Parameter optimization of a grounded dynamic vibration absorber with lever and inerter

Abstract

Mechanical vibration is mostly harmful, and it may not only generate noise but also affect the working life of the equipment. Lever, inerter, and grounded stiffness have good performance in the field of vibration control, but the dynamic vibration absorber simultaneously containing lever, inerter, and grounded stiffness is rarely studied. Based on the grounded dampertype dynamic vibration absorber, a dynamic vibration absorber with lever, inerter, and grounded stiffness is presented. And the optimal system parameters are analytically researched in detail. Firstly, the differential equation of motion is established according to Newton’s second law, and the analytical solution of the system is obtained. According to the amplitudefrequency curve of the system, it is obvious that there are two fixed points unrelated to the damping ratio. Meanwhile, the optimal frequency ratio of the dynamic vibration absorber is obtained based on the fixed-point theory. Under the premise of ensuring the system stability, the optimal grounded stiffness ratio is screened out, and the working range of inerter is further calculated. It is found that the inerter ratio has two working ranges when the coupling term values of magnification ratio and mass ratio are different. Furthermore, the approximate optimal damping ratio is derived by minimizing the maximum value of the amplitudefrequency curve. Using MATLAB, the numerical result is analyzed, and the correctness of analytical results is verified. Compared with other dynamic vibration absorbers under harmonic and random excitations, it is known that the model in this paper can evidently reduce the resonance amplitude and broaden the vibration band of the primary system. These results may provide a theoretical basis for the optimal design of similar dynamic vibration absorbers.