Nonlinear dynamic model with multi-fields coupling effects for giant magnetostrictive actuators

• The magnetic-elastic-thermal coupled constitutive model with eddy current effects is employed.
• A nonlinear dynamic model with multi-fields coupling effects is established.
• The results predicted by the model are coincident with the experimental data in quantity.
• The effects of the dynamic stress and temperature on the effective magnetic field and ensuing magnetization are incorporated.
• The dynamic components of the actuator such as spring loads and damping factors are considered.

This paper addresses the modeling of complex hysteresis behavior for giant magnetostrictive actuator system under magnetically unbiased conditions. The hysteresis behavior is modeled by establishing a novel nonlinear dynamic model with multi-fields coupling effects, in which both the eddy current effects and the change of stress are considered. The former is included in the nonlinear transient constitutive model with magnetic-elastic-thermal coupling effect, which is employed as the basic constitutive equations of Terfenol-D. The latter is characterized through the structural dynamic behavior of actuator system itself, which is modeled by theorem of momentum. The quantitative agreements between numerical simulation results and existing experimental data indicate that nonlinear dynamic model can accurately describe the complex hysteresis behavior of the giant magnetostrictive actuator system not only under quasi-static operating conditions but also under dynamic operating conditions. The numerical simulation results also indicate that both the eddy current effects and structural dynamic behavior are the origin of frequency-dependent hysteresis behavior for giant magnetostrictive actuator system, and demonstrate the significance and necessity of simultaneously considering the eddy current effects and the change of stress in the system-level. Thus, the nonlinear dynamic model established in this paper is a system-lever coupled theoretical model, which can be directly used in the active vibration control and any other engineering application of the giant magnetostrictive actuators.