A hybrid piezoelectric-magnetostrictive vibration absorber (HPMVA) with a mutual shunt circuit: modelling, optimisation and analytical solution

This paper introduces a novel Hybrid Piezoelectric-Magnetostrictive Vibration Absorber (HPMVA) to enhance the performance of conventional electromechanical (or magneto-electromechanical ) vibration absorbers. A proof-of-concept for the HPMVA is introduced through analytical modelling and optimisation, highlighting its potential for enhanced vibration attenuation prior to experimental implementation. The HPMVA incorporates a Piezoelectric (PZT) rod and a Magnetostrictive (MAG) transducer coupled to a single-degree-of-freedom mechanical vibrating host structure. Both the PZT and MAG transducers are connected to a single resonating shunt circuit, forming an electro-magneto vibration absorber. The constitutive equations of motion for this system are derived, and its parametric receptance function is calculated. Utilising h∞ optimisation techniques, numerical results demonstrate that the attenuation performance of a tuned HPMVA consistently surpasses that of comparable PZT Vibration Absorbers (PVAs) and/or MAG Vibration Absorbers (MVAs). The paper also provides an analytical solution for the optimisation of the HPMVA, presenting comprehensive mathematical details. The optimum design is determined based on h∞ optimisation and the equal-peak technique. Verification of the optimised design and optimum formulas confirms that, within the practical range of PZT and MAG coupling factors, a tuned HPMVA can improve absorber performance by up to 50% compared to similar PVAs and MVAs.