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The methods of transform calculus are used to solve several problems in which the transient response of a piezoelectric transducer is of interest. The electrical signal produced by a step function of force is derived, both for open-circuit and resistive loading at the electrical terminals, and the mechanical signal produced by a voltage step is also discussed. The analyses are performed for both the plate transducer in compressional thickness vibration and the bar in compressional length vibration, and the important differences between the two transducers are discussed. The analyses commence with the fundamental piezoelectric equations, and solutions are found which represent successive time-delayed reflections of the mechanical transient between the end faces of the transducer. The results are also discussed with reference to the exact transmission-line electrical equivalent circuits of the transducers, whose development is outlined briefly. Simple equivalent circuits which do not involve lines are described; these make it possible to determine many features of the transient without recourse to the full theoretical analysis.
M. Redwood (Sat,) studied this question.