TRANSIENT RESONANCE OSCILLATIONS OF A SLOW-VARIANT SYSTEM WITH SMALL NON-LINEAR DAMPING—MODELLING AND PREDICTION
✍ Scribed by H. IRRETIER; D.B. BALASHOV
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 213 KB
- Volume
- 231
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
The transient response of a single-degree-of-freedom oscillator with a slow-variant natural frequency and a small non-linear damping is under consideration. The damping is modelled as a sum of elementary power functions with respect to the system velocity. The passage through a resonance which is induced by a sweep of the excitation frequency during run-up or run-down is studied using the Krylov}Bogoljubov asymptotic method. Numerical calculations are presented to demonstrate the validity of the "rst asymptotic approximation. Asymptotic approximations for the maximum transient response and the corresponding excitation frequency are derived analytically in the particular case of a system with linear viscous damping. The obtained formulae are tested numerically and compared to known approximations.