Dynamics and Control of Technical Systems II

0460900 - ÚTAM 2017 RIV CH eng M - Část monografie knihy
Náprstek, Jiří - Fischer, Cyril
Beating effects in a single nonlinear dynamical system in a neighborhood of the resonance.
Dynamics and Control of Technical Systems II. Pfaffikon: Trans Tech Publications, 2016 - (Balthazar, J.; Gonçalves, P.; Náprstek, J.), s. 76-83. ISBN 978-3-0357-1051-9
Grant CEP: GA ČR(CZ) GA15-01035S
Institucionální podpora: RVO:68378297
Klíčová slova: nonlinear dynamics * beating effects * dynamic stability * auto-oscillation
Kód oboru RIV: JM - Inženýrské stavitelství

The exact coincidence of external excitation and basic eigen-frequency of a single degree of freedom (SDOF) nonlinear sy~tem produces stationary response with constant amplitude and phase shift. When the excitation frequency differs from the system eigen-frequency, various types of quasiperiodic 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 mentioned phenomena have been identified 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 sti ll 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 nonlinear differential and algebraic equations serving as a basis for qualitative analytic estimation or numerical description of characteristics of the 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.
Trvalý link: http://hdl.handle.net/11104/0260851