Vibro-impact dynamics /
Luo, Albert C. J.
Vibro-impact dynamics / Albert C.J. Luo and Yu Guo. - 1 online resource.
Includes bibliographical references and index.
VIBRO-IMPACT DYNAMICS; Contents; Preface; 1 Introduction; 1.1 Discrete and Discontinuous Systems; 1.1.1 Discrete Dynamical Systems; 1.1.2 Discontinuous Dynamical Systems; 1.2 Fermi Oscillators and Impact Problems; 1.3 Book Layout; 2 Nonlinear Discrete Systems; 2.1 Definitions; 2.2 Fixed Points and Stability; 2.3 Stability Switching Theory; 2.4 Bifurcation Theory; 3 Complete Dynamics and Fractality; 3.1 Complete Dynamics of Discrete Systems; 3.2 Routes to Chaos; 3.2.1 One-Dimensional Maps; 3.2.2 Two-Dimensional Systems; 3.3 Complete Dynamics of the Henon Map; 3.4 Similarity and Multifractals. 3.4.1 Similar Structures in Period Doubling3.4.2 Fractality of Chaos via PD Bifurcation; 3.4.3 An Example; 3.5 Complete Dynamics of Logistic Map; 4 Discontinuous Dynamical Systems; 4.1 Basic Concepts; 4.2 G-Functions; 4.3 Passable Flows; 4.4 Non-Passable Flows; 4.5 Grazing Flows; 4.6 Flow Switching Bifurcations; 5 Nonlinear Dynamics of Bouncing Balls; 5.1 Analytic Dynamics of Bouncing Balls; 5.1.1 Periodic Motions; 5.1.2 Stability and Bifurcation; 5.1.3 Numerical Illustrations; 5.2 Period-m Motions; 5.3 Complex Dynamics; 5.4 Complex Periodic Motions; 6 Complex Dynamics of Impact Pairs. 6.1 Impact Pairs6.2 Analytical, Simplest Periodic Motions; 6.2.1 Asymmetric Period-1 Motion; 6.2.2 Stability and Bifurcation; 6.2.3 Numerical Illustrations; 6.3 Possible Impact Motion Sequences; 6.4 Grazing Dynamics and Stick Motions; 6.5 Mapping Structures and Periodic Motions; 6.6 Stability and Bifurcation; 7 Nonlinear Dynamics of Fermi Oscillators; 7.1 Mapping Dynamics; 7.2 A Fermi Oscillator; 7.2.1 Absolute Description; 7.2.2 Relative Description; 7.3 Analytical Conditions; 7.4 Mapping Structures and Motions; 7.4.1 Switching Sets and Generic Mappings; 7.4.2 Motions with Mapping Structures. 7.4.3 Periodic Motions and Local Stability7.5 Predictions and Simulations; 7.5.1 Bifurcation Scenario; 7.5.2 Analytical Prediction; 7.5.3 Numerical Simulations; Appendix 7.A; References; Index.
Presents a systematic view of vibro-impact dynamics based on the nonlinear dynamics analysis Comprehensive understanding of any vibro-impact system is critically impeded by the lack of analytical tools viable for properly characterizing grazing bifurcation. The authors establish vibro-impact dynamics as a subset of the theory of discontinuous systems, thus enabling all vibro-impact systems to be explored and characterized for applications. Vibro-impact Dynamics presents an original theoretical way of analyzing the behavior of vibro-impact dynamics that can be exte.
9781118402900 1118402901 9781118402887 111840288X 9781118402917 111840291X 9781118402924 1118402928 9781299188198 1299188192
EB00066781 Recorded Books
450069 MIL
2012047307
Vibration.
Impact.
Shock (Mechanics)
Impact.
Shock (Mechanics)
Vibration.
SCIENCE--Nanoscience.
Impact.
Shock (Mechanics)
Vibration.
Electronic books.
Electronic books.
TA355
620.1/125
Vibro-impact dynamics / Albert C.J. Luo and Yu Guo. - 1 online resource.
Includes bibliographical references and index.
VIBRO-IMPACT DYNAMICS; Contents; Preface; 1 Introduction; 1.1 Discrete and Discontinuous Systems; 1.1.1 Discrete Dynamical Systems; 1.1.2 Discontinuous Dynamical Systems; 1.2 Fermi Oscillators and Impact Problems; 1.3 Book Layout; 2 Nonlinear Discrete Systems; 2.1 Definitions; 2.2 Fixed Points and Stability; 2.3 Stability Switching Theory; 2.4 Bifurcation Theory; 3 Complete Dynamics and Fractality; 3.1 Complete Dynamics of Discrete Systems; 3.2 Routes to Chaos; 3.2.1 One-Dimensional Maps; 3.2.2 Two-Dimensional Systems; 3.3 Complete Dynamics of the Henon Map; 3.4 Similarity and Multifractals. 3.4.1 Similar Structures in Period Doubling3.4.2 Fractality of Chaos via PD Bifurcation; 3.4.3 An Example; 3.5 Complete Dynamics of Logistic Map; 4 Discontinuous Dynamical Systems; 4.1 Basic Concepts; 4.2 G-Functions; 4.3 Passable Flows; 4.4 Non-Passable Flows; 4.5 Grazing Flows; 4.6 Flow Switching Bifurcations; 5 Nonlinear Dynamics of Bouncing Balls; 5.1 Analytic Dynamics of Bouncing Balls; 5.1.1 Periodic Motions; 5.1.2 Stability and Bifurcation; 5.1.3 Numerical Illustrations; 5.2 Period-m Motions; 5.3 Complex Dynamics; 5.4 Complex Periodic Motions; 6 Complex Dynamics of Impact Pairs. 6.1 Impact Pairs6.2 Analytical, Simplest Periodic Motions; 6.2.1 Asymmetric Period-1 Motion; 6.2.2 Stability and Bifurcation; 6.2.3 Numerical Illustrations; 6.3 Possible Impact Motion Sequences; 6.4 Grazing Dynamics and Stick Motions; 6.5 Mapping Structures and Periodic Motions; 6.6 Stability and Bifurcation; 7 Nonlinear Dynamics of Fermi Oscillators; 7.1 Mapping Dynamics; 7.2 A Fermi Oscillator; 7.2.1 Absolute Description; 7.2.2 Relative Description; 7.3 Analytical Conditions; 7.4 Mapping Structures and Motions; 7.4.1 Switching Sets and Generic Mappings; 7.4.2 Motions with Mapping Structures. 7.4.3 Periodic Motions and Local Stability7.5 Predictions and Simulations; 7.5.1 Bifurcation Scenario; 7.5.2 Analytical Prediction; 7.5.3 Numerical Simulations; Appendix 7.A; References; Index.
Presents a systematic view of vibro-impact dynamics based on the nonlinear dynamics analysis Comprehensive understanding of any vibro-impact system is critically impeded by the lack of analytical tools viable for properly characterizing grazing bifurcation. The authors establish vibro-impact dynamics as a subset of the theory of discontinuous systems, thus enabling all vibro-impact systems to be explored and characterized for applications. Vibro-impact Dynamics presents an original theoretical way of analyzing the behavior of vibro-impact dynamics that can be exte.
9781118402900 1118402901 9781118402887 111840288X 9781118402917 111840291X 9781118402924 1118402928 9781299188198 1299188192
EB00066781 Recorded Books
450069 MIL
2012047307
Vibration.
Impact.
Shock (Mechanics)
Impact.
Shock (Mechanics)
Vibration.
SCIENCE--Nanoscience.
Impact.
Shock (Mechanics)
Vibration.
Electronic books.
Electronic books.
TA355
620.1/125