%0 Journal Article
%T Approximate Analytical Solution Of The Piecewise-Smooth Nonlinear Systems Of Multi-Degrees-Of-Freedom ------The Self-Excited Vibration Of The Chinese Cultural Relic Dragon Washbasin<br>多自由度分段光滑非线性系统的近似解——-中华文物龙洗的自激振动
%A Jia Qifen Yu Wen Liu Xijun Wang
%A <br>贾启芬
%A 于雯
%A 刘习军
%A 王大钧
%J 力学学报
%D 2004
%I 
%X Piecewise-smooth nonlinear dynamics system caused by dry friction is becoming hot problems in mechanics with the development of science and technology. The study of nonlinear dynamics including dry friction systems has made many progresses. Because of the complexity of equations, many researches were based on phase-plane orbit analysis and numerical analysis and experimental research. In this paper, a mathematical model of self-excited vibration caused by dry friction between two elastic structures was established using the Chinese cultural relic dragon washbasin as an example. An approximate analytical solution of the piecewise-smooth nonlinear dynamics systems of multi-degrees-of-freedom induced by dry friction was derived by means of averaging method. According to the approximate analytical solution, the curves of relation between swing and rubbing velocity of hands, the relation between swing and natural frequency of hands and the relation between phase angle and rubbing velocity of hands were obtained. The vibration mechanism of the water droplets spurting phenomenon of the Chinese cultural relic dragon washbasin is further explained. The results not only enhanced the precision but also explained qualitatively the whole kinematic process. If the parameters of the system in the design were changed, the design could be optimized according to the related curves, which supplied the theoretical basis for identifying parameter and analysis and research of steady region of this kind of nonlinear vibration systems. Furthermore, the results are in excellent agreement with that of the numerical solution, so that an efficient and credible analytical method to investigate piecewise-smooth nonlinear systems of multi-degrees-of-freedom was given in this paper.
%K dry friction
%K nonlinear vibration
%K piecewise-smooth
%K self-excited vibration
%K average method<br>干摩擦
%K 非线性振动
%K 分段光滑
%K 自激振动
%K 平均法
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=5D344E2AD54D14F8&jid=4100DA4A1A3BA1B0CE5AD99AE1DFB420&aid=F4DF4446BE3D77A1&yid=D0E58B75BFD8E51C&vid=933658645952ED9F&iid=38B194292C032A66&sid=F4BDB5452F9F5642&eid=73648F51F187AC5E&journal_id=0459-1879&journal_name=力学学报&referenced_num=0&reference_num=6