THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

16.5 Transducers 467Figure 16.6. Mechanical strain as a function of magnetic polarization.When a sinusoidally varying magnetic field is applied in the direction of the axisof a bar of ferromagnetic material, the bar will oscillate at double the frequency ofthe applied field. In accordance with the relevant curve in Figure 16.6, a decrease inlength occurs when a field is applied to nickel, regardless of the sense of the field.A negative strain occurs every half cycle. The waveform of the strain occurs as arectified sine curve, with the result that unwanted harmonics may be generated. Apurely sinusoidal wave corresponding to the frequency of the applied field, alongwith a markedly increased energy output, will be obtained if the bar is polarized.This is achieved by simultaneously applying the alternating field and a directmagnetic field of sufficiently high intensity for the value of the resultant field toremain above zero.The maximum output for magnetostriction occurs by operating at the fundamentalfrequency f r of the bar, given by√f r = 1 Y(16.34)2L ρwhere Y is the Young’s modulus for the bar material, ρ is the density of the material,and L is the length of the bar. The term √ Y/ρ in Equation (16.34) also happens tobe the propagation velocity of sound in the material. At resonant frequencies themechanical strains reaches the order of 10 –4 rather than magnitudes in the orderof 10 −6 that prevails in operating at nonresonant frequencies.