The homotopy method for periodic self-excited vibration of a dry-friction system

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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (8) : 153-156.

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The homotopy method for periodic self-excited vibration of a dry-friction system

Zhang Hai-tao1; Ding Qian1, 2

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Abstract

Self-excited vibration induced by dry-friction of a block-on-belt model is studied in this paper. The stability of fixed point of the system is analyzed first. Then the self-excited vibration of the system, including pure slip type and stick-slip type, are investigated by the homotopy method. The second or the third-order analytic approximate solutions can be obtained with high precision, in which the motion characteristics of the system are revealed, by properly choosing the base function sets, initial guess of the solution and auxiliary linear operator respectively. For the stick-slip limit cycle composed by one slip stage and one stick stage, the approximate solution of the slip stage during one period contains secular terms.

Key words

Dry friction / Stability / Self-excited vibration / Stick-slip / Homotopy method

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Zhang Hai-tao; Ding Qian;. The homotopy method for periodic self-excited vibration of a dry-friction system[J]. Journal of Vibration and Shock, 2011, 30(8): 153-156