摘要
建立了由于摩擦引起的两个弹性体之间自激振动的数学模型.利用平均法求出了由干摩擦引起的多自由度分段光滑非线性动力系统的近似解析解,分析了搓动速度、振动频率与振幅的关系曲线,相位角与搓动速度的关系曲线,分析结果与数值解基本吻合.为研究多自由度分段光滑非线性系统提供了一种有效的近似解析分析方法.
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.
出处
《力学学报》
EI
CSCD
北大核心
2004年第3期373-378,共6页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金资助项目(10172046).~~
关键词
干摩擦
非线性振动
分段光滑
自激振动
平均法
dry friction, nonlinear vibration, piecewise-smooth, self-excited vibration, average method
