Applied nonlinear dynamics and chaos of mechanical systems with discontinuities /:
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...
Gespeichert in:
| Weitere Verfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, NJ :
World Scientific,
2000.
|
| Schriftenreihe: | World Scientific series on nonlinear science. Monographs and treatises ;
vol. 28. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xv, 444 pages) : illustrations |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9789812796301 9812796304 |
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| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a 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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| 650 | 0 | |a Chaotic behavior in systems. |0 http://id.loc.gov/authorities/subjects/sh85022562 | |
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| contents | 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. |
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| discipline | Maschinenbau / Maschinenwesen |
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| id | ZDB-4-EBA-ocn827945033 |
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| indexdate | 2025-03-18T14:21:04Z |
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| publisher | World Scientific, |
| record_format | marc |
| series | World Scientific series on nonlinear science. Monographs and treatises ; |
| series2 | World Scientific series in nonlinear science, Series A ; |
| spelling | Applied nonlinear dynamics and chaos of mechanical systems with discontinuities / editors, Marian Wiercigroch, Bram de Kraker. Singapore ; River Edge, NJ : World Scientific, 2000. 1 online resource (xv, 444 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier World Scientific series in nonlinear science, Series A ; vol. 28 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. Machinery, Dynamics of. http://id.loc.gov/authorities/subjects/sh85079394 Nonlinear theories. http://id.loc.gov/authorities/subjects/sh85092332 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Dynamique des machines. Théories non linéaires. Chaos. TECHNOLOGY & ENGINEERING Machinery. bisacsh Chaotic behavior in systems fast Machinery, Dynamics of fast Nonlinear theories fast Comportamento caótico nos sistemas. larpcal Wiercigroch, Marian. Kraker, Bram de. Print version: Applied nonlinear dynamics and chaos of mechanical systems with discontinuities. Singapore ; River Edge, NJ : World Scientific, 2000 9810229275 (DLC) 00028301 (OCoLC)43599180 World Scientific series on nonlinear science. Series A, Monographs and treatises ; vol. 28. http://id.loc.gov/authorities/names/no94008495 |
| spellingShingle | Applied nonlinear dynamics and chaos of mechanical systems with discontinuities / World Scientific series on nonlinear science. Monographs and treatises ; 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. Machinery, Dynamics of. http://id.loc.gov/authorities/subjects/sh85079394 Nonlinear theories. http://id.loc.gov/authorities/subjects/sh85092332 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Dynamique des machines. Théories non linéaires. Chaos. TECHNOLOGY & ENGINEERING Machinery. bisacsh Chaotic behavior in systems fast Machinery, Dynamics of fast Nonlinear theories fast Comportamento caótico nos sistemas. larpcal |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85079394 http://id.loc.gov/authorities/subjects/sh85092332 http://id.loc.gov/authorities/subjects/sh85022562 |
| title | Applied nonlinear dynamics and chaos of mechanical systems with discontinuities / |
| title_auth | Applied nonlinear dynamics and chaos of mechanical systems with discontinuities / |
| title_exact_search | Applied nonlinear dynamics and chaos of mechanical systems with discontinuities / |
| title_full | Applied nonlinear dynamics and chaos of mechanical systems with discontinuities / editors, Marian Wiercigroch, Bram de Kraker. |
| title_fullStr | Applied nonlinear dynamics and chaos of mechanical systems with discontinuities / editors, Marian Wiercigroch, Bram de Kraker. |
| title_full_unstemmed | Applied nonlinear dynamics and chaos of mechanical systems with discontinuities / editors, Marian Wiercigroch, Bram de Kraker. |
| title_short | Applied nonlinear dynamics and chaos of mechanical systems with discontinuities / |
| title_sort | applied nonlinear dynamics and chaos of mechanical systems with discontinuities |
| topic | Machinery, Dynamics of. http://id.loc.gov/authorities/subjects/sh85079394 Nonlinear theories. http://id.loc.gov/authorities/subjects/sh85092332 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Dynamique des machines. Théories non linéaires. Chaos. TECHNOLOGY & ENGINEERING Machinery. bisacsh Chaotic behavior in systems fast Machinery, Dynamics of fast Nonlinear theories fast Comportamento caótico nos sistemas. larpcal |
| topic_facet | Machinery, Dynamics of. Nonlinear theories. Chaotic behavior in systems. Dynamique des machines. Théories non linéaires. Chaos. TECHNOLOGY & ENGINEERING Machinery. Chaotic behavior in systems Machinery, Dynamics of Nonlinear theories Comportamento caótico nos sistemas. |
| work_keys_str_mv | AT wiercigrochmarian appliednonlineardynamicsandchaosofmechanicalsystemswithdiscontinuities AT krakerbramde appliednonlineardynamicsandchaosofmechanicalsystemswithdiscontinuities |