平均化法によるFrenkel-Kontorovaモデルの非線形解析

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  • 壽 龍治
    独立行政法人 国立高等専門学校機構 東京工業高等専門学校
  • 高田 宗一朗
    独立行政法人 国立高等専門学校機構 東京工業高等専門学校

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  • Nonlinear analysis of Frenkel-Kontorova model using method of averaging

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<p>In conventional work, the occurrence of super-lubrication has been pointed out using the Frenkel-Kontorova model (FK model). Friction phase diagrams have been developed to describe the occurrence of friction and super-lubrication based on two sliding conditions: solid-interaction and sliding velocity. In this paper, a nonlinear vibration analysis of the three-degree-of-freedom FK model is performed using the method of averaging method. The averaging equation is derived by considering only center-of-mass motion of FK chain in the super-lubrication phenomenon. As a result, only the amplitude equation was obtained for the center-of-mass motion. In addition, the averaging equation was solved numerically. From the results, phase diagram is obtained using the velocity of the center-of-mass and the nonlinear coefficient. The result shows that the trajectory becomes more complicated as the nonlinear coefficient increases, and the characteristics of the center-of-mass mode of motion can be captured when friction occurs.</p>

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