Validated linear dynamic model of electrically-shunted magnetostrictive transducers with application to structural vibration control

This paper presents a linear model of the fully-coupled electromechanical behavior of a generally-shunted magnetostrictive transducer. The impedance and admittance representations of the model are reported. The model is used to derive the effect of the shunt's electrical impedance on the storage modulus and loss factor of the transducer without neglecting the inherent resistance of the transducer's coil. The expressions are normalized and then shown to also represent generally-shunted piezoelectric materials that have a finite leakage resistance. The generalized expressions are simplified for three shunts: resistive, series resistive-capacitive, and inductive, which are considered for shunt damping, resonant shunt damping, and stiffness tuning, respectively. For each shunt, the storage modulus and loss factor are plotted for a wide range of the normalized parameters. Then, important trends and their impact on different applications are discussed. An experimental validation of the transducer model is presented for the case of resistive and resonant shunts. The model closely predicts the measured response for a variety of operating conditions. This paper also introduces a model for the dynamic compliance of a vibrating structure that is coupled to a magnetostrictive transducer for shunt damping and resonant shunt damping applications. This compliance is normalized and then shown to be analogous to that of a structure that is coupled to a piezoelectric material. The derived analogies allow for the observations and equations in the existing literature on structural vibration control using shunted piezoelectric materials to be directly applied to the case of shunted magnetostrictive transducers.