Theory of the vibrating ferromagnetic reed

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Abstract
The complete theory of the magnetomechanical pole effect is given. This effect refers to the change of the resonance frequency of a ferromagnetic reed or bar vibrating in an axial magnetic field, in the absence of intrinsic effects such as the ΔE effect. From the general formulation (arbitrarily shaped reed, reed and field may be inhomogeneous) we derive explicit expressions for the frequency spectrum and vibration modes within the single-pole approximation. This applies to reeds with constant magnetization. The first-order corrections due to nonconstant magnetization are given. The second-order corrections are shown to vanish. The field dependence of the attenuation is derived. With appropriate choice of the field inhomogeneity the pole effect can be strongly enhanced, inverted, or exactly compensated to zero.