Revealing the mechanism causing stepwise maximum bounce height changes in a collision system and its engineering application

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K03942
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 20010:Mechanics and mechatronics-related
• Research Institution: Oita National College of Technology
• Principal Investigator: Karube Shu 大分工業高等専門学校, 機械工学科, 教授 (70370054)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: 衝突振動 / カオス転移現象 / 分岐 / バウンシングボール

Outline of Final Research Achievements

The bouncing ball system is a simple collision system. Previously, we studied the bouncing ball system numerically and experimentally, and discovered a new bifurcation structure in which the maximum height of the ball increases stepwise and non-smoothly when the frequency of the oscillating table is continuously increased, even though the bouncing ball is in a chaotic state.
In this study, we focused on the time interval between the takeoff and landing of the ball, and found that this bifurcation occurs when this interval and the vibration period of the table are nearly integer multiples.
In addition, we performed the same experiment as the bouncing ball system with another collision system that mimics the rigid overhead line and pantograph of a subway. As a result, we confirmed a stepwise increase trend similar to that of the bouncing ball system. However, there were some differences, such as not all of the generated vibrations being chaotic.

Free Research Field

機械力学

Academic Significance and Societal Importance of the Research Achievements

殆どの機械装置は，部品と部品の間に隙間が存在するため，衝突振動が発生しやすい．衝突振動による弊害として，例えば歯車の歯打ちによる騒音の発生，パンタグラフの離線現象などがある．本研究で対象とするバウンシングボール系は最も単純な衝突振動系であり，本系で発生する階段状カオス転移現象は他の機械系にも潜んでいる可能性が高い．階段状カオス転移現象は，一定の振幅の振動が急激に増加する現象であるため，本現象の発生メカニズムを解明することで，突発的に生じるようにみえる機械系の衝突振動を回避することが可能になると期待できる．