A model for the ΔE effect in magnetostrictive transducers

Changes in elastic moduli of between 0.4-18% are common in ferromagnetic materials such as nickel and iron when their magnetization is changed. However, extremely large moduli changes of up to 160% are observed in the rare earth-iron compounds R-Fe-2, which can be advantageously utilized in design of smart structure systems. A nonlinear, hysteretic and magnetoelastically coupled model is presented and used to quantify the changes in resonance frequency exhibited by a loaded magnetostrictive transducer under varied bias magnetizations. The model is constructed in three steps. In the first, the magnetization of the magnetostrictive material is quantified by considering the energy lost to hysteresis as the magnetic field and operating stresses vary. In the second step, a quartic law is used to quantify the magnetostriction arising from domain rotations in the material. The material response, of the type found in linearly elastic solids, is considered in the final step by means of force balancing in the magnetostrictive material. This yields a PDE system with magnetostrictive inputs and boundary conditions given by the transducerload characteristics. The solution to the PDE system provides displacements and accelerations in the material. Fast Fourier Transform (FFT) analysis is then used to quantify the frequency-domain acceleration response from which the transducer's resonance frequency is calculated. Model results are compared with published experimental data.