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Main Title: On some aspects of the dynamic behavior of the softening Duffing oscillator under harmonic excitation
Author(s): Wagner, Utz von
Lentz, Lukas
Type: Article
Language Code: en
Abstract: The Duffing oscillator is probably the most popular example of a nonlinear oscillator in dynamics. Considering the case of softening Duffing oscillator with weak damping and harmonic excitation and performing standard methods like harmonic balance or perturbation analysis, zero mean solutions with large amplitudes are found for small excitation frequencies. These solutions produce a ”nose-like” curve in the amplitude–frequency diagram and merge with the inclining resonance curve for decreasing (but non-vanishing) damping. These results are presented without any additional discussion in several textbooks. The present paper discusses the accurateness of these solutions by introducing an error estimation in the harmonic balance method showing large errors. Performing a modified perturbation analysis leads to solutions with non-vanishing mean value, showing very small errors in the harmonic balance error analysis.
URI: https://depositonce.tu-berlin.de/handle/11303/10946
http://dx.doi.org/10.14279/depositonce-9836
Issue Date: 26-Feb-2016
Date Available: 20-Mar-2020
DDC Class: 531 Klassische Mechanik, Festkörpermechanik
Subject(s): softening Duffing oscillator
harmonic balance
perturbation analysis
License: http://rightsstatements.org/vocab/InC/1.0/
Journal Title: Archive of Applied Mechanics
Publisher: Springer
Publisher Place: Berlin ; Heidelberg [u.a.]
Volume: 86
Publisher DOI: 10.1007/s00419-016-1123-y
Page Start: 1383
Page End: 1390
EISSN: 1432-0681
ISSN: 0939-1533
Appears in Collections:FG Mechatronische Maschinendynamik » Publications

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