多自由度碰撞振动系统在特定激励下的动力学特性及其工程应用

Based on the increment-dimensional precise integration method, the stochastic averaging method, the pseudo excitation method, the mapping theory and the principle of superposition theory, this project is to explore and obtain the efficient algorithms of the theoretical solution (an approximate analytic solution with higher accuracy) of the periodic motion and the piecewise compound mapping (the transition mapping of the non-smooth place especially considered)of the double-degree-of-freedom vibro-impact (both single-side and double-side impact) system the dry friction included under the harmonic excitation, broad-band(or narrow-band) noise interference or random excitation. Then with the theoretical calculation, the numerical simulation method of the vibration characteristics of the system will be gained. Further the dynamics of the system (such complicated dynamics behavior as the bifurcation in two parameters change and the high-dimensional sliding bifurcation) will be studied, which reveals the influence rules that the system parameters have on the system response. As the engineering applications, the random vibration from the electromagnetic vibrator should be considered. The random response characteristics of the shaker (4-degree-of- freedom system) will be investigated through using the electromagnetic vibrator as the repulse excitation and the system parameters will be optimized according to the effect of the falling sands. On the basis of the stiffness of the wheels and the rubber nodes of the double-side vehicle dampers, we will establish a coupling model of the vehicle and railway that is closer to the actual condition.Then the vertical random vibration response of the railway vehicle (22-degree-of-freedom system) will be studied under the condition of the excitation of the rugged railway in order to optimize the structural parameters of the vehicle.

本项目基于增维精细积分法、随机平均法、虚拟激励法、映射理论和叠加原理等理论，探求并获得含干摩擦的双自由度碰撞（单、双侧碰撞）振动系统在简谐激励、宽窄带噪声干扰、随机激励下周期运动理论解（有较高精度的近似解析解）的有效算法和系统的分段复合映射（着重考虑在非光滑处的转换映射），结合理论计算获得系统振动特性的有效数值仿真方法，进而研究系统的动力学特性（如两个参数变化下的分岔、高维Sliding分岔等复杂动力学行为），揭示系统参数对系统响应的影响规律。作为工程应用，考虑电磁作动器地基的随机振动，研究以电磁作动器为激励的冲击振动落砂机(4自由度) 的随机响应特性，并考虑落砂效果对系统参数进行优化；考虑轮对刚度和车辆阻尼器两端的橡胶节点，建立更接近实际的车辆和轨道耦合模型，进而研究轨道高低不平顺激励下的铁道车辆的垂向随机振动响应(22自由度)，从而优化车辆的结构参数。

在现实的工程领域中，碰撞振动系统常常受到摩擦和随机因素的影响，如实际系统动力学模型的非线性元件的线性化处理，以及外界环境随机干扰，弹簧系数、阻尼系数、恢复系数和激振力都可能是随机的参数。而对含摩擦的碰撞振动系统在随机干扰、随机激励或其与简谐联合作用下的动力学特性研究较少（因为随着系统自由度的增加，并考虑摩擦和随机因素，碰撞振动系统的动力学特性会变得越复杂，研究工作也越困难），因此在碰撞振动系统的基础上考虑摩擦和附加随机干扰来进行动力学分析对今后的工程应用更具有指导意义。.本项目建立了几类含摩擦及间隙的碰撞振动系统在简谐激励、随机干扰作用下的力学模型和运动方程，给出振子运动情况的判断条件，用chebyshev多项式逼近获得系统随机响应的近似理论解，数值仿真分析了系统摩擦诱导振动的特性，并讨论了系统关键参数对系统动力学特性的影响,结果表明系统在不同参数下存在复杂多样的摩擦诱导振动形式：稳定周期摩擦振动、概周期摩擦粘滞振动、概周期瞬时摩擦诱导振动、颤振碰撞、摩擦诱导粘滞擦边碰撞振动及摩擦诱导粘滞混沌振动等。计算Duffing系统在双参数平面上最大Lyapunov指数的分布特性，讨论了Duffing系统在双参数平面上的分岔特性，结果发现在双参数平面上系统发生叉式分岔，出现具有缺边现象的两个不同区域，存在两吸引子共存现象，随刚度系数的不断增加系统出现了倍周期分岔曲线环，而且倍周期分岔曲线环内不断嵌套新的倍周期分岔曲线环；系统外激励频率较小时常引起颤振运动。作为应用，考虑车轮刚度和车辆悬架系统橡胶节点，研究了轨道高低不平顺激励下的铁道车辆的垂向随机振动响应，揭示系统参数对系统响应的影响规律, 给出了部分系统参数的最优取值范围。.本项目研究的部分结果，可为机械系统（如单列圆柱滚子轴承系统，车辆悬挂系统等）的动态优化设计、系统安全性与可靠性及工业噪声控制提供理论基础。