Theoretical study of the pulsed ultrasonic field radiated by a nonuniformly vibrating planar piston source

Abstract

A mathematical method is presented for evaluating the transient field radiated by a pulsed planar piston set in an infinite rigid bafffle and having an arbitrary spatial velocity distribution. The method allows for the field to be found at a point or averaged over a finite receiving surface. The approach taken is based on an expanded convolution integral representation of the transient field using a generalized spatial impulse response function development. To illustrate the effect of a nonuniform source and finite receiver on the detected transient field, the generalized spatial impulse response is plotted for several receiver sizes and source distributions representable by analytic functions. Then corresponding plots are presented for two piston velocity waveforms: A Gaussian pulse and a Gaussian‐modulated sinusoidal burst. Lastly, the relationship of this theoretical method to other mathematical descriptions of the field radiated by a planar piston is discussed. In particular, the “plane” and “edge” wa...