Static and Dynamic Delta E Effect in Magnetostrictive Materials with Application to Electrically-Tunable Vibration Control Devices

Magnetostrictive materials transfer energy between the magnetic and mechanical domains as they magnetize in response to applied stresses and deform in response to applied magnetic fields. The deformation that arises from this coupling directly causes the material’s effective elastic moduli to depend on stress and magnetic field. This phenomenon, known as the ∆E effect, can be electrically modulated using electromagnets. Devices having an electrically-tunable stiffness can be developed by harnessing this effect. Such devices have broad application to the field of vibration control, particularly in instances where the vibration source or operating regime change over time. Although the static ∆E effect has been extensively measured in many manmade magnetostrictive materials, such as Galfenol (FeGa) and Terfenol-D (TbDyFe), this tunability has been seldom applied to the development of vibration control devices. Real-time tuning of the elastic moduli (i.e., the dynamic ∆E effect) has not been studied. Further, the effects of dynamic stress on the constitutive behavior of magnetostrictive materials are largely unknown, despite their critical importance to the modeling and design of many magnetostrictive systems, including dynamic sensors, energy harvesters, vibration dampers, and stiffness tuning devices. This work analytically, numerically, and experimentally explores the effects of dynamic stress on magnetostrictive materials and the use of the static and dynamic ∆E effect in the development of novel vibration control devices. ii Measurements of the quasi-static elastic response of Galfenol reveal that the Young’s modulus and ∆E effect are stiffer and smaller, respectively, for small amplitude applied stresses than for large amplitude applied stresses. The ∆E effect of solid and laminated samples is found to be equal, despite the laminated sample’s 17 % lower modulus under saturated conditions. The static ∆E effect in Galfenolbased composite beams that are applied as adaptive vibration absorbers is studied by constructing nonlinear, dynamic models of their vibratory response. The absorber’s resonant frequencies are shown to be controllable below an input power threshold via changes in the bias magnetic field. Resonant frequency tunability increases with the Galfenol element’s volume fraction and offset from the bending axis. Mechanically-induced magnetic diffusion in linear and nonlinear cylindrical ferromagnets is investigated. Analytical time and frequency domain solutions of linear diffusion are derived for the first time. The solutions are non-dimensionalized and used to define a skin depth and cut-off frequency, which can be used for design purposes. This diffusion causes the material’s effective magnetoelastic coupling coefficient and elastic modulus to be complex-valued and frequency dependent. The effects of material property variations on the nonlinear diffusion response are studied numerically. A novel characterization of Galfenol’s constitutive response to dynamic stress is presented along with a detailed experimental methodology that ensures the accuracy of the measurements. Solid and laminated Galfenol rods exhibit cut-off frequencies of 44 to 105 Hz and about 1 kHz, respectively. The mechanical loss factor of the solid rod reaches 0.13 due to eddy current-induced damping. The dynamic ∆E effect is studied using a magnetostrictive transducer designed for high speed stiffness switching. Electromechanical modeling of the transducer