Nonlinear dynamical analysis and parameters optimization of four semi-active on-off dynamic vibration absorbers

Abstract

In this paper the averaging method is used to research the approximately analytical solution of a semi-active on-off dynamic vibration absorber (DVA). At first the approximately analytical solutions for the two existing semi-active on-off DVAs, named as velocity-velocity based ground-hook control and displacement- velocity based ground-hook control, are established by the averaging method. Then two other new semi-active on-off DVAs, named as velocity-displacement based ground-hook control and displacement-displacement based ground-hook control, are presented for the first time in this paper and also researched analytically. Moreover, all the optimal parameters of the four semi-active DVAs, including the stiffness and the maximum and minimum damping ratio of the subsystem, are optimized to make the peak of the displacement transmissibility curve minimum, based on the amplitude-frequency equations from approximately analytical solutions. The comparisons of the displacement transmissibility obtained from the approximate solutions and the numerical ones are fulfilled, and the results certify that the approximate solutions have satisfactory precision. At last, the statistical results of the stochastic responses of the primary systems, including the original single degree-of-freedom system, the optimally passive DVA system, and the four semi-active on-off DVA systems, are obtained when subject to random excitation. The results show that the two new semi-active DVAs presented in this paper are almost as excellent as the existing two semi-active DVAs, and all of the four semi-active DVAs have better control performance than the optimally passive DVA.