Nonlinear optimal frequency control for dynamic vibration absorber and its application

Abstract

A principal limitation of passive dynamic vibration absorber (DVA) lies in its intrinsic design constraint, as it is tuned to a specific resonant frequency, rendering it less effective at mitigating vibrations over a variable frequency range. To ensure that the DVA retains its vibration reduction capability under loads with time-varying frequencies, this paper proposes a method for designing the optimal suspension frequency based on the external load frequency. The approach involves altering the stiffness of the DVA through semi-active or active control to achieve the optimal suspension frequency and the best vibration reduction performance. In this study, the ratio R between the optimal suspension frequency and the load frequency is defined, and the nonlinear characteristic of R, based on the lowest vibration transmission rate, is studied using a two degree-of-freedom DVA model. Furthermore, an optimal suspension frequency variation control strategy based on load frequency identification is presented. Combined with the typical load with time-varying frequency encountered in metro vehicles, a multi-body dynamics theoretical model and a rigid–flexible coupling dynamics model are established to verify the effectiveness of the nonlinear optimal frequency control. Finally, the full-size railway vehicle roller rig is used to verify the correctness of the principle of optimal frequency curve. The research results show that when the mass ratio is 0.1, compared with rigid suspension, the nonlinear optimal frequency control can reduce the root mean square (RMS) value of the carbody’s entire time period acceleration during variable speed operation by 62.2%, and the maximum RMS value is reduced by 83.6%. In nonlinear control, unlike passive DVA, the vibration is never higher than that of rigid suspension within a specific velocity range. Compared with linear control strategy, nonlinearity can further reduce the elastic vibration. The test results from roller rig indicate that the semi-active DVA can effectively reduce the elastic vibrations of the carbody, while also validating the correctness of the nonlinear optimal suspension frequency principle. Therefore, the nonlinear frequency control in this study can provide reference for structural vibration control under loads with time-varying frequencies.