接地式三要素型动力吸振器的H_∞优化  

H_∞ OPTIMIZATION OF THE GROUNDED THREE-ELEMENT TYPE DYNAMIC VIBRATION ABSORBER

作　　者：王孝然[1] 申永军[1] 杨绍普[1] 

机构地区：[1]石家庄铁道大学机械工程学院,石家庄050043

出　　处：《动力学与控制学报》2016年第5期448-453,共6页Journal of Dynamics and Control

基　　金：国家自然科学基金(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：以一种接地式三要素型动力吸振器为对象,研究了基于H∞优化准则的系统参数最优解析解.首先,将串联型粘弹性模型引入到接地式的动力吸振器中,并建立了运动微分方程,得到了系统的解析解.随后,以系统的解析解为研究对象发现该系统存在着三个固定点,利用固定点理论将三个固定点调到了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,并依据H∞优化准则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,并证明了接地式三要素型动力吸振器有较好的吸振效果.Taking a new type of the grounded three-element type dynamic vibration absorber as the research ob- ject, the optimal analytical solution is studied based on H∞ optimization principle in this paper. Firstly, a series viscoelastic model is introduced into the grounded dynamic vibration absorber, and the analytical solution of the system is obtained based on the established motion differential equation. Three fixed points are found in the am- plitude-frequency curves of the primary system. Moreover, the design formulae for the optimal tuning ratio and the optimal stiffness ratio of the dynamic vibration absorber are developed by adjusting the three fixed points to the same height according to the fixed point theory. Then, the optimal damping ratio is obtained by minimizing the maximum value of the amplitude-frequency curves according to H∞ optimization principle. In addition, the com- parison between the numerical solution and the analytical solution is investigated. It verifies the correctness of the analytical solution, and illustrates that the grounded three-element type dynamic vibration absorber exhibites bet- ter performance of vibration absorption.

关 键 词：动力吸振器 固定点理论 H∞优化 参数优化 

分 类 号：TB535.1[理学—物理]