Theoretical and Experimental Analysis of a Tuneable Vibration Absorber using Acceleration and Displacement Feedback

This study is concerned with the analysis and design of a tuneable vibration absorber, which is composed by a flexible beam with a clamping block in the middle and two masses symmetrically mounted at two ends. The free length of the beam is used to accommodate piezoelectric strain actuators. The two masses at the ends are equipped with inertial accelerometers. Firstly, this arrangement is used to generate two independent acceleration feedback control loops that produce virtual mass effects, which consequently shift the absorbing frequency of the device. Secondly, the accelerometer output is time-integrated twice in order to implement displacement feedback loops that generate virtual changes in the beam stiffness to shift the characteristic frequency of the device. The two feedback approaches are first analysed theoretically, using a mobility-impedance approach, and then experimentally on a prototype absorber unit. The stability of the feedback loops is studied using the Nyquist criterion in order to estimate the limits on the tuneable range of frequencies which are set by the maximum stable feedback gain. The study indicates that the stability margins for the acceleration feedback loops substantially depend on the application of an appropriate low-pass filter. This is due to unfavourably large amplitudes of the sensor-actuator frequency response functions at higher frequencies. In contrast, implementation of displacement feedback naturally yields a favourable roll-off at higher frequencies and gives better stability margins. The maximum feedback gain is however limited at low-frequencies due to the frequency response of the analogue double-integrator. Nevertheless, the use of an integrator with a cut-off frequency low enough results in good stability margins that allow for a relatively large shift of the characteristic frequency of the absorber by the active displacement feedback control.