Parameters Design And Dynamical Analysis Of Dynamic Vibration Absorber

Dynamic vibration absorber (DVA) is one of effective manners of vibrationsuppression, which is a subsystem attached to the primary system. Currently, DVAcould present satisfactory control performance for suppressing deterministic andrandom vibration. In recent years, the research and application of passive andsemi-active DVA has been made considerable progress. This paper will address thepassive and semi-active DVA for analysis in three aspects.Firstly, perturbation method is used to study parameters design of the passiveDVA analytically, where primary system is with viscous damping, and the algebraicequations with optimal parameters is obtained. Based on the results, the resonanceamplitude of the transfer function can basically meet the requirements.Secondly, the averaging method is used to research the approximately analyticalsolution of semi-active on-off dynamic vibration absorber. The approximate solutionsfor the existing two semi-active on-off DVAs, named as VVBG and DVBG, areestablished. Then two other new semi-active on-off DVAs, named as DDBG andVDBG, are presented in this paper and also researched analytically. The results certifythat the approximate solutions have satisfactory precision, and the semi-active on-offDVA have better control performance than the optimally passive DVA.Finally, the four semi-active on-off DVAs are extended to the generalizedcircumstances, where the Duffing type s nonlinear stiffness is considered. Theaveraging method is used to analytically study semi-active on-off DVAs withnonlinear stiffness again. The comparisons of the displacement transmissibilityobtained from the approximate solutions and the numerical ones are fulfilled, and theresults certify the satisfactory precision of the approximate solutions. If the nonlinearstiffness of the primary system and the subsystem becomes greater, the displacementtransmissibility of the primary system will increase in the low-frequency band, anddecrease in the high-frequency band. The semi-active on-off DVAs with nonlinearstiffness have better control performance than the optimal passive DVA when subject to single-frequency excitation or random excitation.