Coupled BE–FE based vibroacoustic modal analysis and frequency sweep using a generalized resolvent sampling method

• Published in: Computer methods in applied mechanics and engineering Vol. 345; pp. 518 - 538
• Main Authors: Liang, Tengfei, Wang, Junpeng, Xiao, Jinyou, Wen, Lihua
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2019; Elsevier BV
• Subjects: Acoustic coupling; Algorithms; Boundary element method; Computation; Coupled boundary and finite element method; Finite element method; Frequency analysis; Frequency ranges; Frequency response; Frequency sweep; Industrial applications; Mathematical analysis; Modal analysis; Nonlinear analysis; Numerical methods; Sampling; Sound–structure interaction; Subspaces; Coupled boundary and finite element method; Frequency sweep; Modal analysis; Sound–structure interaction
• DOI: 10.1016/j.cma.2018.09.038
• ISSN: 0045-7825

For several decades, the coupled boundary element and finite element (BE–FE) approach has been recognized as a potential tool for modeling sound–structure interaction problems. However, till now, the frequency response computation, frequency sweep and modal analysis, which are key ingredients for the characterization of a vibro-acoustic system, are still challenging due to the lack of effective numerical methods to deal with the complicated coupled matrices. We contribute to this subject in the following three aspects. Firstly, a fast coupled method is established using the acoustic BEM accelerated by the kernel-independent directional algorithm and the conventional structural FEM. The method uses quadratic elements and allows for non-matching meshes across the interfaces, and thus is accurate and versatile in a wide frequency range. Secondly, based on the Keldysh theorem of analytic matrix functions, a generalized resolvent sampling method is developed to construct the response subspaces for given excitations in a certain frequency range. By using the resulting response subspaces, a projection-based fast frequency sweep algorithm and a nonlinear eigensolver for modal analysis have been developed. Lastly, a numerical scheme for fast computation of the reduced system matrices in the fast sweep algorithm and the eigensolver is proposed, and several rules for practical applications of the proposed algorithms are discussed. The computational performance of the proposed methods has been tested and confirmed by academic benchmarks and a large-scale industrial application.