Time-domain acoustic pressure fields from axisymmetric impulse sources by Rayleigh's Integral

Abstract

This paper shows how Rayleigh's Integral is used to efficiently and rapidly calculate time-domain pressure waveforms and wavefronts radiated from a planar baffle due to axisymmetric normal impulse accelerations that converge toward or expand away from a fixed center of symmetry. These accelerations are prescribed with simple functional forms and histories. The Rayleigh Integrals are evaluated by Gaussian integrations that seem peculiarly suited to the integrands. The acoustic fields are presented as “snapshots” of pressure contours of the evolving wavefront structures emerging from the baffle surface, and as functions of time at selected key points. As a bonus, significant insights are provided by graphs of slant range versus time that clearly identify key signal paths from the source points to the field points. The presented methods avoid the complexities inherent in more standard transform and harmonic source treatments. They also provide insights into actual acoustic fields generated by impulsive sources, as, e.g., above the ground surface over a deeply buried explosion. [J. R. Banister and W. V. Hereford, J. Geophys. Res. 96(D3), 5185-5193 (1991)] Simpler examples were reported earlier. [S. I. Warshaw, JASA 77, S60 (1985); JASA 79, S90 (1986); JASA 80, S106 (1986), and 12 ICA Toronto, L3-6 (1986)]