Contact Mechanics: Proceedings of the 3rd Contact Mechanics by João A. C. Martins, Manuel D. P. Monteiro Marques (auth.)

By João A. C. Martins, Manuel D. P. Monteiro Marques (auth.)

This quantity comprises forty four papers provided on the 3rd touch Mechanics overseas Symposium (CMIS 2001) held in Praia da Consola9ao, Peniche (portugal), June 17-21,2001. This Symposium used to be the direct continuation of the 1st CMIS held in Lausanne (1992) and in Carry-Le-Rouet (1994). different comparable conferences, in what matters clinical issues and individuals, happened within the nineties at l. a. Grande Motte (1990), Vadstena (1996), Ferrara (1997), Munich (1998) and Grenoble (1999). The Symposium geared toward amassing researchers with pursuits in a variety of themes in theoretical, computational and experimental touch mechanics. the decision for papers pointed out themes in tribology, mathematical formulations and research, numerical tools in non-smooth mechanics, impression difficulties, instabilities and technological difficulties. the whole variety of members was once 102, from Universities and study Institutes of nineteen international locations. The medical Committee reviewed 102 submitted abstracts, and the ultimate software consisted of 6 major lectures, forty three oral communications and 36 poster displays (see Appendix A). The papers during this e-book correspond to nearly the entire major lectures and oral communications, and they're assembled in five chapters: • Dynamics and influence • Instabilities, Oscillations and Waves • touch types, effects and purposes • Mathematical research • Numerical equipment. We thank the entire authors for his or her necessary contributions to this quantity. we're indebted to the individuals of the clinical Committee for his or her assist in refereeing the submitted abstracts and manuscripts. We additionally thank the sequence editor, Prof. Graham Gladwell, for his assistance within the revision process.

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Extra info for Contact Mechanics: Proceedings of the 3rd Contact Mechanics International Symposium, Praia da Consolação, Peniche, Portugal, 17–21 June 2001

Example text

But, we must ensure that admitting the wider class of solutions MMA will not introduce parasitic solutions. This is the aim of the following theorem. Theorem 6 Let (Ta, qa) be the solution for problem II furnished by corollary 5, and (T, q) be an arbitmry solution for problem II. Then, there exists a real number To (0 < To ~ min{Ta, T}) such that: ql[O,To[ = qal[O,To[· In other terms, there is local uniqueness for problem II. Local uniqueness is the difficult part in the study of well-posed ness of problem II.

Introduction Newton's classical kinematic impact law provides a way to calculate the postimpact velocities of two colliding particles. It reverses the sign of the relative velocity 'Y at the impact and takes into account dissipation by a coefficient of restitution € such that 'Y+ = -€ 'Y-. When this impact law is applied to multi contact problems, a formulation in terms of inequalities is required, such as done by Pfeiffer and Glocker (1996). Here we assume in addition that"the coefficients of restitution of the different contacts are all equal to each other.

Since such a structure appears systematically in the modelling of the dynamics of rigid bodies systems with perfect bilateral constraints, we are led to make the following definition. Definition 1 A simple discrete mechanical system is a pair (Q, f) where: • Q is a finite-dimensional Riemannian manifold called the configuration manifold. • f: TQ X lR+ mapping. -+ T*Q is a mapping satisfying (1), called the force Now, consider an arbitrary smooth motion q(t) of the system. The power of inertial forces is by definition the time derivative of the kinetic energy: :tK(q,q) = :t~llq(t)II:(t) = (~q(t),q(t)) q(t) = /~~q(t),q(t)) , \ q(t) where D/dt denotes the covariant derivative along the curve q(t) associated with the Levi-Civita connection, and ~ the isomorphism from TQ onto T*Q canonically associated with the Riemannian metric.

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