidly varying responses. In this paper, we review the use of a greedy reduced basis scheme for the efficient solution in a frequency range. The reduced basis is spanned by responses of the system at certain frequencies that are chosen iteratively based on the response that is currently worst approximated in each step. The approximations at intermediate frequencies as well as the a posteriori estimations of associated errors are computed using a least squares solver. The proposed scheme is applied to the solution of an interior acoustic problem with boundary element method (BEM) and to the solution of coupled structural acoustic problems with finite element method and BEM. The computational times are compared to those of a conventional frequencywise strategy. The results illustrate the efficiency of the method.

Spurious numerical damping in the collocation boundary element method is considered for plane sound waves in two-dimensional ducts subjected to rigid and absorbing boundary conditions. Its extent is quantified in both conditions based on a damping model with exponential decay, and meshes of linear and quadratic continuous elements are studied. An exponential increase of numerical damping with respect to frequency is found and the results suggest an upper bound for given element-to-wavelength ratios. The quantification of numerical damping is required for evaluation of meshes covering a large number of waves, and real damping phenomena can be prevented from overestimation.

Despite the potential and the increasing popularity of the boundary element method (BEM), modal analyses based on BEM are not yet put into engineering practice, mainly due to the lack of efficient solvers for the underlying nonlinear eigenvalue problem (EVP). In this article, we review a subspace iteration method based on FEAST for the solution of vibroacoustic EVPs involving the finite element method (FEM) and BEM. The subspace is obtained by applying a spectral projector and is computed by contour integration, whereas the contour is also used to subsequently solve the projected EVP by rational approximation. The computation of the projection matrices is addressed by two approaches. In the case of heavy fluid loading, we solve the underlying coupled linear systems by an iterative block Krylov method. In the case of light fluid loading, we exploit the fact that the coupled system admits accurate model order reduction solely based on the structural subsystem. Applications to a spherical shell and to a musical bell indicate that only a few contour points are required for an accurate solution without inducing spurious eigenvalues. The results are compared with those of a contour integral method and illustrate the efficiency of the proposed eigensolver.

The modern scope of boundary element methods (BEM) for acoustics is reviewed in this paper. Over the last decades the BEM has gained popularity despite suffering from shortcomings, such as fictitious eigenfrequencies and poor scalability due to its dense and frequency-dependent coefficient matrices. Recent research activities have been focused on alleviating these drawbacks to enhance BEM usability across industry and academia. This paper reviews what is commonly known as direct BEM for linear time-harmonic acoustics. After introducing the boundary integral formulation of the Helmholtz equation for interior and exterior acoustic problems, recommendations are given regarding the boundary meshing and treatment of the non-uniqueness problem. It is shown how frequency sweeps and modal analyses can be carried out with BEM. Further extensions for efficient modeling of large-scale problems, including fast BEM and solutions methods, are surveyed. Additionally, this review paper discusses new application areas for modern BEM, such as viscothermal wave propagation, surface contribution analyses, and simulation of periodically arranged structures as found in acoustic metamaterials.