含负刚度元件的三要素型动力吸振器的参数优化  

Parameter optimization of three-element type dynamic vibration absorber with negative stiffness

作　　者：王孝然[1] 申永军[1] 杨绍普[1] 邢海军[1] 

机构地区：[1]石家庄铁道大学机械工程学院,河北石家庄050043

出　　处：《振动工程学报》2017年第2期177-184,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(11372198);河北省高等学校创新团队领军人才计划(LJRC018);河北省高等学校高层次人才科学研究项目(GCC2014053);河北省高层次人才资助项目(A201401001)

摘　　要：提出了一种含有负刚度弹簧元件的三要素型动力吸振器模型,对该模型最优参数进行了研究。首先,建立了系统的运动微分方程,得到了系统的解析解,发现该系统存在着3个固定点。利用固定点理论将3个固定点调到同一高度得到了动力吸振器的最优调谐比和最优刚度比设计公式,根据负刚度的特性得到了在保证系统稳定情况下的最优负刚度比,通过最小化幅频曲线的最大值得到了系统最优阻尼比设计公式。最后,通过数值解与解析解的对比说明了解析解的正确性。并通过与3种典型动力吸振器模型在简谐激励和随机激励情况下的对比,说明了此模型在主系统减振方面具有很大的优势,减振效果远优于3种已有动力吸振器模型,为设计新型动力吸振器模型提出了理论上的参考。A new kind of three-element type dynamic vibration absorber （DVA） with negative-stiffness spring is studied in de- tail. At first, the analytical solution of the system is obtained based on the established motion differential equation. Three fixed points are found in the amplitude-frequency curves of the primary system. The design formulae for the optimal tuning ratio and optimal stiffness ratio of the DVA are obtained by adjusting the three fixed points to the same height according to the fixed- point theory. According to the characteristics of negative-stiffness element, the optimal negative stiffness ratio is obtained and it could keep the system stable. Then the optimal damping ratio is obtained by minimizing the maximum value of the amplitude-frequency curves. The comparison between the analytical solution and the numerical one verifies the correctness of the analytical solution. The comparisons the presented DVA with three other traditional DVAs under the harmonic and random excitations show that the presented DVA in this paper performs better in vibration absorption. This result could provide theoretical basis for the optimal design of similar DVAs.

关 键 词：振动控制 动力吸振器 负刚度 固定点理论 参数优化 

分 类 号：O328[理学—一般力学与力学基础] TH113.1[理学—力学]