Mode Localization and Frequency Veering in a Non-Conservative Mechanical System With Dissimilar Components
✍ Scribed by S. Natsiavas
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 310 KB
- Volume
- 165
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
A singular perturbation method is applied in carrying out an investigation on the connection between frequency veering and mode localization phenomena in a two-degree-offreedom damped linear oscillator. The components of the system examined are dissimilar, and as a result the modes are localized for most of the combinations of the parameters. However, the natural frequencies become close, leading to curve veering, only for some special combinations of the parameters. A typical mathematical consequence is that regular perturbation expansions of the natural frequencies, in terms of a single parameter, break down in the vicinity of curve veering. In the present study, damping effects are included and this breakdown is shown to happen for the natural frequencies as well as the damping ratios of the system examined. This difficulty is eventually overcome by applying the method of matched asymptotic expansions. Accurate, uniformly valid expressions are derived for both the frequencies of free oscillation and the corresponding damping ratios.