Semi-active vibration control unit tuned to maximise electric power dissipation

This paper proposes a local approach for the on-line tuning of a semi-active vibration control unit, which is set to reduce the resonant response of target low-order flexural modes of distributed structures subject to broadband stochastic disturbances. The idea is to have multiple self-contained units, which can be fixed on thin walled structures to reduce flexural vibration and sound radiation at low audio frequencies where the dynamics of the structures is controlled by the resonant response of low-order flexural modes. The unit is formed by an electromagnetic seismic transducer connected to a resistive-inductive shunt. The proposed local tuning criterion is based on the maximisation of the time-averaged electrical power dissipated by the shunt. Both simulation and experimental results are presented for a setup where a unit is mounted on a thin plate model wall-structure excited by a broadband random force and is set to reduce the resonant response of target flexural modes. The paper investigates the physics of four tuning criteria with reference to the resonant response of the target flexural natural modes. First, the minimisation of the time-averaged total flexural kinetic energy of the plate; second, the maximisation of the time-averaged vibration power absorbed by the unit; third, the maximisation of the time-averaged mechanical power dissipated by the transducer and fourth, the maximisation of the time-averaged electrical power dissipated by the coil and shunt. The paper shows that, for small mechanical and Eddy currents damping effects of the transducer, the maximisation of the time-averaged electric power dissipated by the coil and shunt gives similar tuning parameters, and thus comparable vibration control effects, than the reference cost function based on the minimisation of the time-averaged total flexural kinetic energy of the plate.