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Quasi-periodic response types of a single non-linear dynamic system in resonance and out of resonance domains
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SYSNO ASEP 0447396 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Quasi-periodic response types of a single non-linear dynamic system in resonance and out of resonance domains Author(s) Náprstek, Jiří (UTAM-F) RID, ORCID, SAI
Fischer, Cyril (UTAM-F) RID, SAI, ORCIDNumber of authors 2 Source Title Proceedings of ICoEV 2015. International conference on engineering vibration. - Ljubljana : CTP National and University Library of Slovenia, 2015 / Boltežar M. - ISBN 978-961-6536-97-4 Pages s. 662-671 Number of pages 10 s. Publication form Medium - C Action International conference on engineering vibration Event date 07.09.2015-10.09.2015 VEvent location Lublaň Country SI - Slovenia Event type WRD Language eng - English Country SI - Slovenia Keywords non-linear dynamics ; quasi-periodic response ; post-critical processes ; dynamic stability Subject RIV JM - Building Engineering R&D Projects GA15-01035S GA ČR - Czech Science Foundation (CSF) Institutional support UTAM-F - RVO:68378297 Annotation 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. Workplace Institute of Theoretical and Applied Mechanics Contact Kulawiecová Kateřina, kulawiecova@itam.cas.cz, Tel.: 225 443 285 Year of Publishing 2016
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