干摩擦自激振动周期解的同伦方法

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振动与冲击 ›› 2011, Vol. 30 ›› Issue (8) : 153-156.

论文

干摩擦自激振动周期解的同伦方法

张海涛1; 丁千1, 2

作者信息 +

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

Zhang Hai-tao1; Ding Qian1, 2

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文章历史 +

摘要

针对一类单质体-传输带干摩擦系统，首先对系统平衡点进行稳定性分析，然后利用同伦方法研究系统的纯滑动和粘滞滑动形式的干摩擦自激振动。通过适当选取基函数，定义初始猜测解、辅助线性算子和非线性算子，计算到二阶或三阶近似即可得到精度较高的解析近似解。由于粘-滑极限环的由两个阶段组成，具有非光滑特点，在计算其滑动阶段时，可以允许近似解中出现长期项。

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.

导出引用

张海涛;丁千;. 干摩擦自激振动周期解的同伦方法 [J]. 振动与冲击, 2011, 30(8): 153-156

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