Effects of time delay on the dynamical behavior of nonlinear beam on elastic foundation under periodic loadings: Chaotic detection and it control
In this paper, we analyze the effects of the time-delay feedback position on the dynamical behavior of the nonlinear beam on elastic foundation under periodic external force and the chaos control. Firstly, by using the formulation of Lagrange as well as geometric analysis, the nonlinear equation of...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-04-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722000900 |
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| author | Fabien Kenmogne Michael Soup Teoua Ouagni Hervé Simo Alain Soup Tewa Kammogne Blaise Ngwem Bayiha Martine Limi Wokwenmendam Emmanuel Elong François Ngapgue |
| author_facet | Fabien Kenmogne Michael Soup Teoua Ouagni Hervé Simo Alain Soup Tewa Kammogne Blaise Ngwem Bayiha Martine Limi Wokwenmendam Emmanuel Elong François Ngapgue |
| author_sort | Fabien Kenmogne |
| collection | DOAJ |
| description | In this paper, we analyze the effects of the time-delay feedback position on the dynamical behavior of the nonlinear beam on elastic foundation under periodic external force and the chaos control. Firstly, by using the formulation of Lagrange as well as geometric analysis, the nonlinear equation of the system with time-delay is established. In this case, the system rests on a Winkler-type elastic foundation soil that acts on its bottom interface (soil-beam). Secondly, the equilibrium points are found, their stability studied and the condition of Hopf bifurcation established. Thirdly, by using the Melnikov process, the analytical constraints necessary to have chaos or not as a behavior of the system are sought, which is confirmed by numerical investigations, with plotting of the time series, Lyapunov exponent and the bifurcation diagram, which are used to study the effects of time-delay on dynamical behavior of the system. This time-delay being used as a control parameter. The results show that when the value of time delay is small, the ergodic tori and resonance cycles with different rotation numbers on the torus can be observed. When the value of time-delay increases the chaos behaviors take place in the system. Taking into account the fact that chaotic situations are considered disturbance and are harmful for operation, the control method based on the time-delay parameter is used to quench and also to prevent chaotic behaviors. |
| first_indexed | 2024-12-13T10:31:17Z |
| format | Article |
| id | doaj.art-66f256724b3f40ef85b1eee2c4bac97e |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-13T10:31:17Z |
| publishDate | 2022-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-66f256724b3f40ef85b1eee2c4bac97e2022-12-21T23:50:50ZengElsevierResults in Physics2211-37972022-04-0135105305Effects of time delay on the dynamical behavior of nonlinear beam on elastic foundation under periodic loadings: Chaotic detection and it controlFabien Kenmogne0Michael Soup Teoua Ouagni1Hervé Simo2Alain Soup Tewa Kammogne3Blaise Ngwem Bayiha4Martine Limi Wokwenmendam5Emmanuel Elong6François Ngapgue7Department of Civil Engineering, Higher Teacher Training College of the Technical Education, University of Douala, Cameroon; Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototype, Faculty of Science, University of Yaoundé I, Po Box 812, Yaoundé, Cameroon; Corresponding author at: Department of Civil Engineering, Higher Teacher Training College of the Technical Education, University of Douala, Cameroon.Laboratoire de Mécanique et de Modélisation des Systèmes Physiques L2MSP, Faculté des Sciences, Université de Dschang, B.P. 067, Dschang, CameroonLaboratory of Modeling and Simulation in Engineering, Biomimetics and Prototype, Faculty of Science, University of Yaoundé I, Po Box 812, Yaoundé, Cameroon; Department of Mechanical Engineering, the University Institute of Technology, P.O. Box 455, The University of Ngaoundéré, CameroonLaboratory of Electronics and Signal Processing, Faculty of Science, University of Dschang, Po Box 067, Dschang, CameroonDepartment of Civil Engineering, Higher Teacher Training College of the Technical Education, University of Douala, CameroonDepartment of Mechanical and Industrial Engineering, National High Polytechnic Institute (NAHPI), The University of Bamenda (UBa), CameroonDepartment of Civil Engineering, Higher Teacher Training College of the Technical Education, University of Douala, CameroonLaboratoire de Mécanique et de Modélisation des Systèmes Physiques L2MSP, Faculté des Sciences, Université de Dschang, B.P. 067, Dschang, CameroonIn this paper, we analyze the effects of the time-delay feedback position on the dynamical behavior of the nonlinear beam on elastic foundation under periodic external force and the chaos control. Firstly, by using the formulation of Lagrange as well as geometric analysis, the nonlinear equation of the system with time-delay is established. In this case, the system rests on a Winkler-type elastic foundation soil that acts on its bottom interface (soil-beam). Secondly, the equilibrium points are found, their stability studied and the condition of Hopf bifurcation established. Thirdly, by using the Melnikov process, the analytical constraints necessary to have chaos or not as a behavior of the system are sought, which is confirmed by numerical investigations, with plotting of the time series, Lyapunov exponent and the bifurcation diagram, which are used to study the effects of time-delay on dynamical behavior of the system. This time-delay being used as a control parameter. The results show that when the value of time delay is small, the ergodic tori and resonance cycles with different rotation numbers on the torus can be observed. When the value of time-delay increases the chaos behaviors take place in the system. Taking into account the fact that chaotic situations are considered disturbance and are harmful for operation, the control method based on the time-delay parameter is used to quench and also to prevent chaotic behaviors.http://www.sciencedirect.com/science/article/pii/S2211379722000900Nonlinear beamTime delayElastic foundationMelnikov theory of chaosControl of chaos |
| spellingShingle | Fabien Kenmogne Michael Soup Teoua Ouagni Hervé Simo Alain Soup Tewa Kammogne Blaise Ngwem Bayiha Martine Limi Wokwenmendam Emmanuel Elong François Ngapgue Effects of time delay on the dynamical behavior of nonlinear beam on elastic foundation under periodic loadings: Chaotic detection and it control Results in Physics Nonlinear beam Time delay Elastic foundation Melnikov theory of chaos Control of chaos |
| title | Effects of time delay on the dynamical behavior of nonlinear beam on elastic foundation under periodic loadings: Chaotic detection and it control |
| title_full | Effects of time delay on the dynamical behavior of nonlinear beam on elastic foundation under periodic loadings: Chaotic detection and it control |
| title_fullStr | Effects of time delay on the dynamical behavior of nonlinear beam on elastic foundation under periodic loadings: Chaotic detection and it control |
| title_full_unstemmed | Effects of time delay on the dynamical behavior of nonlinear beam on elastic foundation under periodic loadings: Chaotic detection and it control |
| title_short | Effects of time delay on the dynamical behavior of nonlinear beam on elastic foundation under periodic loadings: Chaotic detection and it control |
| title_sort | effects of time delay on the dynamical behavior of nonlinear beam on elastic foundation under periodic loadings chaotic detection and it control |
| topic | Nonlinear beam Time delay Elastic foundation Melnikov theory of chaos Control of chaos |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722000900 |
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