基于高性能低频隔振器的动力学与振动控制研究

发布时间：2018-08-17 16:10

【摘要】：近年来,随着科学技术突飞猛进的发展,各种重大基础设施(如,高层建筑,路、桥结构,核反应堆,重载高速列车等)和高端设备(如,精密加工仪器、激光探测仪、引力波探测装置等)对力学环境(如,冲击、随机激励,及地震波等含有危险的低频振动信号的环境)的要求越来越高,从而使得其对隔振器性能的要求也越来越高。由于传统的线性隔振器通常仅适用于固有频率远低于激励频率的情况,且尽管主动隔振器能够实现预期的隔振目标,但往往存在成本高、稳定性差、结构复杂、难以操作和维护等缺点,因此,研究非线性低频被动隔振器及提出改善其性能的动力学和控制理论的工作势在必行。本论文将通过崭新的视角,从因具有低频特征而备受关注的准零刚度非线性隔振器的复杂动力学研究出发,提出能够有效地改善低频隔振性能并实现抗冲击保护的理论和方法。本论文的主要内容与成果可以概括如下:建立了一个考虑重载的准零刚度隔振器的模型,并得到了其简化的数学模型。该模型的原型是由与质量块联结的垂向正刚度弹簧和在水平方向处于压缩状态并能在垂向运动时提供负刚度的一对弹簧构成。基于局部和全局分岔的理论,全面分析了该系统的复杂动力学现象及其存在规律和产生机理:展示了各种动力学响应在双参数空间中分布的拓扑结构,研究了各种响应的动力学特征,如相轨线的旋转数和对称性等;通过Floquet理论和数值延拓方法,得到了各参数下周期解的局部分岔模式;通过对吸引阱与吸引子的相图和周期鞍的不变流形的分析,阐明了混沌激变和阱边界变形的全局分岔机理。同时,揭示了与分岔分析相关的大量的非线性动力学现象和特征,包括共振舌头、跳跃现象、幅频响应特征、混沌海、暂态混沌、光滑的部分Wada阱等,及其产生机理。研究了所提出的准零刚度隔振器在简谐力和基础位移两种激励作用下的隔振性能和影响隔振有效性的非线性因素。通过平均法得到了该系统主共振解的幅频响应关系,并提出了对几何配置参数和刚度比参数的优化方法。提出了非线性隔振器传递率的评价公式,并对数值的和解析的结果进行了对比,表明解析结果能够很好地评价隔振系统的隔振性能,但同时需要充分地考虑该系统复杂而又丰富的动力学现象,如多解共存等。基于吸引子与吸引阱的相图的分析,提出了初值控制的思想,用于解决多解共存条件下小幅周期一解无法实现振动隔离的难题。提出了一种能够改善准零刚度系统隔振性能的分段阻尼控制方法。该控制方法依赖于相对位移预设值,通过切换阻尼的软模式和硬模式来实现:软模式是指系统在小阻尼下运动的情况,而硬模式是小阻尼与控制阻尼共同作用的工作模式。该控制方法不仅能够极大程度地降低隔振频率,同时可以提高对高频激励的隔振性能,并实现终端冲击保护。为了实现该控制目标,两个关键的问题需要解决:抑制与理想的周期一轨道共存的周期三轨道和实现相对位移预设值的最优化选取。同时,研究表明,该控制方法可以成功地阻止冲击危害的产生,并能够使得冲击下的响应快速地进入预期的理想轨道。
[Abstract]:In recent years, with the rapid development of science and technology, a variety of major infrastructure (such as high-rise buildings, roads, bridges, nuclear reactors, heavy-haul high-speed trains, etc.) and high-end equipment (such as precision machining instruments, laser detectors, gravitational wave detection devices, etc.) on the mechanical environment (such as impact, random excitation, seismic waves and other dangerous low-frequency. Because the traditional linear isolator is only suitable for the case where the natural frequency is far lower than the excitation frequency, and although the active isolator can achieve the desired vibration isolation target, it often has high cost, poor stability and complex structure. Therefore, it is imperative to study the nonlinear low frequency passive isolator and put forward the dynamics and control theory to improve its performance. In this paper, from a new perspective, starting from the complex dynamics research of quasi-zero stiffness nonlinear isolator which has attracted much attention due to its low frequency characteristics, the energy is proposed. The main contents and achievements of this paper can be summarized as follows: A quasi-zero stiffness isolator model considering heavy load is established and its simplified mathematical model is obtained. The prototype of the model is composed of a vertical positive stiffness spring connected with a mass block. A pair of springs that are compressed horizontally and can provide negative stiffness in vertical motion. Based on the theory of local and global bifurcation, the complex dynamical phenomena, their existence laws and production mechanisms of the system are comprehensively analyzed. The topological structures of the dynamic responses in the two-parameter space are shown, and each of them is studied. The local bifurcation modes of periodic solutions under various parameters are obtained by Floquet theory and numerical continuation method, and the global bifurcation mechanism of chaotic catastrophe and well boundary deformation is clarified by analyzing the phase diagrams of the trap and the attractor and the invariant manifold of the periodic saddle. At the same time, a large number of nonlinear dynamic phenomena and characteristics related to bifurcation analysis are revealed, including resonance tongue, jumping phenomena, amplitude-frequency response characteristics, chaotic sea, transient chaos, smooth partial Wada well, and their generating mechanism. The isolation of the proposed quasi-zero stiffness isolator under two excitations of simple harmonic force and base displacement is studied. The amplitude-frequency response relationship of the main resonance solution of the system is obtained by averaging method, and the optimization method of geometric configuration parameters and stiffness ratio parameters is proposed. The evaluation formula of the transmission rate of the nonlinear isolator is proposed, and the numerical and analytical results are compared, showing that the analytical method is effective. The results show that the isolation performance of the isolation system can be well evaluated, but the complex and abundant dynamic phenomena, such as the coexistence of multiple solutions, need to be fully considered. A piecewise damping control method is proposed to improve the isolation performance of a quasi-zero stiffness system. The control method relies on the relative displacement preset value and is realized by switching the soft mode and the hard mode of damping: the soft mode refers to the motion of the system with small damping, while the hard mode is the interaction of the small damping and the control damping. The control method can not only greatly reduce the vibration isolation frequency, but also improve the vibration isolation performance of high frequency excitation and achieve terminal impact protection. To achieve this control goal, two key problems need to be solved: suppressing the periodic three-track coexisting with the ideal periodic one-track and realizing relative displacement preconditioning. At the same time, the study shows that the control method can successfully prevent the occurrence of impact hazards, and can make the response under impact quickly enter the desired ideal orbit.
【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TB535

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