Bifurcation and chaos in nonsmooth mechanical systems:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2003
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| Schriftenreihe: | World Scientific series on nonlinear science
v. 45 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (pages 507-530) and index 1. Introduction to discontinuous ODEs. 1.1. Introduction. 1.2. Filippov's theory. 1.3. Aizerman's theory. 1.4. Examples. 1.5. Boundary value problem -- 2. Mathematical background for multivalued formulations. 2.1. Origin of nonlinearities. 2.2. Smooth and nonsmooth nonlinearities. 2.3. Examples and dynamical equilibria. 2.4. Existence and uniqueness. 2.5. Stochastic frame -- 3. Numerical schemes and analytical methods. 3.1. Numerical schemes. 3.2. Analytical methods -- 4. Properties of numerical schemes. 4.1. Dynamics of systems with friction or elastoplastic terms. 4.2. Systems with impacts. 4.3. Conclusion -- 5. Bifurcations of a particular van der Pol-Duffing oscillator. 5.1. The analysed system and the averaged equations. 5.2. "0" type bifurcations. 5.3. Complex bifurcations. 5.4. Observations of strange attractors using numerical simulations -- 6. Stick-slip oscillator with two degrees of freedom. 6.1. Introduction. 6.2. Disc -- flexible arm oscillator. 6.3. Two horizontally situated masses -- 7. Piecewise linear approximations. 7.1. Introduction. 7.2. Exact and approximated models. 7.3. Approximation and global dynamic behavior. 7.4. Numerical results. 7.5. Conclusion -- 8. Chua's circuit with discontinuities. 8.1. Introduction. 8.2. Mechanical realizations of Chua's circuit. 8.3. Generalized double scroll Chua's circuit -- 9. Mechanical system with impacts and modal approaches. 9.1. Introduction. 9.2. Single degree of freedom system. 9.3. Two degrees of freedom systems. 9.4. Conclusion -- 10. One DOF mechanical system with friction. 10.1. Introduction. 10.2. Modelling the pendulum with friction. 10.3. Numerical results. 10.4. The Melnikov analysis. 10.5. Conclusion 11. Modelling the dynamical behaviour of elasto-plastic systems. 11.1. Rheological systems with "friction" -- 12. A mechanical system with 7 DOF. 12.1. Mathematical model. 12.2. Numerical results and comments for finite k3 -- 13. Stability of singular periodic motions in single degree of freedom vibro-impact oscillators and grazing bifurcations. 13.1. Introduction. 13.2. Mechanical system and change of coordinates. 13.3. Local expansion of the Poincaré map. 13.4. Stability of the nondifferentiable fixed point. 13.5. Applications. 13.6. Conclusion -- 14. Triple pendulum with impacts. 14.1. Introduction. 14.2. Investigated pendulum and governing equations (without impacts). 14.3. Introduction of the obstacles. 14.4. Calculation of the fundamental solution matrices for dynamical systems with impacts. 14.5. Simplification of the system. 14.6. The method used for integration of the system and its accuracy. 14.7. Numerical examples. 14.8. Concluding remarks -- 15. Analytical prediction of stick-slip chaos. 15.1. Introduction. 15.2. The Melnikov's method. 15.3. Analyzed system. 15.4. Analytical results -- 16. Thermoelasticity, wear and stick-slip movements of a rotating shaft with a rigid bush. 16.1. Introduction -- 17. Control for discrete models of buildings including elastoplastic terms. 17.1. Introduction. 17.2. Reminder about Prandtl rheological model. 17.3. The studied models with n DOF. 17.4. Existence and uniqueness results. 17.5. Numerical scheme. 17.6. Control procedure. 17.7. Algorithm of control. 17.8 Numerical results for a system with 3 DOF. 17.9. Extension to nonlinear cases. 17.10. Conclusion This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments |
| Beschreibung: | 1 Online-Ressource (xvii, 543 pages) |
| ISBN: | 9789812564801 9812564802 |
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| 490 | 0 | |a World Scientific series on nonlinear science |v v. 45 | |
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| 500 | |a 1. Introduction to discontinuous ODEs. 1.1. Introduction. 1.2. Filippov's theory. 1.3. Aizerman's theory. 1.4. Examples. 1.5. Boundary value problem -- 2. Mathematical background for multivalued formulations. 2.1. Origin of nonlinearities. 2.2. Smooth and nonsmooth nonlinearities. 2.3. Examples and dynamical equilibria. 2.4. Existence and uniqueness. 2.5. Stochastic frame -- 3. Numerical schemes and analytical methods. 3.1. Numerical schemes. 3.2. Analytical methods -- 4. Properties of numerical schemes. 4.1. Dynamics of systems with friction or elastoplastic terms. 4.2. Systems with impacts. 4.3. Conclusion -- 5. Bifurcations of a particular van der Pol-Duffing oscillator. 5.1. The analysed system and the averaged equations. 5.2. "0" type bifurcations. 5.3. Complex bifurcations. 5.4. Observations of strange attractors using numerical simulations -- 6. Stick-slip oscillator with two degrees of freedom. 6.1. Introduction. 