Qualitative Analysis of Nonsmooth Dynamics

Qualitative Analysis of Nonsmooth Dynamics

A Simple Discrete System with Unilateral Contact and Coulomb Friction

1st Edition - April 4, 2016

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  • Authors: Alain Léger, Elaine Pratt
  • Hardcover ISBN: 9781785480942
  • eBook ISBN: 9780081012017

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Description

Qualitative Analysis of Nonsmooth Dynamics: A Simple Discrete System with Unilateral Contact and Coulomb Friction explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems. By analyzing these non-regularities successively this work explores the set of equilibria and properties of periodic solutions of elementary mechanical systems, where no classical results issued from the theory of ordinary differential equations are readily available, such as stability, continuation or approximation of solutions. The authors focus on unilateral contact in presence of Coulomb friction and show, in particular, how any regularization would greatly simplify the mathematics but lead to unacceptable physical responses.

Key Features

  • Explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems
  • Includes theoretical results concerning the full investigation of the behavior under constant or oscillating loadings, even in the case of the simplest mechanical systems
  • Provides a focus on unilateral contact in presence of Coulomb friction
  • Helps you gain an accurate understanding of how the transition occurs to ensure the safe use of any machine involving rotating or sliding mechanisms

Readership

PhD students, researchers, academics and engineers in the field of mechanical engineering

Table of Contents

  • Introduction
    Chapter 1. The Model
    Chapter 2. Mathematical Formulation
    Chapter 3. The Equilibrium States
    Chapter 4. Stability
    Chapter 5. Exploring the Case of the Linear Restoring Force
    Chapter 6. The Case of the Nonlinear Restoring Force
    Chapter 7. Open Problems and Challenges

Product details

  • No. of pages: 222
  • Language: English
  • Copyright: © ISTE Press - Elsevier 2016
  • Published: April 4, 2016
  • Imprint: ISTE Press - Elsevier
  • Hardcover ISBN: 9781785480942
  • eBook ISBN: 9780081012017

About the Authors

Alain Léger

Alain Leger received his PhDs in Mathematics and Sciences from the University Pierre et Marie Curie, Paris. He held positions as research engineer and senior research at EDF and CNRS respectively. He is the co-manager of the International Scientific Coordination Network of 'Wave Propagation in Complex Media'. His research areas lie in the mechanics of solids and structure, unilateral problems within the dynamics of discrete systems, bifurication theory and wave propagation in complex media.

Affiliations and Expertise

Research Associate, Mechanics and Acoustics Laboratory, CNRS, Marseille, France

Elaine Pratt

Elaine Pratt obtained her PhD in Numerical Analysis in 1979 from the University of Provence. She has held the position of Senior Lecturer at the Univeristy of Provence and the University Aix-Marseille. Her research interests include mathematical and numerical analysis applied to mechanical problems, the study of contact friction and non-smooth dynamics of discrete mechanical systems.

Affiliations and Expertise

Researcher, University Aix-Marseille, Marseille, France

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