Magnetostrictive wires of diameter in the nanometer scale have been proposed for application
as acoustic sensors [Downey et al., 2008], [Yang et al., 2006]. The sensing mechanism is
expected to operate in the bending regime. In the first part of this work, we derive a variational
theory for the bending of magnetostrictive nanowires starting from a full 3-dimensional continuum
theory of magnetostriction. We recover a theory which looks like a typical Euler-Bernoulli
bending model but includes an extra term contributed by the magnetic part of the energy. The
solution of this variational theory for an important, newly developed magnetostricitve alloy
cf. [Clark et al., 2000]
is compared with the result of experiments on actual
cf. [Downey, 2008]
which shows agreement.
In the next part of this thesis, Multilayered wires of diameter in the nanometer scale with
periodic layering of non-magnetic copper and ferromagnetic galfenol segments are studied. The
numerical computation of the physics of magnetization for such geometries is very costly computationally.
We use the theory of periodic homogenization to understand the overall behavior
of such structures. We first determine a “homogenized theory” after which this “homogenized
model” is used to study the nucleation and stability of staturated states. Thus we get a broad
generalization of what is known in the magnetic literature as the “fanning model” first introduced
in [Jacobs and Bean, 1955] for a chain of spheres geometry. Some further numerical work
on computing M vs H curves for such geometries is also presented.
University of Minnesota Ph.D. dissertation. April 2012. Major: Aerospace Engineering and Mechanics. Advisor: Richard D James. 1 computer file (PDF); v, 121. pages.
Krishnan, Shankar Narayan.
Asymptotic models in magnetostriction with application to design of sensors..
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