Applied nonlinear dynamics and chaos of mechanical systems with discontinuities / editors, Marian Wiercigroch, Bram de Kraker.

Includes bibliographical references.

Print version record.

Preface; Contents; Chapter 1 Preliminaries; 1.1 Introduction; 1.2 Scope of the Book; 1.2.1 Outlining the Basis and Methods; 1.2.2 Impacting Systems; 1.2.3 Systems with Dry Friction; 1.2.4 Complex Mechanical Systems; Bibliography; Chapter 2 Mathematical Models of Mechanical Systems with Discontinuities; 2.1 Introduction; 2.2 Modelling Discontinuous Systems by Discontinuous Functions; 2.2.1 Numerical Algorithm; 2.2.2 Symmetrically Piecewise Linear Oscillator; 2.2.3 Experimental Bifurcation Diagrams; 2.3 Modelling Discontinuities by Smooth Functions; 2.3.1 Smoothing Discontinuities.

2.3.2 A symmetrically Piecewise Linear Oscillator2.4 Concluding Remarks; Bibliography; Chapter 3 Temporal and Spatial DiscontinuityTransformations; 3.1 Introduction; 3.2 Non-smooth Transformations of Positional Variables: Elimination of Constraints; 3.3 Non-smooth Transformation of Arguments; 3.3.1 Non-smooth Oscillating Time: Sawtooth Temporal Transformations; 3.3.2 Transformation of Set of First-order Equations of Motion; 3.3.3 Transformation of Set of Second-order Equations of Motion; 3.4 Periodic Impulsive and Discontinuous Excitations; 3.5 Use of Method of Averaging; 3.6 Conclusions.

4.4.5 4-DOF Beam with Nonlinear Support4.4.6 Concluding Remarks; Bibliography; Chapter 5 Impact Oscillator; 5.1 Introduction; 5.2 Theoretical Analysis of Periodic Impact Motion and its Stability; 5.3 Existence Regions of Impact Motions; 5.4 From Periodic into Chaotic Impacts; 5.4.1 Feigenbaum Period Doubling Cascade; 5.4.2 Grazing Bifurcation with Hysteresis; 5.4.3 The Interrupted Feigenbaum Cascade; 5.4.4 Interruption of the Saddle-Node Instability Development; 5.5 Influence of the Stop Compliance on the Impact Oscillator Behaviour; 5.6 Conclusions; Acknowledgement; Bibliography.

Chapter 6 Dynamics of Piecewise Linear Oscillators6.1 Introduction; 6.2 Dynamical System -- Periodic Response; 6.2.1 Linear Harmonic Motions; 6.2.2 Single-sided Contact Motions; 6.2.3 Double-sided Contact Motions; 6.2.4 Symmetric Motions; 6.3 Stability of Periodic Motions; 6.4 Bifurcation Analysis; 6.5 Multiple Degree of Freedom Systems; 6.6 Some Extensions; 6.7 Numerical Results; 6.8 Conclusions; Bibliography; Chapter 7 Quenching of Self-Excited Vibrations by Impact Damper; 7.1 Introduction; 7.2 Quenching of 1-DOF Self-Excited System; 7.2.1 Theoretical Analysis; 7.2.2 Experimental Studies.

Rapid developments in nonlinear dynamics and chaos theory have led to publication of many valuable monographs and books. However, most of these texts are devoted to the classical nonlinear dynamics systems, for example the Duffing or van der Pol oscillators, and either neglect or refer only briefly to systems with motion-dependent discontinuities. In engineering practice a good part of problems is discontinuous in nature, due to either deliberate reasons such as the introduction of working clearance, and/or the finite accuracy of the manufacturing processes. The main objective of this volume is.

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