Eg. Williams, IMAGING THE SOURCES ON A CYLINDRICAL-SHELL FROM FAR-FIELD PRESSURE MEASURED ON A SEMICIRCLE, The Journal of the Acoustical Society of America, 99(4), 1996, pp. 2022-2032
This paper provides a method to identify which areas on a vibrating cy
lindrical shell body radiate to the far field. Of particular interest
is the identification of these surface ''hot spots'' (as a function of
frequency) from pressure measurements made in the far field on a circ
le with the source at the center, located in the same plane as the axi
s of the shell. In this paper a simple formula is derived using a rigo
rous mathematical approach for the backpropagation of this far-field d
ata to the surface of the shell. The accuracy of this approach is test
ed with numerical and experimental data. It is shown over a wide frequ
ency range that far-field data can accurately predict the acoustic sou
rce regions on the shell in the same plane as the measured data. These
regions are quantified using a new concept, supersonic acoustic inten
sity. Implied in the success of this approach is a general rule that a
coustic sources on a cylindrical body which radiate to the far field,
radiate dominantly in the direction defined by the plane passing throu
gh the shell axis and the source.