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

Abstract 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 HPMVA is introduced using analytical modelling and optimisation, highlighting its potential for enhanced vibration attenuation before 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, creating an electro-magneto vibration absorber. The constitutive equations of motion for this system are derived, and its parametric receptance function is calculated. Utilising <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>h</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> optimisation techniques, the 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>h</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> 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 boost the absorber performance by up to 50% compared to similar PVAs and MVAs.