Complex shear modulus of a magnetorheological elastomer

In our previous study (Zhou 2003 Smart Mater Struct. 12 139-46), a technique to extract the field-induced shear modulus through an experiment testing the responded acceleration of a system composed of a magnetorheological elastomer (MRE) and a cuprous mass was introduced. In this paper, we present a different data processing method, based on the Steiglitz-McBride iteration method, to recover the complex shear modulus of an MRE in the frequency domain through the measured force excitation and responded acceleration of the mass in the above-mentioned experiment. The recovered complex shear modulus is analyzed in three ranges of the frequency domain: low-frequency range, moderate-frequency range, and high-frequency range. In the low-frequency range (<250 Hz), the shear modulus is a bell-type curve rising with the applied magnetic field. The average shear modulus over this frequency range is proportional to the applied magnetic field until magnetic saturation is reached. The maximum tn chan-e of the average shear Modulus over this range is found to be above 55% of the zero-field value. The above phenomenon reaffirms that the subquadratic field dependence, which arises from the saturation of the maorietization near the poles of closely spaced pairs of spheres, must be taken into account. In the moderate-frequency range and high-frequency ranae, the shear modulus is too complex to be analyzed completely by the proposed method. However, some interesting phenomena are also revealed by the proposed method. For instance, the shear modulus increases with frequency at least with the order of a quadratic polynomial, and the shear modulus is not significantly affected by the applied magnetic field.