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Main Title: On Artifacts in Nonlinear Dynamics
Author(s): Wagner, Utz von
Lentz, Lukas
Type: Conference Object
Is Part Of: 10.34658/9788393531257
Language Code: en
Abstract: Nonlinear oscillations are of permanent interest in the field of dynamics of mechanical and mechatronical systems. There exist several well-known semi-analytical methods like Harmonic Balance, perturbation analysis or multiple scales for such problems. We reconsider in our presentation the method of Harmonic Balance but add some additional steps in order to avoid artifacts and get information about the stability. The classical method of Harmonic Balance is therefore added by an error criterion, which considers the neglected terms. Looking on this error for increasing ansatz orders, it can be decided whether a solution exists or is an artifact of the method. For the low error solutions, a stability analysis is performed. As example, an extended Duffing oscillator with additional nonlinear damping and excitation is considered showing regions of separated island solutions. Also a nonlinear piezo-beam energy harvesting system is investigated. The described method enables to calculate solutions in a rapid manner with comparable low effort, to get an overview over regular responses of nonlinear systems.
Issue Date: 2017
Date Available: 20-Mar-2020
DDC Class: 621 Angewandte Physik
Subject(s): nonlinear oscillations
harmonic balance
perturbation analysis
Duffing oscillator
energy harvesting
Sponsor/Funder: DFG, 253161314, Untersuchung des nichtlinearen dynamischen Verhaltens von stochastisch erregten Energy Harvesting Systemen mittels Lösung der Fokker-Planck-Gleichung
Proceedings Title: Vibration, Control and Stability of Dynamical Systems - DSTA 2017
Editor: Awrejcewicz, Jan
Kaźmierczak, Marek
Mrozowski, Jerzy
Olejnik, Paweł
Publisher: Lodz University of Technology
Publisher Place: Lodz
Number: 1
Page Start: 525
Page End: 536
ISBN: 978-83-935312-5-7
Appears in Collections:FG Mechatronische Maschinendynamik » Publications

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