含惯容和接地刚度的黏弹性动力吸振器的参数优化  

Parameter optimization of viscoelastic dynamic vibration absorber with inerter and grounded stiffness

作　　者：范舒铜 申永军 FAN Shu-tong;SHEN Yong-jun(School of Mechanical Engineering,Shijazhuang Tiedao University,Shijiazhuang 050043,China;State Key Laboratory 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,河北石家庄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,河北石家庄050043

出　　处：《振动工程学报》2022年第4期814-825,共12页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(U1934201,11772206)。

摘　　要：将带有黏弹性特性的Maxwell模型引入系统中,提出一种含惯容和接地刚度的动力吸振器,并对该模型进行参数优化。建立系统的动力学方程并求出解析解,发现幅频曲线中存在三个固定点。利用固定点理论将系统的三个固定点调整到同一高度,得到系统的最优频率比和最优刚度比,并根据H_(∞)优化准则求出系统的最优阻尼比。在参数优化过程时,发现惯容比在一定范围内,有两组适合该模型的最优参数,进而确定不同惯容比所对应的最优参数。考虑实际工程应用并保证系统的稳定性,对比两组参数的优化结果,在常规参数下确定了惯容比的最佳工作范围。分析惯容比在最佳工作范围内外系统参数的选择对系统响应的影响,给出了在实际工程应用中的建议。与已有的动力吸振器在简谐激励和随机激励下的减振效果进行比较,说明恰当地选取惯容比可使系统有明显的减振优势,为设计动力吸振器提供理论依据。The Maxwell model with viscoelastic characteristics was introduced into the system to propose a new dynamic vibration absorber(DVA)with inerter and grounded stiffness,and the system parameters were optimized.The analytical solution was obtained based on the established dynamic equation.Three fixed-points were found in the amplitude-frequency curves.The optimal frequency ratio and optimal stiffness ratio of the DVA were determined by adjusting the three fixed points to the same height according to the fixed points theory,and the optimal damping ratio of the system was also obtained according to H∞optimization criterion.In the process of parameter optimization,when the inerter ratio was within a certain range,two groups of optimal parameters suitable for the model were found,and then the optimal parameters corresponding to different inerter ratios were determined.Considering the practical engineering application and ensuring the system stability,the optimization results of the two groups of parameters were compared,and the optimal working range of the inerter ratio was determined under the conventional parameters.The influence of the choice of system parameters on the system response inside and outside the optimal working range of inerter ratios was analyzed,and the suggestions in the practical engineering application were given.Compared with the existing dynamic vibration absorbers under harmonic excitation and random excitation,it shows that the system has obvious vibration reduction advantages by selecting the appropriate inerter ratio,which provides a theoretical basis for the design of new dynamic vibration absorbers.

关 键 词：动力吸振器 惯容 接地刚度 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]