含间隙碰撞振动系统的非线性振动特性

Nonlinear Vibration Characteristics of a Vibro-impact System with Clearance

基于广义Hertz接触理论,建立了含对称间隙结构的碰撞振动动力学模型,采用四-五阶Runge-Kutta法进行了数值求解,并通过分析不同频率比、激振力幅值和间隙下的分岔图、相图、Poincaré图和功率谱图研究了该模型的非线性振动特性.结果表明:随着频率比、激振力幅值和间隙的改变,碰撞振动系统出现了周期、倍周期和混沌运动;频率比和激振力幅值对系统的非线性振动特性影响很大,出现了较宽的混沌带,而间隙对系统响应的影响相对较小,但在较小间隙的变化范围内,系统的振动特性变化却较显著.

A dynamic model for vibro-impact system with clearance has been established based on generalized Hertz contact theory,which is numerically solved by 4-5 order Runge-Kutta method.Non-linear vibration characteristics of the model is studied by analyzing the bifurcation diagrams,the phase diagram,the Poincaré maps and the power spectrum chart respectively obtained at different frequency ratios,exci-ting force amplitudes and clearances.Results show that period,period doubling and chaotic motion occur in the vibro-impact system with the variation of frequency ratio,amplitude of exciting force and size of clearance,among which the frequency ratio and amplitude of exciting force play an important role in influencing the non-linear vibration characteristics,when broad chaotic bands appear;the size of clearance effects little on the system response,however,within the small variation range of clearance,the vibration characteristics change greatly.