Experimental characterization of a nonlinear vibration absorber using free vibration

Abstract

Knowledge of the nonlinear characteristics of a vibration absorber is important if its performance is to be predicted accurately when connected to a host structure. This can be achieved theoretically, but experimental validation is necessary to verify the modelling procedure and assumptions. This paper describes the characterization of such an absorber using a novel experimental procedure. The estimation method is based on a free vibration test, which is appropriate for a lightly damped device. The nonlinear absorber is attached to a shaker which is operated such that the shaker works in its mass-controlled regime, which means that the shaker dynamics, which are also included in the measurement, are considerably simplified, which facilitates a simple estimation of the absorber properties. From the free vibration time history, the instantaneous amplitude and instantaneous damped natural frequency are estimated using the Hilbert transform. The stiffness and damping of the nonlinear vibration absorber are then estimated from these quantities. The results are compared with an analytical solution for the free vibration of the nonlinear system with cubic stiffness and viscous damping, which is also derived in the paper using an alternative approach to the conventional perturbation methods. To further verify the approach, the results are compared with a method in which the internal forces are balanced at each measured instant in time.