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中文摘要：
以四自由度迟滞非线性随机振动模型为研究对象,以速度和位移立方的模型来模拟振动系统的迟滞非线性力,并以Monte Carlo法模拟随机位移激励,对迟滞非线性随机系统的动力学特性进行分析.通过系统的Poincare截面、分岔图及最大Lyapunov指数分析了系统迟滞非线性力各参数对系统混沌状态的影响.研究表明,非线性刚度系数对振动系统混沌状态的影响较小,线性阻尼项和线性刚度项次之,而非线性阻尼项的影响最为明显.不仅证明了非线性振动系统随机混沌振动现象的存在,更重要的是可以为非线性振动系统参数的合理取值提供理论依据.
英文摘要：
A vibration model with nonlinear with four DOF was proposed. A usual cubic velocity and a usual cubic displacement were used to simulate nonlinear hysteretic force of vibration system, and random excitations were simulated with Monte-Carlo method. Based on Poincare section, fork picture and Lyapunov Index, the effect of hysteretic force＇ s parameters of system to chaos was analyzed. The results showed that nonlinear stiffness term affected the least to chaos of vibration system, nonlinear affected secondly, nonlinear damping term affected the most. The article not only proved the existence of random chaos in vibration system with nonlinearity, but also provided theoretical foundation for selecting parameters of vibration system with nonlinearity probably.
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