Generation and Detection of Sound by Distributed Piezoelectric Sources

This paper develops a theoretical method of obtaining the frequency response and electrical equivalent circuit of piezoelectric sources and detectors in which the piezoelectric stress hD is not spatially uniform. A wave equation is derived from a one‐dimensional formulation of the piezoelectric relations, and Green's functions are used to obtain solutions for the generated stress waves in terms of the Fourier transform of the spatial distribution of piezoelectric stress. Both acoustically matched and unmatched sources are treated. The complex electrical impedance is also developed. Expressions are obtained for the voltage and current generation in detection, and conditions for maximum power transfer are considered. Illustrative examples include sources with uniform, sawtooth, and Gaussian distributions of piezoelectric stress, both matched and unmatched. Optimization of response by choice of source distribution is illustrated. Arrays of sources are also treated, both with and without piezoelectric interactions between sources.