Date
2021-12-14Subject
620 Engineering Periodische BewegungNichtlineares dynamisches SystemNäherungsverfahrenFinite-Differenzen-MethodeHarmonische BalanceMetadata
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On a hybrid approximation concept for self-excited periodic oscillations of large-scale dynamical systems
Abstract
When approximating periodic solutions in the context of large-scale dynamical systems involving strong local nonlinearities, efficiency is of special interest. Hence, the literature suggests a combination of two approximation methods for increasing the ratio of computational cost to accuracy. Within this contribution, a combination of Finite Difference and Harmonic Balance method is proposed. Due to the usage of Harmonic Balance it is shown, that the resulting equations only depend on the degrees of freedom that are affected by nonlinear forces. As an application, a self-excited limit cycle of a chain of oscillators is approximated and results are compared against numerical time integration to highlight qualitative accuracy.
Citation
In: Proceedings in applied mathematics and mechanics (PAMM) Volume 21 / Issue 1 (2021-12-14) eissn:1617-7061Sponsorship
Gefördert im Rahmen des Projekts DEALCitation
@article{doi:10.17170/kobra-202112165264,
author={Kappauf, Jonas and Hetzler, Hartmut},
title={On a hybrid approximation concept for self-excited periodic oscillations of large-scale dynamical systems},
journal={Proceedings in applied mathematics and mechanics (PAMM)},
year={2021}
}
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2022-02-15T17:11:42Z 2022-02-15T17:11:42Z 2021-12-14 doi:10.17170/kobra-202112165264 http://hdl.handle.net/123456789/13623 Gefördert im Rahmen des Projekts DEAL eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ 620 On a hybrid approximation concept for self-excited periodic oscillations of large-scale dynamical systems Aufsatz When approximating periodic solutions in the context of large-scale dynamical systems involving strong local nonlinearities, efficiency is of special interest. Hence, the literature suggests a combination of two approximation methods for increasing the ratio of computational cost to accuracy. Within this contribution, a combination of Finite Difference and Harmonic Balance method is proposed. Due to the usage of Harmonic Balance it is shown, that the resulting equations only depend on the degrees of freedom that are affected by nonlinear forces. As an application, a self-excited limit cycle of a chain of oscillators is approximated and results are compared against numerical time integration to highlight qualitative accuracy. open access Kappauf, Jonas Hetzler, Hartmut doi:10.1002/pamm.202100143 Periodische Bewegung Nichtlineares dynamisches System Näherungsverfahren Finite-Differenzen-Methode Harmonische Balance publishedVersion eissn:1617-7061 Issue 1 Proceedings in applied mathematics and mechanics (PAMM) Volume 21 false e202100143
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