On the stability of quasi-static paths of a linearly elastic system with friction

Martins, J. A. C.; Marques, Manuel D.P. Monteiro; Rebrova, Natalia

doi:10.1007/3-540-31761-9_39

Cited by 1 publication

(2 citation statements)

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“…The proof of this Lemma adapts to the present context of a particle with nonprescribed normal force, some arguments used by Marques [Mon94] and Martins et al [MMR06] for cases with prescribed normal force. The full proof can be found again in [MMRS06] .…”

Section: Remark 42mentioning

confidence: 69%

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New Results on the Stability of Quasi-Static Paths of a Single Particle System With Coulomb Friction and Persistent Contact

Schmid

Martins²,

Rebrova³

2007

Topics on Mathematics for Smart Systems

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In this paper we announce some new mathematical results on the stability of quasistatic paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle.A quasi-static path is said to be stable at some value of the load parameter if, for some finite interval of the load parameter thereafter, the dynamic solutions behave continuously with respect to the size of the initial perturbations (as in Lyapunov stability) and to the smallness of the rate of application of the external forces, ε (as in singular perturbation problems). In this paper we prove sufficient conditions for stability of quasi-static paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle. The present system has the additional difficulty of its non-smoothness: the friction law is a multivalued operator and the dynamic evolutions of this system may have discontinuous accelerations.

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Section: Remark 42mentioning

confidence: 69%

“…The remaining task is to estimate the integral ε 2 λ 0 u t (s)ū t XS(s) ds. This uses the results proved in Lemma 4.1 and adapts the argument in [MMR06] to the present case of non-prescribed normal force. The full proof can be found in the article [MMRS06] .…”

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confidence: 85%