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Damping optimization of the excited mechanical system using dimension reduction

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  • Tomljanović, Zoran

Abstract

We consider a mechanical system excited by a periodic external force. The main problem is to determine the best damping matrix to be able to minimize the system average displacement amplitude. Damping optimization usually includes optimization of damping positions and corresponding damping viscosities. Since the objective function is non-convex, a standard optimization approach requires a large number of objective function evaluations. We first propose a dimension reduction approach that calculates approximation of the average displacement amplitude and additionally we efficiently use a low rank update structure that appears in the external damping matrix. Moreover, an error bound which allows determination of appropriate approximation orders is derived and incorporated within the optimization method. We also present a theoretical error bound that allows determination of effective damping positions. The methodology proposed here provides a significant acceleration of the optimization process. The gain in efficiency is illustrated in numerical experiments.

Suggested Citation

  • Tomljanović, Zoran, 2023. "Damping optimization of the excited mechanical system using dimension reduction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 24-40.
    • Handle: RePEc:eee:matcom:v:207:y:2023:i:c:p:24-40
    DOI: 10.1016/j.matcom.2022.12.017
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    References listed on IDEAS

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    1. Truhar, Ninoslav & Tomljanović, Zoran & Veselić, Krešimir, 2015. "Damping optimization in mechanical systems with external force," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 270-279.
    2. Truhar, Ninoslav & Tomljanović, Zoran & Puvača, Matea, 2019. "Approximation of damped quadratic eigenvalue problem by dimension reduction," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 40-53.
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