含放大机构的三要素型动力吸振器的H_(∞)优化  

H_(∞) optimization of 3-factor type dynamic vibration absorber with amplification mechanism

作　　者：周子博 申永军 杨绍普[1,2] ZHOU Zibo;SHEN Yongjun;YANG Shaopu(School of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;State Key Lab of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)

机构地区：[1]石家庄铁道大学机械工程学院,石家庄050043 [2]石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室,石家庄050043

出　　处：《振动与冲击》2022年第5期158-165,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(U1934201,11772206)。

摘　　要：提出了一种含放大机构的三要素型动力吸振器模型,研究了基于H_(∞)优化准则的系统参数最优解析解。首先,将三要素型黏弹性模型与放大机构引入动力吸振器中,通过拉氏变换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独立于阻尼比的三个固定点,利用固定点理论将三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。最后依据H_(∞)优化准则通过最小化幅频曲线的峰值得到了系统最优阻尼比设计公式,并通过数值仿真验证了解析解的正确性。与三种经典动力吸振器在简谐激励下进行了对比,证明了该模型有更好的吸振效果。Here,a 3-factor type dynamic vibration absorber model with amplification mechanism was proposed,and the optimal analytical solution to the system parameters based on H_(∞)optimization criterion was studied.Firstly,the 3-factor type viscoelastic model and amplification mechanism were introduced into the dynamic vibration absorber,and the analytical solution to the system was obtained using Laplace transform.Then,the analytical solution to the system was taken as the study object to find that there are 3 fixed points independent of damping ratio in the system.The 3 fixed points were adjusted to the same height by using the fixed-point theory to obtain design formulas for the optimal tuning ratio and the optimal stiffness ratio of the proposed absorber.Finally,the optimal damping ratio’s design formula of the system was obtained through minimizing the peak value of the system response amplitude-frequency curve according to H_(∞)optimization criterion.The correctness of the analytical solution was verified with numerical simulation.Comparing the results obtained using the proposed 3-factor type dynamic vibration absorber model with those obtained using 3 classical dynamic vibration absorbers under simple harmonic excitation,it was shown that the proposed model has better vibration absorption effect.

关 键 词：动力吸振器 放大机构 固定点理论 H_(∞)优化 

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