6.2. Disc -- flexible arm oscillator. 6.3. Two horizontally situated masses -- 7. Piecewise linear approximations. 7.1. Introduction. 7.2. Exact and approximated models. 7.3. Approximation and global dynamic behavior. 7.4. Numerical results. 7.5. Conclusion -- 8. Chua's circuit with discontinuities. 8.1. Introduction. 8.2. Mechanical realizations of Chua's circuit. 8.3. Generalized double scroll Chua's circuit -- 9. Mechanical system with impacts and modal approaches. 9.1. Introduction. 9.2. Single degree of freedom system. 9.3. Two degrees of freedom systems. 9.4. Conclusion -- 10. One DOF mechanical system with friction. 10.1. Introduction. 10.2. Modelling the pendulum with friction. 10.3. Numerical results. 10.4. The Melnikov analysis. 10.5. Conclusion | ||
| 500 | |a 11. Modelling the dynamical behaviour of elasto-plastic systems. 11.1. Rheological systems with "friction" -- 12. A mechanical system with 7 DOF. 12.1. Mathematical model. 12.2. Numerical results and comments for finite k3 -- 13. Stability of singular periodic motions in single degree of freedom vibro-impact oscillators and grazing bifurcations. 13.1. Introduction. 13.2. Mechanical system and change of coordinates. 13.3. Local expansion of the Poincaré map. 13.4. Stability of the nondifferentiable fixed point. 13.5. Applications. 13.6. Conclusion -- 14. Triple pendulum with impacts. 14.1. Introduction. 14.2. Investigated pendulum and governing equations (without impacts). 14.3. Introduction of the obstacles. 14.4. Calculation of the fundamental solution matrices for dynamical systems with impacts. 14.5. Simplification of the system. 14.6. The method used for integration of the system and its accuracy. 14.7. Numerical examples. 14.8. Concluding remarks -- 15. Analytical prediction of stick-slip chaos. 15.1. Introduction. 15.2. The Melnikov's method. 15.3. Analyzed system. 15.4. Analytical results -- 16. Thermoelasticity, wear and stick-slip movements of a rotating shaft with a rigid bush. 16.1. Introduction -- 17. Control for discrete models of buildings including elastoplastic terms. 17.1. Introduction. 17.2. Reminder about Prandtl rheological model. 17.3. The studied models with n DOF. 17.4. Existence and uniqueness results. 17.5. Numerical scheme. 17.6. Control procedure. 17.7. Algorithm of control. 17.8 Numerical results for a system with 3 DOF. 17.9. Extension to nonlinear cases. 17.10. Conclusion | ||
| 500 | |a This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments | ||
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| 650 | 7 | |a Bifurcation theory |2 fast | |
| 650 | 7 | |a Chaotic behavior in systems |2 fast | |
| 650 | 7 | |a Differential equations, Nonlinear |2 fast | |
| 650 | 4 | |a Bifurcation theory | |
| 650 | 4 | |a Chaotic behavior in systems | |
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Datensatz im Suchindex
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| author | Awrejcewicz, J., (Jan) |
| author_facet | Awrejcewicz, J., (Jan) |
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| author_sort | Awrejcewicz, J., (Jan) |
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| id | DE-604.BV043157948 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:19:15Z |
| institution | BVB |
| isbn | 9789812564801 9812564802 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028582139 |
| oclc_num | 61048703 |
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| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xvii, 543 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | World Scientific |
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| series2 | World Scientific series on nonlinear science |
| spelling | Awrejcewicz, J., (Jan) Verfasser aut Bifurcation and chaos in nonsmooth mechanical systems Jan Awrejcewicz, Claude-Henri Lamarque Singapore World Scientific 2003 1 Online-Ressource (xvii, 543 pages) txt rdacontent c rdamedia cr rdacarrier World Scientific series on nonlinear science v. 45 Includes bibliographical references (pages 507-530) and index 1. Introduction to discontinuous ODEs. 1.1. Introduction. 1.2. Filippov's theory. 1.3. Aizerman's theory. 1.4. Examples. 1.5. Boundary value problem -- 2. Mathematical background for multivalued formulations. 2.1. Origin of nonlinearities. 2.2. Smooth and nonsmooth nonlinearities. 2.3. Examples and dynamical equilibria. 2.4. Existence and uniqueness. 2.5. Stochastic frame -- 3. Numerical schemes and analytical methods. 3.1. Numerical schemes. 3.2. Analytical methods -- 4. Properties of numerical schemes. 4.1. Dynamics of systems with friction or elastoplastic terms. 4.2. Systems with impacts. 4.3. Conclusion -- 5. Bifurcations of a particular van der Pol-Duffing oscillator. 5.1. The analysed system and the averaged equations. 5.2. "0" type bifurcations. 5.3. Complex bifurcations. 5.4. Observations of strange attractors using numerical simulations -- 6. Stick-slip oscillator with two degrees of freedom. 