Screen LibraryApplied 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...
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| Corporate Authors: | |
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| Group Author: | ; |
| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore ; River Edge, N.J. : |
| Publication Dates: | 2000. |
| Literature type: | eBook |
| Language: | English |
| Series: |
World Scientific series in nonlinear science, Series A ; vol. 28 |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/3345#t=toc |
| Summary: |
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 to provide a general methodology for describing, solving and analysing discontinuous systems. It is compiled from the dedicated contributions written by experts in the field of applied nonlinear dynamics and chaos. The main focus is on mechanical engineering problems where clearances, piecewise stiffness, intermittent contact, variable friction or other forms of discontinuity occur. Practical applications include vibration absorbers, percussive drilling of hard materials and dynamics of metal cutting. |
| Carrier Form: | 1 online resource (xv,444pages) : illustrations. |
| Bibliography: | Includes bibliographical references. |
| ISBN: | 9789812796301 |
| Index Number: | TJ173 |
| CLC: | TH113-532 |
| Contents: |
ch. 1. Preliminaries. 1.1. Introduction. 1.2. Scope of the book -- ch. 2. Mathematical models of mechanical systems with discontinuities. 2.1. Introduction. 2.2. Modelling discontinuous systems by discontinuous functions. 2.3. Modelling discontinuities by smooth functions. 2.4. Concluding remarks -- ch. 3. Temporal and spatial discontinuity transformations. 3.1. Introduction. 3.2. Non-smooth transformations of positional variables: Elimination of constraints. 3.3. Non-smooth transformation of arguments. 3.4. Periodic impulsive and discontinuous excitations. 3.5. Use of method of averaging. 3.6. Conclusions -- ch. 4. Extensions of cell mapping for discontinuous systems. 4.1. Introduction. 4.2. Simple cell mapping. 4.3. Parameter variation method for cell mapping. 4.4. Cell mapping for multi-DOF systems -- ch. 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. 5.5. Influence of the stop compliance on the impact oscillator behaviour. 5.6. Conclusions -- ch. 6. Dynamics of piecewise linear oscillators. 6.1. Introduction. 6.2. Dynamical system - Periodic response. 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 -- ch. 7. Quenching of self-excited vibrations by impact damper. 7.1. Introduction. 7.2. Quenching of 1-DOF self-excited system. 7.3. Quenching of vortex-induced vibration of 2-DOF system by an impact damper. 7.4. Conclusions -- ch. 8. Dynamic phenomena in gear boxes. 8.1. Introduction. 8.2. Modelling of gear systems. 8.3. Vibrations of a gear system with piecewise linear function of stiffness. 8.4. Additional nonlinearities. 8.5. Influence of noise. 8.6. Remarks and conclusions -- ch. 9. Rigorous methods and numerical results for dry friction problems. 9.1. Lyapunov exponents for non-smooth systems. 9.2. Application of conley index theory to non-smooth systems. 9.3. Numerical analysis of a friction oscillator. 9.4. Conclusions. ch. 10. Forced self-excited vibration with dry friction. 10.1. Introduction. 10.2. Theoretical analysis. 10.3. Numerical calculation. 10.4. Preloaded compliance system. 10.5. Conclusions -- ch. 11. Stick-slip and the phase-space reconstruction. 11.1. Introduction. 11.2. Phase-space reconstructions. 11.3. Example stick-slip oscillators. 11.4. Diagnosis of reconstruction singularities. 11.5. Reconstruction with additional observer. 11.6. Remarks. 11.7. Conclusions -- ch. 12. Multidegree of freedom systems with dry friction. 12.1. Introduction. 12.2. Numerical algorithms. 12.3. 2-DOF dry friction model. 12.4. Conclusions -- ch. 13. Dynamic instabilities in spinning disks. 13.1. Introduction to the dynamics of spinning disks. 13.2. Fundamental theory of flexural vibrations in plates. 13.3. Theory of vibration of rotating flexible membranes. 13.4. Incorporating imperfections. 13.5. Introducing transversely located mass-spring-damper system. 13.6. Nonconservative follower forces in rotating disk problems. 13.7. Combining negative [symbol]-velocity characteristics with parametric excitation. 13.8. Conclusions -- ch. 14. Impacts and dry friction. 14.1. Mathematical model of impact-dry-friction pair. 14.2. Condition of motion with impacts and after-impact dead zones. 14.3. Conditions of motion with dry friction and dead zones between stops. 14.4. Mathematical model of impact-dry-friction damper. 14.5. Characteristics of dampers with optimised parameters. 14.6. Conclusions -- ch. 15. Nonlinear dynamics of orthogonal metal cutting. 15.1. Introduction. 15.2. Previous work. 15.3. Mathematical modelling of MT-CP interactions. 15.4. Experimental studies. 15.5. Concluding remarks -- ch. 16. Dynamics of ultrasonic drilling of hard materials. 16.1. Introduction. 16.2. Previous work. 16.3. Mathematical modelling. 16.4. Experimental studies. 16.5. Conclusions. |