接地式三要素型动力吸振器性能分析

利用固定点理论优化接地类型的动力吸振器得到的结果可能不是全局最优参数,在选择其他参数时主系统可以获得更小的振幅, 接地类型动力吸振器的优化问题值得进一步研究. 因此,以一种接地式三要素型动力吸振器为对象,通过研究系统参数变化对固 定点位置与主系统最大振幅的影响,得到了此吸振器的局部最优参数并分析了它的性能. 首先建立了此系统模型的运动微分方程, 得到了主系统振幅放大因子,发现系统存在3个与阻尼无关的固定点. 固定点中幅值较大点随系统参数变化的趋势可以代表最大振 幅随系统参数变化的趋势,因此利用盛金公式得到了固定点幅值的表达式. 为了更加精确,进一步使用数值算法得到了最大振幅与 系统参数的关系图,发现系统中存在局部最优参数. 通过对比接地式吸振器与接地三要素型吸振器的最大振幅随系统参数变化的趋 势,得到了接地式三要素型吸振器的局部最优参数,并发现当固有频率比小于局部最优频率比时,接地式三要素型吸振器模型主系 统的最大振幅要远小于接地式动力吸振器模型. 

PERFORMANCE ANALYSIS OF GROUNDED THREE-ELEMENT DYNAMIC VIBRATION ABSORBER1)

In grounded dynamic vibration absorbers (DVA), the changing tendencies of the fixed-point amplitude with the natural frequency ratio are not monotonous. Thus, the results obtained by optimizing this type DVA based on classical fixed-point theory may be the local optimum parameters. The primary system can obtain smaller amplitudes when selecting other parameters. The optimization of grounded type DVAs are worthy to further study. In addition, the damper of the DVA inevitably has some elasticity. Accordingly, a grounded three-element DVA is studied by analyzing the influence of system parameters on fixed-point positions and maximum amplitude in this paper. The local optimum parameters of the DVA are obtained and the performance is investigated. Firstly, the motion differential equation of the system is established, and the amplitude amplification factor of the primary system is obtained. It is found that there are three fixed-points independent of damping on the amplitude-frequency response curve. In most cases, by optimizing the damping ratio, the tendency of the larger of the fixed point changing with the system parameters can represent the tendency of the maximum amplitude changing with the system parameters. Therefore, the expressions of the fixed-point are obtained by using the Shengjin's formula. For more accuracy, the numerical algorithm is used to obtain the relationship between the maximum amplitude and the system parameters, and it is found that there are local optimum parameters in the system. Finally, in order to obtain the local optimum parameters the grounded three-element DVA is compared with the grounded DVA. The study shows that the local optimum parameters of the two DVAs are the same except the stiffness ratio. When the natural frequency is smaller than local optimum frequency ratio, the maximum amplitude of the primary system of the grounded three-element DVA model is much smaller than that of the grounded DVA.