On the (in)stability of quasi-static paths of smooth systems: definitions and sufficient conditions
✍ Scribed by J. A. C. Martins; N. V. Rebrova; V. A. Sobolev
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 96 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.707
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✦ Synopsis
A concept of stability of quasi-static paths is discussed in this paper that takes into account the existence of fast (dynamic) and slow (quasi-static) time scales in the evolution of many mechanical systems. The proposed concept is essentially a continuity property with respect to the smallness of the initial perturbations (as in Lyapunov stability) and the smallness of the quasi-static loading rate (that plays the role of the small parameter in singular perturbation problems). A related concept of attractiveness is also proposed. Several examples illustrate the relevance of the deÿnitions. Su cient conditions for attractiveness or for instability of quasi-static paths of smooth systems are proved.