On a hybrid approximation concept for self‐excited periodic oscillations of large‐scale dynamical systems. Issue 1 (14th December 2021)

• Record Type: Journal Article
• Authors: Kappauf, Jonas; Hetzler, Hartmut
• 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.202100143
• Languages: English
• ISSNs: 1617-7061

Abstract

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.