6.1. Introduction. 6.2. Disc -- flexible arm oscillator. 6.3. Two horizontally situated masses -- 7. Piecewise linear approximations. 7.1. Introduction. 7.2. Exact and approximated models. 7.3. Approximation and global dynamic behavior. 7.4. Numerical results. 7.5. Conclusion -- 8. Chua's circuit with discontinuities. 8.1. Introduction. 8.2. Mechanical realizations of Chua's circuit. 8.3. Generalized double scroll Chua's circuit -- 9. Mechanical system with impacts and modal approaches. 9.1. Introduction. 9.2. Single degree of freedom system. 9.3. Two degrees of freedom systems. 9.4. Conclusion -- 10. One DOF mechanical system with friction. 10.1. Introduction. 10.2. Modelling the pendulum with friction. 10.3. Numerical results. 10.4. The Melnikov analysis. 10.5. Conclusion 11. Modelling the dynamical behaviour of elasto-plastic systems. 11.1. Rheological systems with "friction" -- 12. A mechanical system with 7 DOF. 12.1. Mathematical model. 12.2. Numerical results and comments for finite k3 -- 13. Stability of singular periodic motions in single degree of freedom vibro-impact oscillators and grazing bifurcations. 13.1. Introduction. 13.2. Mechanical system and change of coordinates. 13.3. Local expansion of the Poincaré map. 13.4. Stability of the nondifferentiable fixed point. 13.5. Applications. 13.6. Conclusion -- 14. Triple pendulum with impacts. 14.1. Introduction. 14.2. Investigated pendulum and governing equations (without impacts). 14.3. Introduction of the obstacles. 14.4. Calculation of the fundamental solution matrices for dynamical systems with impacts. 14.5. Simplification of the system. 14.6. The method used for integration of the system and its accuracy. 14.7. Numerical examples. 14.8. Concluding remarks -- 15. Analytical prediction of stick-slip chaos. 15.1. Introduction. 15.2. The Melnikov's method. 15.3. Analyzed system. 15.4. Analytical results -- 16. Thermoelasticity, wear and stick-slip movements of a rotating shaft with a rigid bush. 16.1. Introduction -- 17. Control for discrete models of buildings including elastoplastic terms. 17.1. Introduction. 17.2. Reminder about Prandtl rheological model. 17.3. The studied models with n DOF. 17.4. Existence and uniqueness results. 17.5. Numerical scheme. 17.6. Control procedure. 17.7. Algorithm of control. 17.8 Numerical results for a system with 3 DOF. 17.9. Extension to nonlinear cases. 17.10. Conclusion This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments MATHEMATICS / Differential Equations / General bisacsh Bifurcation theory fast Chaotic behavior in systems fast Differential equations, Nonlinear fast Bifurcation theory Chaotic behavior in systems Differential equations, Nonlinear Mechanisches System (DE-588)4132811-5 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Mechanisches System (DE-588)4132811-5 s Chaostheorie (DE-588)4009754-7 s 1\p DE-604 Lamarque, Claude-Henri Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=135170 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Awrejcewicz, J., (Jan) Bifurcation and chaos in nonsmooth mechanical systems MATHEMATICS / Differential Equations / General bisacsh Bifurcation theory fast Chaotic behavior in systems fast Differential equations, Nonlinear fast Bifurcation theory Chaotic behavior in systems Differential equations, Nonlinear Mechanisches System (DE-588)4132811-5 gnd Chaostheorie (DE-588)4009754-7 gnd |
| subject_GND | (DE-588)4132811-5 (DE-588)4009754-7 |
| title | Bifurcation and chaos in nonsmooth mechanical systems |
| title_auth | Bifurcation and chaos in nonsmooth mechanical systems |
| title_exact_search | Bifurcation and chaos in nonsmooth mechanical systems |
| title_full | Bifurcation and chaos in nonsmooth mechanical systems Jan Awrejcewicz, Claude-Henri Lamarque |
| title_fullStr | Bifurcation and chaos in nonsmooth mechanical systems Jan Awrejcewicz, Claude-Henri Lamarque |
| title_full_unstemmed | Bifurcation and chaos in nonsmooth mechanical systems Jan Awrejcewicz, Claude-Henri Lamarque |
| title_short | Bifurcation and chaos in nonsmooth mechanical systems |
| title_sort | bifurcation and chaos in nonsmooth mechanical systems |
| topic | MATHEMATICS / Differential Equations / General bisacsh Bifurcation theory fast Chaotic behavior in systems fast Differential equations, Nonlinear fast Bifurcation theory Chaotic behavior in systems Differential equations, Nonlinear Mechanisches System (DE-588)4132811-5 gnd Chaostheorie (DE-588)4009754-7 gnd |
| topic_facet | MATHEMATICS / Differential Equations / General Bifurcation theory Chaotic behavior in systems Differential equations, Nonlinear Mechanisches System Chaostheorie |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=135170 |
| work_keys_str_mv | AT awrejcewiczjjan bifurcationandchaosinnonsmoothmechanicalsystems AT lamarqueclaudehenri bifurcationandchaosinnonsmoothmechanicalsystems |