When does the method of harmonic balance give a correct prediction for mechanical systems?
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Date
2023Type
- Journal Article
Abstract
We investigate the validity of the harmonic balance method for nonlinear, multi-degree-of-freedom mechanical system with time-periodic forcing and linear damping. We provide conditions under which an approximate periodic solution obtained from this method correctly signals the existence of an actual periodic response of the full nonlinear system. These conditions improve classical results from the literature and provide a-priori computable conditions for the validity and accuracy of the harmonic balance method. Our proof is based on Newton's method in Banach spaces for an appropriately chosen functional. We also derive error bounds for the harmonic balance method and illustrate these on mechanical examples. Show more
Publication status
publishedExternal links
Journal / series
Applicable AnalysisVolume
Pages / Article No.
Publisher
Taylor & FrancisSubject
Harmonic balance; Newton's method; Periodic solution; Nonlinear mechanical systemOrganisational unit
03973 - Haller, George / Haller, George
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