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Main Title: On the detection of artifacts in Harmonic Balance solutions of nonlinear oscillators
Author(s): Wagner, Utz von
Lentz, Lukas
Type: Article
Language Code: en
Abstract: Harmonic Balance is a very popular semi-analytic method in nonlinear dynamics. It is easy to apply and is known to produce good results for numerous examples. Adding an error criterion taking into account the neglected terms allows an evaluation of the results. Looking on the therefore determined error for increasing ansatz orders, it can be evaluated whether a solution really exists or is an artifact. For the low-error solutions additionally a stability analysis is performed which allows the classification of the solutions in three types, namely in large error solutions, low error stable solutions and low error unstable solution. Examples considered in this paper are the classical Duffing oscillator and an extended Duffing oscillator with nonlinear damping and excitation. Compared to numerical integration, the proposed procedure offers a faster calculation of existing multiple solutions and their character.
Issue Date: 6-Sep-2018
Date Available: 19-Mar-2020
DDC Class: 510 Mathematik
Subject(s): nonlinear dynamics
harmonic balance method
Duffing oscillator
Journal Title: Applied Mathematical Modelling
Publisher: Elsevier
Publisher Place: Amsterdam [u.a.]
Volume: 65
Publisher DOI: 10.1016/j.apm.2018.08.013
Page Start: 408
Page End: 414
EISSN: 1872-8480
ISSN: 0307-904X
Appears in Collections:FG Mechatronische Maschinendynamik » Publications

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