2021 Fiscal Year Final Research Report
New development in analysis of coupled oscillator systems focusing on resonance between oscillation modes
| Project/Area Number |
18K11476
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 61040:Soft computing-related
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| Research Institution | Chiba Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Keywords | 結合振動子 / 波動 / 摂動法 / 振動モード |
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| Outline of Final Research Achievements |
In this study, we distinguish between non degenerate and degenerate modes of the frequency components in the analysis of a coupled oscillator system for applying averaging method, which is one of the perturbation methods. This study investigates mutually-coupled bistable oscillators where there are diverse coexisting solutions. By investigating stabilities of the theoretically-obtained solutions, we find the existing solutions in the coupled oscillator system. Some of them correspond to the propagating wave solutions where the quasi-periodic pulse wave travels in the oscillator array. In addition, we also confirm that there are qualitatively the same propagating wave phenomena in the experimental results.
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| Free Research Field |
非線形動力学
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| Academic Significance and Societal Importance of the Research Achievements |
離散的な振動子が多数結合される系は多自由度となり, 自由度の数だけ振動モードが発生し, この振動モードの理解がこのような系の適切な設計に欠かせない. 振動の減衰・復元メカニズムなどに非線形性が関与する場合に, 振動エネルギーが局在化する現象やその応用に関して注目されているが, このような非線形系では単純な振動モードの重ね合わせとして議論できないことが, その適切な活用や設計を妨げる障壁となっている. 本研究で想定した振動モード間の共鳴は, 非線形結合振動子系では自然に起こりうると考えられ, 本研究で用いた解析手法を同様に用いれば, 移動型の振動解や発振パターン解析への波及効果が見込める.
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