Self-synchronized phenomena generated in coupled self-excited oscillators with stick-slip motion

Tomoki Ono, Takahiro Kondou, Yasuhiro Bonkobara

Research output: Contribution to journalArticle

Abstract

A simple nonlinear system generating the self-synchronization is developed in order to clarify the occurrence mechanism of the phenomena. This system consists of two nonlinear self-excited oscillators with Coulomb friction and the stick-slip motion is generated. These two oscillators are directly coupled in series by a coil-spring and a dashpot. The self-synchronized phenomena generated in this system are investigated analytically and experimentally. The validity of the analytical model and the computational method based on the shooting method are verified by comparing the computational results and the experimental results. It is clarified that two types of the self-synchronized solutions exist in this system and the vibration patterns of the self-synchronized solutions are closely related to the undamped free vibration characteristics of the model without Coulomb friction. In addition, the differences between the occurrence mechanisms of the self-synchronized solutions are analytically confirmed by examining the energy transmission between two oscillators through the coupling element. It is also proved that the unstable regions caused by the internal resonance exist in the solution branch in which two oscillators vibrate nearly in phase.

Original languageEnglish
Pages (from-to)28-42
Number of pages15
JournalNihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
Volume77
Issue number773
Publication statusPublished - 2011

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Stick-slip
Friction
Computational methods
Nonlinear systems
Analytical models
Synchronization

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Mechanics of Materials
  • Industrial and Manufacturing Engineering

Cite this

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title = "Self-synchronized phenomena generated in coupled self-excited oscillators with stick-slip motion",
abstract = "A simple nonlinear system generating the self-synchronization is developed in order to clarify the occurrence mechanism of the phenomena. This system consists of two nonlinear self-excited oscillators with Coulomb friction and the stick-slip motion is generated. These two oscillators are directly coupled in series by a coil-spring and a dashpot. The self-synchronized phenomena generated in this system are investigated analytically and experimentally. The validity of the analytical model and the computational method based on the shooting method are verified by comparing the computational results and the experimental results. It is clarified that two types of the self-synchronized solutions exist in this system and the vibration patterns of the self-synchronized solutions are closely related to the undamped free vibration characteristics of the model without Coulomb friction. In addition, the differences between the occurrence mechanisms of the self-synchronized solutions are analytically confirmed by examining the energy transmission between two oscillators through the coupling element. It is also proved that the unstable regions caused by the internal resonance exist in the solution branch in which two oscillators vibrate nearly in phase.",
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AU - Ono, Tomoki

AU - Kondou, Takahiro

AU - Bonkobara, Yasuhiro

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N2 - A simple nonlinear system generating the self-synchronization is developed in order to clarify the occurrence mechanism of the phenomena. This system consists of two nonlinear self-excited oscillators with Coulomb friction and the stick-slip motion is generated. These two oscillators are directly coupled in series by a coil-spring and a dashpot. The self-synchronized phenomena generated in this system are investigated analytically and experimentally. The validity of the analytical model and the computational method based on the shooting method are verified by comparing the computational results and the experimental results. It is clarified that two types of the self-synchronized solutions exist in this system and the vibration patterns of the self-synchronized solutions are closely related to the undamped free vibration characteristics of the model without Coulomb friction. In addition, the differences between the occurrence mechanisms of the self-synchronized solutions are analytically confirmed by examining the energy transmission between two oscillators through the coupling element. It is also proved that the unstable regions caused by the internal resonance exist in the solution branch in which two oscillators vibrate nearly in phase.

AB - A simple nonlinear system generating the self-synchronization is developed in order to clarify the occurrence mechanism of the phenomena. This system consists of two nonlinear self-excited oscillators with Coulomb friction and the stick-slip motion is generated. These two oscillators are directly coupled in series by a coil-spring and a dashpot. The self-synchronized phenomena generated in this system are investigated analytically and experimentally. The validity of the analytical model and the computational method based on the shooting method are verified by comparing the computational results and the experimental results. It is clarified that two types of the self-synchronized solutions exist in this system and the vibration patterns of the self-synchronized solutions are closely related to the undamped free vibration characteristics of the model without Coulomb friction. In addition, the differences between the occurrence mechanisms of the self-synchronized solutions are analytically confirmed by examining the energy transmission between two oscillators through the coupling element. It is also proved that the unstable regions caused by the internal resonance exist in the solution branch in which two oscillators vibrate nearly in phase.

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