Study on model reduction for position optimization of acoustic black holes. Issue 1 (14th December 2021)

• Record Type: Journal Article
• Authors: Meyer, Christian H.; Lerch, Christopher; Rothe, Sebastian; Hoffmann, Steffen; Langer, Sabine C.; Lohmann, Boris; Rixen, Daniel J.
• Editors: Kaliske, M.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 21:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-12-14
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202100123
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Noise radiation of plate structures is a common problem with the design of machines in mechanical engineering. Noise can be reduced by designing passive damping measures. One of these measures can be the application of an 'acoustic black hole' (ABH). It is a targeted adaptation of the thickness of plate‐like structures to direct the acoustically critical bending waves to a certain region – the ABH. There, an applied damping material can dissipate the vibration energy very efficiently. A major challenge in design of this measure is to find an optimal position of the ABH with respect to low vibrations. Optimization can be a tedious task, especially for complex industrial geometries where the dicretized equations of motion can have millions DoF. This contribution shows on the example of a study on a rectangular plate how model reduction can help to reduce the computational costs for this position optimization. Three different reduction methods are shown: First, a condensation of internal state variables from the viscoelastic evolution equations via Schur complement. Second, modal truncation applied to the condensed equations from the first method and third, moment matching applied to the full order model. Computed mean squared‐admittance levels are compared to show the accuracy of the methods. Speed‐up and accuracy results show that Schur complement and moment matching are promising approaches while a naive modal truncation can lead to wrong results.