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Application of a Krylov subspace method for an efficient solution of acoustic transfer functions
(2021)
Solving acoustic radiation problems, arising from systems including fluid–structure interaction, is of interest in many engineering applications. Computing frequency response functions over a large frequency range is a concern in such applications. A method which solves the Helmholtz equation for multiple frequencies in one step is the matrix-Padé-via-Lanczos connection for unsymmetric systems, as presented by Wagner et al. [1]. The present work is based on Ref. [1] and presents a method for efficiently computing frequency responses over a frequency range for coupled structural-acoustic problems, where the structure and the acoustic near field are discretized with finite elements and an analytical Dirichlet-to-Neumann map approximates the far field. The method is based on a Krylov-subspace projection technique which derives a matrix-valued Padé approximation for a restricted area in the near field and the pressure field on a spherical boundary. On the spherical boundary, where the finite domain is truncated, the non-local modified Dirichlet-to-Neumann operator is applied as a low-rank update matrix. The present contribution extends this method and incorporates new techniques for a more stable model reduction through the Lanczos algorithm and a novel weighted adaptive windowing technique. Further, structural damping is incorporated, for computing the acoustic radiation of a harmonically excited plate. These computed results are compared with acoustic measurements in an anechoic chamber and verified with computational results obtained with a commercial code that uses the perfectly matched layer method.
This work addresses the efficient numerical simulation of time-harmonic vibroacoustic problems in unbounded domains, with a focus on fluid-structure interaction. The underlying mathematical model is a second-order dynamical system arising from the coupling of structural and acoustic domains, incorporating material damping effects, relevant in structural acoustics and noise control applications. A central novelty of the proposed method is its unified computational framework that supports two distinct strategies for treating unbounded fluid domains: (1) non-local absorbing boundary conditions based on Dirichlet-to-Neumann map, and (2) infinite elements, which extend the computational domain rather than truncate it. Both approaches are integrated into a consistent formulation that enables flexible and accurate modeling of exterior wave propagation. To efficiently evaluate frequency-domain transfer functions, the method employs model order reduction using the Padé-via-Lanczos technique. While this algorithm typically targets first-order systems, the present approach uses a Schur complement strategy to reduce the second-order system in a way that maintains computational efficiency and storage requirements comparable to first-order formulations. Importantly, the framework seamlessly embeds both interior structural damping and the additional dissipation introduced by the acoustic-domain truncation into the model-order reduction process. The exterior acoustic field is represented via spherical harmonic expansions, with expansion coefficients computed from the reduced system. Numerical results demonstrate the method’s accuracy, efficiency, and scalability, making it well-suited for high-fidelity vibroacoustic analysis in unbounded domains.
Beim Kauf eines Pkw wird der akustische Qualitätseindruck eines Fahrzeugantriebstrangs stetig relevanter. Die wahrgenommene Geräuschqualität des Motoraggregates nimmt hierbei eine Schlüsselrolle ein. Aufgrund der Ausprägung einzelner Störgeräusche wird jene Geräuschqualität negativ beeinflusst. Diese als unangenehm empfundenen Geräuschkomponenten gilt es im Rahmen der Fahrzeugentwicklung
weiter zu reduzieren, wobei die Identifikation und Bewertung störender Geräuschanteile am Motorgesamtgeräusch Voraussetzungen für eine effektive Akustikoptimierung sind. Vor allem das impulshafte Tickergeräusch wird bei Otto-DI-Motoren als besonders lästig eingestuft, weswegen dieser Beitrag darauf abzielt, die tickernden Geräuschanteile aus dem Gesamtgeräusch zu analysieren und zu bewerten. Hierzu wurde eine empirische Formel entwickelt, welche die tickernden Geräuschanteile in ihrer Intensität in Grenzen einstufen kann. Diese ist rein empfindungsbasiert und besteht aus der Impulshaftigkeit, der Lautheit sowie der Schärfe des Motorgesamtgeräusches.
Wie auch bei anderen psychoakustischen Bewertungsskalen wurde die Benotung von 1 (sehr tickernd) bis 10 (nicht tickernd) vorgenommen. Anhand von Hörversuchen mithilfe einer Expertenjury konnte die Tickergeräuschbewertungsformel anschließend verifiziert werden. Hiernach kann präzise ausgesagt werden, in welchen Motorkennfeldbereichen das Tickergeräusch die Angenehmheit des Motorgesamtgeräusches untergräbt.
