Response of an Axially-Loaded Terfenol-D Rod to a Harmonic Base Excitation

Abstract

Performance characteristics of the giant magnetostrictive alloy, Terfenol-D, have been studied by many researchers for actuation, sensing and energy harvesting applications. Mathematical models characterizing the magneto-elastic behavior and describing the effects of bias conditions — compressive prestress and magnetic bias — on the material performance, have been developed. For the most part, the models used to describe the material are linear models that can hide essential features of the dynamic performance. While nonlinear constitutive models of Terfenol-D exist, such models have not been utilized to study the dynamic frequency response characteristics that are essential towards a comprehensive understanding of its performance in actuation, sensing or energy harvesting. To address this problem, this effort investigates the role of empirically determined material nonlinearities in the dynamic performance of Terfenol-D. Towards that objective, a polynomial type stress-strain relation is used to construct a nonlinear distributed-parameters model for a Terfenol-D rod fixed at one end and mass loaded at the other while being subjected to a sinusoidal base excitation. Additionally, the model accounts for the rod being subjected to an axial prestress prior to excitation. Using the method of multiple scales, the nonlinear frequency response of the rod is investigated by obtaining analytical expressions for the steady-state response amplitude. It is demonstrated that the axial prestress results in a shift in the fundamental vibration frequencies of the rod and a change in the effective nonlinearity of the system. A qualitative analysis of the solution reveals that, the magnitude of axial load can be used to maximize the response amplitude over a larger bandwidth of frequencies.