Static and Motional Impedance of a Magneto-Striction Resonator

The equivalent series inductance and resistance of a long solenoid with nickel-steel bar has been investigated in relation to the excitation frequency for frequencies up to 14000 cycles per second. Beyond 400 cycles per second, after which only a negligible flux penetrates to the center of the bar, the inductance varies inversely with the square root of the frequency, and the resistance directly with the square root of the frequency. The product of the resistance and inductance is substantially constant over the frequency range; also, the power factor angle of the bar is substantially constant. The field for the higher frequencies is shown to be confined largely to the circumference of the bar, at which zone the greater part of the magnetostrictive force is produced. The results are discussed in relation to the theory of flux distribution in the bar. The effect of motion of the bar under the action of magnetostriction has been measured in terms of the motional impedance, and a circle diagram obtained. The ratio of motional resistance to reactance, in the vicinity of mechanical resonance of the bar, is of the order of magnitude of one to six thousand. The theory of total impedance, static and motional, is given, and the nature of the angular displacement of the resonant circle indicated.