Limit cycle stability of two degree of freedom system under deterministic and random perturbation

0429317 - ÚTAM 2015 RIV PT eng C - Conference Paper (international conference)
Náprstek, Jiří - Fischer, Cyril
Limit cycle stability of two degree of freedom system under deterministic and random perturbation.
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.), s. 1943-1956. ISBN 978-972-752-165-4. ISSN 2311-9020.
[International Conference on Structural Dynamics. EURODYN 2014 /9./. Porto (PT), 30.06.2014-02.07.2014]
R&D Projects: GA ČR(CZ) GC13-34405J
Institutional support: RVO:68378297
Keywords : non-linear dynamics * dynamic stability * limit cycles * random vibrations * Markov processes
Subject RIV: JM - Building Engineering
http://paginas.fe.up.pt/~eurodyn2014/CD/papers/271_MS11_ABS_1024.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0234463