Beating Effects in a Single Nonlinear Dynamical System in a Neighborhood of the Resonance

Abstract:

The exact coincidence of external excitation and basic eigen-frequency of a single degree of freedom (SDOF) nonlinear 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. Theabove 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 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 nonlinear differential and algebraic equations serving as a basis for qualitativeanalytic 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.

• Periodical: Applied Mechanics and Materials (Volume 849)
• Pages: 76-83
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.849.76
• Online since: August 2016
• Authors: Jiří Náprstek*, Cyril Fischer
• Keywords: Auto-Oscillation, Beating Effects, Dynamic Stability, Nonlinear Dynamics

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