Tuning of a shunted electromagnetic vibration absorber based on the maximisation of the electrical power dissipated

This paper investigates a local tuning approach for a shunted electromagnetic vibration absorber, which is based on the maximisation of the electrical power dissipated by the coil and shunt components. The study considers a simplified problem with a single-degree-of-freedom mechanical hosting system, which is excited by a white noise stochastic force. The hosting system is equipped with a coil-magnet seismic transducer, which is connected to a resistive-inductive shunt. The study examines the effectiveness of the shunted electromagnetic vibration absorber with respect to the following cost functions. Firstly, the reference cost function, which is based on the minimisation of the time-averaged kinetic energy of the hosting system. Secondly, the local cost functions, which are based on: the maximisation of the time-averaged vibration power absorbed by the shunted electromagnetic vibration absorber; the maximisation of the time-averaged mechanical power dissipated by the electromagnetic transducer and the maximisation of the time-averaged electrical power dissipated by the coil and the shunt. The study shows that, provided the transducer is lightly damped, the local cost function based on the maximisation of the electrical power dissipated by the coil and the shunt gives the same optimal tuning parameters than the reference cost function. Therefore, provided the electromagnetic transducer is properly designed, the shunt can be suitably tuned by maximising the time-averaged electrical power dissipated by the coil and shunt. This is a rather appealing practical solution since it can be implemented locally without the need of measuring the response of the hosting system and also it can be implemented in the shunt circuit without the need of extra sensors.