A lumped parameter model of the longitudinal NiMnGa transducer based on piezomagnetic equations

The NiMnGa alloy is a typical magnetic shape memory alloy with up to 6% immense strain, high energy density, and low effective elastic modulus. These comprehensive characteristics make it possible to realize a low-frequency underwater acoustic transducer. To describe the field-induced dynamic strain, an equivalent circuit model (ECM) of a longitudinal NiMnGa transducer is presented as a lumped parameter model, which couples magnetics, mechanics, and acoustics. In this paper, we focus on the piezomagnetic equations as the constitutive relationship of the NiMnGa element with a dynamic magnetic field. Furthermore, combined with the dynamic kinetic equation, the equivalent circuit is derived, and it has the advantage of containing acoustical terminals. The proposed model can predict the resonance frequency, effective stiffness, and input impedance of the NiMnGa transducer. Finally, a finite element model (FEM) is developed to verify the lumped parameter model. The results indicate that the spring's stiffness increases the resonance frequency, while the mass load is on the contrary, and they both agree well with the results of ECM. In addition, the FEM and ECM can also predict the dynamic responses, which provide a guideline for the design of longitudinal NiMnGa transducers.