Parameters optimization of a dynamic vibration absorber with inerter and grounded stiffness

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. © 2021, Chinese Journal of Theoretical and Applied Mechanics Press. All right reserved.