一种含惯容和接地刚度的动力吸振器参数优化

PARAMETERS OPTIMIZATION OF A DYNAMIC VIBRATION ABSORBER WITH INERTER AND GROUNDED STIFFNESS

大多数机械振动属于有害振动,不仅会产生噪声还会降低设备的使用寿命和工作性能.接地刚度和惯容这两种器件均能改变系统的固有频率,在振动控制领域中有着良好的效果.但目前的大部分研究仅着眼于单一元件对系统产生的影响,而此类吸振器逐渐难以满足设备对振动控制需求的增长.在Voigt型动力吸振器模型的基础上,提出了一种含有惯容和接地刚度的新型动力吸振器模型,详细研究了该模型的最优设计参数,推导出最优设计公式的解析解.首先通过牛顿第二定律建立起二自由度系统的运动微分方程,计算出系统解析解,发现系统存在3个与阻尼比无关的固定点,利用固定点理论得到了动力吸振器的最优频率比.为保证系统稳定性,筛选最优接地刚度比时,发现不恰当的惯容系数会导致系统产生失稳现象,进而推导出惯容最佳工作范围,最终得到了最优接地刚度比和近似最优阻尼比.分析了惯容系数取值在最佳范围以外时系统的工作情况,并给出了实际应用中的建议.通过数值仿真验证了推导得到解析解的正确性.与多种已有的动力吸振器在简谐激励和随机激励的工况下进行对比,说明了该模型能够大幅降低主系统振幅,拓宽减振频带,为设计新型吸振器提供了理论依据.

Most mechanical vibrations are detrimental that not only generate noise but also reduce the service life and operating performance of the equipment.As two common components,grounded stiffness and inerter can change the natural frequency of the system,which has good effect in the field of vibration control.However,most of the current research only focuses on the impact of a single component on the system,and the vibration absorber is gradually difficult to meet the growth of performance demand for vibration control.Based on the typical Voigt-type dynamic vibration absorber,a novel dynamic vibration absorber model with inerter and grounded stiffness is presented.The optimal parameters of the presented model are studied in detail,and the analytical solution of the optimal design formula is derived.First of all,the motion differential equation of the two degree-of-freedom system is established through Newton’s second law,and from the system analytical solution it is found that the system has three fixed points unrelated to the damping ratio.The optimal frequency ratio of the dynamic vibration absorber is obtained based on the fixed-point theory.When screening the optimal grounded stiffness ratio,it is found that the inappropriate inerter coefficient will cause the system to generate instability.Then the best working range of the inerter is derived,and finally the optimal grounded stiffness ratio and approximate optimal damping ratio are also obtained.The working condition when the inerter coefficient is not within the best range is discussed,and the suggestions in practical application are given.The correctness of the analytical solution is verified by numerical simulation.Compared with other dynamic vibration absorbers under harmonic and random excitations,it is verified that the presented DVA can greatly reduce the amplitude of the primary system,widen the vibration reduction frequency band,and provide a theoretical basis for the design of new type of DVAs.