System Non-Linearities Induced by Skyhook Dampers

Abstract

The nonlinearities induced by skyhook dampers are studied experimentally and analytically using a single degree of freedom base-excited system that is representative of the systems that such dampers are often used in. The experimental results are used to show that the nonlinearities introduced by skyhook dampers manifest themselves as high frequency peaks in the frequency spectrum of the system response. More precisely, using a pure tone input with a known frequency, it is shown that these peaks occur at odd multiples of the system input (or driving) frequency. Using a Fourier series analysis, it is proven that the nonlinearities are caused by the switching policy of skyhook dampers, in which the damper force is changed according to the relative sign of the sprung mass absolute velocity and the relative velocity across the damper. The analysis shows that the skyhook damper force always contains a frequency component that is equal to the frequency of the system input (as is expected for a linear system), in addition to other frequencies that are odd multiples of the input frequency. The damping force peak that occurs at the input frequency is necessary for controlling the forced response of the system. The peaks at higher frequencies, however, are not desirable – although always present – because they introduce corresponding peaks in the system response that can cause ancillary vibration problems. For most systems, the high frequency peaks can significantly diminish any isolation benefits that are gained by the skyhook damper. When using skyhook dampers, such effects must be considered and their impact on the system dynamics studied carefully.