Quasi-periodic response types of a single non-linear dynamic system in resonance and out of resonance domains

0447396 - ÚTAM 2016 RIV SI eng C - Conference Paper (international conference)
Náprstek, Jiří - Fischer, Cyril
Quasi-periodic response types of a single non-linear dynamic system in resonance and out of resonance domains.
Proceedings of ICoEV 2015. International conference on engineering vibration. Ljubljana: CTP National and University Library of Slovenia, 2015 - (Boltežar, M.), s. 662-671. ISBN 978-961-6536-97-4.
[International conference on engineering vibration. Lublaň (SI), 07.09.2015-10.09.2015]
R&D Projects: GA ČR(CZ) GA15-01035S
Institutional support: RVO:68378297
Keywords : non-linear dynamics * quasi-periodic response * post-critical processes * dynamic stability
Subject RIV: JM - Building Engineering

The exact coincidence of external excitation and basic eigen-frequency of a single degree of freedom (SDOF) non-linear system produces stationary response with constant amplitude and phase shift. When the excitation frequency differs from the system eigen-frequency, various types of quasi-periodic response occur having a character of a beating process. The period of beating changes from infinity in the resonance point until a couple of excitation periods outside the resonance area. The above phenomena have been identified qualitatively in many papers including authors contributions. Nevertheless investigation of internal structure of a quasi-period and its dependence on the difference of excitation and eigen-frequency is still missing. Combinations of harmonic balance and small parameter methods are used for qualitative analysis of the system in mono- and multi-harmonic versions. They lead to non-linear differential and algebraic equations serving as a basis for qualitative analytic estimation or numerical description of characteristics of quasi-periodic system response. Zero, first and second level perturbation techniques are used. Appearance, stability and neighborhood of limit cycles is evaluated. Numerical phases are based on simulation processes and numerical continuation tools. Parametric evaluation and illustrating examples are presented.
Permanent Link: http://hdl.handle.net/11104/0249295