CAJ | 학술논문

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.
기우엄의Hertz접촉이론,건립료함대칭간극결구적팽당진동동역학모형,채용사-오계Runge-Kutta법진행료수치구해,병통과분석불동빈솔비、격진력폭치화간극하적분차도、상도、Poincaré도화공솔보도연구료해모형적비선성진동특성.결과표명：수착빈솔비、격진력폭치화간극적개변,팽당진동계통출현료주기、배주기화혼돈운동;빈솔비화격진력폭치대계통적비선성진동특성영향흔대,출현료교관적혼돈대,이간극대계통향응적영향상대교소,단재교소간극적변화범위내,계통적진동특성변화각교현저.
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.