Nonlinear Dynamics and Chaos in Systems with Discontinuous Support
Non-smooth systems are abundant in nature being usually related to physical systems with dry friction, impact and backlash. These systems operate in different modes, and the transition from one mode to another can often be idealized as an instantaneous or discrete transition. Since the time scale of...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2006/371630 |
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| _version_ | 1832555873194475520 |
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| author | Sandor Divenyi Marcelo Amorim Savi Luiz Fernando Penna Franca Hans Ingo Weber |
| author_facet | Sandor Divenyi Marcelo Amorim Savi Luiz Fernando Penna Franca Hans Ingo Weber |
| author_sort | Sandor Divenyi |
| collection | DOAJ |
| description | Non-smooth systems are abundant in nature being usually related to physical systems with dry friction, impact and backlash. These systems operate in different modes, and the transition from one mode to another can often be idealized as an instantaneous or discrete transition. Since the time scale of this transition is much smaller than the scale of the individual modes dynamics, its mathematical modeling can be lead as non-smooth. This contribution uses a smoothened switch model to analyze non-smooth systems. The procedure seems to be effective to deal with this kind of system, presenting advantages for the numerical implementation. As an application of the general formulation, a single-degree of freedom oscillator with discontinuous support is analyzed. System dynamical behavior shows a rich response, presenting dynamical jumps, bifurcations and chaos. |
| format | Article |
| id | doaj-art-9f608c3014a443f19d0a6393dcf6ff24 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-9f608c3014a443f19d0a6393dcf6ff242025-02-03T05:47:01ZengWileyShock and Vibration1070-96221875-92032006-01-01134-531532610.1155/2006/371630Nonlinear Dynamics and Chaos in Systems with Discontinuous SupportSandor Divenyi0Marcelo Amorim Savi1Luiz Fernando Penna Franca2Hans Ingo Weber3Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, COPPE, 21.941.972, Rio de Janeiro, RJ, P.O. Box 68.503, BrazilDepartment of Mechanical Engineering, Universidade Federal do Rio de Janeiro, COPPE, 21.941.972, Rio de Janeiro, RJ, P.O. Box 68.503, BrazilCSIRO Petroleum, Drilling Mechanics, Kensington WA 6151, P.O. Box 1130, Bentley WA 6102, AustraliaPontifícia Universidade Católica do Rio de Janeiro, Department of Mechanical Engineering, 22.453.900, Rio de Janeiro, RJ, BrazilNon-smooth systems are abundant in nature being usually related to physical systems with dry friction, impact and backlash. These systems operate in different modes, and the transition from one mode to another can often be idealized as an instantaneous or discrete transition. Since the time scale of this transition is much smaller than the scale of the individual modes dynamics, its mathematical modeling can be lead as non-smooth. This contribution uses a smoothened switch model to analyze non-smooth systems. The procedure seems to be effective to deal with this kind of system, presenting advantages for the numerical implementation. As an application of the general formulation, a single-degree of freedom oscillator with discontinuous support is analyzed. System dynamical behavior shows a rich response, presenting dynamical jumps, bifurcations and chaos.http://dx.doi.org/10.1155/2006/371630 |
| spellingShingle | Sandor Divenyi Marcelo Amorim Savi Luiz Fernando Penna Franca Hans Ingo Weber Nonlinear Dynamics and Chaos in Systems with Discontinuous Support Shock and Vibration |
| title | Nonlinear Dynamics and Chaos in Systems with Discontinuous Support |
| title_full | Nonlinear Dynamics and Chaos in Systems with Discontinuous Support |
| title_fullStr | Nonlinear Dynamics and Chaos in Systems with Discontinuous Support |
| title_full_unstemmed | Nonlinear Dynamics and Chaos in Systems with Discontinuous Support |
| title_short | Nonlinear Dynamics and Chaos in Systems with Discontinuous Support |
| title_sort | nonlinear dynamics and chaos in systems with discontinuous support |
| url | http://dx.doi.org/10.1155/2006/371630 |
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