This book contains theoretical and application-oriented methodsto treat models of dynamical systems involving non-smoothnonlinearities.
The theoretical approach that has been retained and underlined inthis work is associated with differential inclusions of mainlyfinite dimensional dynamical systems and the introduction ofmaximal monotone operators (graphs) in order to describe models ofimpact or friction. The authors of this book master themathematical, numerical and modeling tools in a particular way sothat they can propose all aspects of the approach, in both adeterministic and stochastic context, in order to describe realstresses exerted on physical systems. Such tools are very powerfulfor providing reference numerical approximations of the models.Such an approach is still not very popular nevertheless, eventhough it could be very useful for many models of numerous fields(e.g. mechanics, vibrations, etc.).
This book is especially suited for people both in research andindustry interested in the modeling and numerical simulation ofdiscrete mechanical systems with friction or impact phenomenaoccurring in the presence of classical (linear elastic) ornon-classical constitutive laws (delay, memory effects, etc.). Itaims to close the gap between highly specialized mathematicalliterature and engineering applications, as well as to also givetools in the framework of non-smooth stochastic differentialsystems: thus, applications involving stochastic excitations(earthquakes, road surfaces, wind models etc.) are considered.
1. Some Simple Examples.
2. Theoretical Deterministic Context.
3. Stochastic Theoretical Context.
4. Riemannian Theoretical Context.
5. Systems with Friction.
6. Impact Systems.
About the Authors
Jérôme Bastien is Assistant Professor at theUniversity Lyon 1 (Centre de recherche et d'Innovation sur lesport) in France.
Frédéric Bernardin is a Research Engineer atDépartement Laboratoire de Clermont-Ferrand (DLCF), Centred'Etudes Techniques de l'Equipement (CETE), Lyon, France.
Claude-Henri Lamarque is Head of Laboratoire Géomatériauxet Génie Civil (LGCB) and Professor at Ecole des TravauxPublics de l'Etat (ENTPE), Vaulx-en-Velin, France.