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Limit cycle stability of two degree of freedom system under deterministic and random perturbation
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SYSNO ASEP 0429317 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Limit cycle stability of two degree of freedom system under deterministic and random perturbation Author(s) Náprstek, Jiří (UTAM-F) RID, ORCID, SAI
Fischer, Cyril (UTAM-F) RID, SAI, ORCIDNumber of authors 2 Source Title Proceedings of the 9th International Conference on Structural Dynamics. EURODYN 2014. - Porto : European Association for Structural Dynamics (EASD), 2014 / Cunha A. ; Caetano E. ; Ribeiro P. ; Müller G. - ISSN 2311-9020 - ISBN 978-972-752-165-4 Pages s. 1943-1956 Number of pages 14 s. Publication form Medium - C Action International Conference on Structural Dynamics. EURODYN 2014 /9./ Event date 30.06.2014-02.07.2014 VEvent location Porto Country PT - Portugal Event type WRD Language eng - English Country PT - Portugal Keywords non-linear dynamics ; dynamic stability ; limit cycles ; random vibrations ; Markov processes Subject RIV JM - Building Engineering R&D Projects GC13-34405J GA ČR - Czech Science Foundation (CSF) Institutional support UTAM-F - RVO:68378297 UT WOS 000354786602076 Annotation Multi-degree of freedom (MDOF) non-linear systems are characterized by a number of response types. Limit Cycles (LC) are of the most important representing typical post-critical response type of many systems. They can be encountered in aeroelasticity, earthquake engineering, high speed traffic mechanics, plasma physics, optics, etc. Stable and unstable LCs should be distinguished. The aspect of stability and non-stability impresses on LC the character of an attractor or a repulser. Normal form of governing stochastic differential system with Gaussian white noise perturbations is considered. LC stability investigation is conducted on the basis of the relevant Fokker-Planck (FP) equation. The stochastic differential system with multi-component additive and multiplicative perturbation is then constructed and transformed into FP equation with respect to special toroidal coordinate system around the LC. Perturbation of PDF stability is then analyzed in the meaning of the mean value and variance using stochastic moments decomposition. As a demonstration one and two degree of freedom non-linear systems are discussed. This illustrating cases were selected because of their relevance with the aero-elastic post-critical response types of a slender beam in a cross-flow. Strong and weak attributes of the approach used are evaluated together with an outline of the future works. Workplace Institute of Theoretical and Applied Mechanics Contact Kulawiecová Kateřina, kulawiecova@itam.cas.cz, Tel.: 225 443 285 Year of Publishing 2015 Electronic address http://paginas.fe.up.pt/~eurodyn2014/CD/papers/271_MS11_ABS_1024.pdf
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