The equivalent circuit of the magnetostriction oscillator

The Joule effect in magnetostriction is defined by the relation S = λ B , where S is the stress produced by a small increment of induction B of an existing induction B 0 ; and the converse effect by the relation H = κξ, where H is the magnetic field produced by a small strain ξ. Conservation of energy requires that κ = 4πλ. These equations are used in investigating the motion of a magnetostriction oscillator consisting of a closed circular ring inside a toroid, eddy currents and hysteresis being taken into account. It is shown that the oscillator can be represented by an equivalent electrical circuit comprising a pair of parallel impedances Z c , Z m , in series with an impedance Z l , where Z l represents leakage impedance and Z c impedance due to core flux in the absence of motion, while Z m is a resonant shunt to Z c and represents the effect of the motion. Expressions for the elements of the circuit in terms of the fundamental constants of the material are given. The circle-diagram of impedances is deduced, and the modifying effects of eddy currents and hysteresis are investigated. Some simple geometrical relations between the vectors in the diagram are derived. It is shown that the size of the circle diagram for solid material having a large value of λ depends mainly upon permeability and resistivity and only slightly upon λ, and that a high degree of resonance may be associated with poor magnetostriction quality; the circle-diagram may, in fact, lead to erroneous conclusions unless interpreted in the light of an adequate theory. An experimental investigation of the resonant radial vibrations of solid and laminated nickel rings verifies the theoretical deductions and leads to numerical values of λ and κ in agreement with values deduced from the work of Masumoto and Nara and of McKeehan and Cioffi. For nickel in the annealed state, λ=1.76 × 10 4 and κ = 22.1 × 10 4 at a point on the curve corresponding to H 0 = 14.5 gauss.