skip to content
Bifurcation and chaos in nonsmooth mechanical systems Preview this item
ClosePreview this item

Bifurcation and chaos in nonsmooth mechanical systems

Author: J Awrejcewicz; Claude-Henri Lamarque
Publisher: Singapore ; River Edge, NJ : World Scientific, 2003.
Series: World Scientific series on nonlinear science., Series A,, Monographs and treatises ;, v. 45.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
Getting this item's online copy... Getting this item's online copy...

Find a copy in the library

Getting this item's location and availability... Getting this item's location and availability...

WorldCat

Find it in libraries globally
Worldwide libraries own this item

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Awrejcewicz, J. (Jan).
Bifurcation and chaos in nonsmooth mechanical systems.
Singapore ; River Edge, NJ : World Scientific, 2003
(OCoLC)53362322
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: J Awrejcewicz; Claude-Henri Lamarque
ISBN: 9812564802 9789812564801
OCLC Number: 61048703
Description: 1 online resource (xvii, 543 pages) : illustrations (some color).
Contents: 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.
Series Title: World Scientific series on nonlinear science., Series A,, Monographs and treatises ;, v. 45.
Responsibility: Jan Awrejcewicz, Claude-Henri Lamarque.

Abstract:

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.
Retrieving notes about this item Retrieving notes about this item

Reviews

User-contributed reviews

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.