Six‐parameter characterization and optimum design of a mass‐loaded longitudinally vibrating transducer

Abstract

Longitudinal vibrators constructed from segmented ceramic tubes have been extensively used as electroacoustic transducers of active sonar arrays. In an earlier effort, this author extended Martin's theory of vibrations of longitudinally polarized ferroelectric cylinders to the case of a practical transducer driving a radiation load via a light square piston at one end and mass loaded at the other (H. S. C. Wang, Final Technical Report, Optimum Phase Shading Technology Development and Evaluation Program. Hughes Aircraft Company, June 1977). It was demonstrated there that the driving‐point admittance of such a transducer can be formulated in terms of five parameters: namely, the characteristic impedance of the ceramic tube, the time constants of the ceramic tube and the tail mass, the electromechanical transformation ratio, and the longitudinally clamped capacitance. From this formulation, with the addition of a resistance representing internal power loss as the sixth parameter, and by defining an object function. O.F. = ∑ n=1N wn⋅|Yn − Yn(d)|, where wn is a scalar weight, Yn. and Yn(d) are the driving‐point admittance and its desired value at the nth of N frequency points, an optimum transducer design procedure based on the steepest descent search for the minimum of the O.F. has been developed.