Impacts in Mechanical Systems: Analysis and Modelling (Lecture Notes in Physics, 551)

✍ Scribed by Bernard Brogliato

• Publisher: Springer
• Year: 2000
• Tongue: English
• Leaves: 272
• Edition: 2000
• Category: Library

✦ Synopsis

This volume constitutes an advanced introduction to the field of analysis, modeling and numerical simulation of rigid body mechanical systems with unilateral constraints. The topics include Moreau's sweeping process, the numerical analysis of nonsmooth multibody systems with friction, the study of energetical restitution coefficients for elasto-plastic models, the study of stability and bifurcation in systems with impacts, and the development of a multiple impact rule for Newton's cradle and the simple rocking model. Combining pedagogical aspects with innovative approaches, this book will not only be of interest to researchers working actively in the field, but also to graduate students wishing to get acquainted with this field of research through lectures written at a level also accessible to nonspecialists.

✦ Table of Contents

Chapter 1
1 Introduction
2 Some preliminaries from convex analysis and fucntional analysis
3 First-order Problems
3.1 The Lipschitz continuous sweeping process
3.2 An application: Evolution of a quasi-static mechanical system
3.3 The state-dependent sweping process
3.4 Additional remarks
4 Second-order problems
5 Applications to the dynamics of unilateral contact
5.1 Frictionless unilateral contact
5.2 Unilateral contact with friction
References
Chapter 2
Introduction
Normal Contact Force – Penalized Method
Tangential Contact Force – Penalized Method
Continuous Motion
Setting of the Dynamic Equations.
Integration scheme
Application to the Dynamic Equations
Modelling of Frictional Contact
Principle of the Method
Formulation and Resolution of a Problem of Optimization under Constraints
Existence, Uniqueness, Convergence
Our Approach
Treatment of the Shocks
Formulation of the problem
Taking into Account of a Normal Restitution Coefficient
Important Concepts
Industrial Example - C60 Circuit Breaker
First Experiment
Second Experiment
Conclusion
Acknowledgement
References
Chapter 3
1 Introduction
2 System Formulation
2.1 Unilateral Constraints
2.2 Equations of Smooth Motion
2.3 Impacts
2.4 Multiple Impacts
3 Stability of Regular Periodic Impact Motions
3.1 Concepts of Stability of Motion with Impacts
3.2 Poincaré Maps
3.3 Non-degenerate Periodic Motions
3.3.1 Definition
3.3.2 Linearization
3.3.3 Stability Conditions
3.3.4 Bifurcations
4 Grazing Incidence
4.1 Appearance of Grazing
4.2 An Autonomous One-Degree of Freedom System
4.2.1 One Unilateral Constraint
4.2.2 Double Unilateral Contraint
4.3 One-Degree-of-Freedom System with Periodic Forcing
4.4 Multiple Degrees of Freedom
5 Multiple Collisions
5.1 Orthogonality Conditions
5.2 Variation of Periodic Orbit
5.3 Stability Conditions
5.4 Bifurcations
Acknowledgements
References
Chapter 4
1. Introduction
2. Impact Process
3. ‘Rigid’ Body Impact Theory for Smooth Hard Bodies
4. Extended Hertz Theory for Elastic-Plastic Impact
4.1 Elastic Indentation from Normal Contact Force
4.2 Indentation at Yield of Elastic-Plastic Bodies
4.3 Fully Plastic Indentation
4.4 Elastic Unloading from Fully Plastic Indentation
4.5 Energetic Coefficient of Restitution
5. Effect of Tangential Compliance Between Colliding Bodies
5.1 Normal Relative Velocity for Collinear Impact
5.2 Tangential Relative Velocity for Collinear Impact and Dry Friction
5.3 Change of Relative Velocity for Different Slip Processes
5.4 Example: Oblique Impact Of Sphere
5.5 Maximum Force From Oblique Impact Of Sphere
5.6 Discrete Modelling of Tangential Compliance
6. Chain Reactions From Impact In Multi-Body System
6.1 Example: Collinear Impact In Row Of Identical Spheres
6.2 Example: Impact Response Of Multi-body System With Graduated Properties
7. CONCLUSION
Acknowledgement
References
Chapter 5
1 Introduction
2 Multiple collisions in an N-Ball Chain
2.1 Three ball chain
2.2 Impulse Correlation Ratio
2.3 The solution method
2.4 Multiple impacts
2.5 Post impact bouncing patterns of a three ball cradle
2.6 Generalization of the three ball approach to N-balls
2.7 I termittent collisions
2.8 Special Examples
2.9 Experiments
2.10 Experimental veri .cation of the Impulse Correlation Ratio
2.11 Experimental observation of the small center ball behavior
3 Multiple collisions of a rocking block
3.1 Problem Description
3.2 Impulse Correlation Ratio
3.3 Velocity impulse relationships
3.4 The single impact case
3.5 Multiple Sequences of Impacts
3.6 Numerical analysis example
4 Discussion and conclusion
References