Transient fluid reaction on a baffled plane piston of arbitrary shape

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Abstract
The inverse Laplace transform of the frequency-dependent radiation impedance of a baffled piston, i.e., its impulse response, is a function which is more directly related to the geometry of the piston than the impedance itself. It is here shown how this function can be described in terms of a finite pulse called the characteristic pulse, whose shape depends on that of the piston, and that its evaluation depends on a relatively simple integration around the piston's contour. A number of examples show that the characteristic pulse can be evaluated exactly for certain piston shapes. Geometrical features of the piston's shape, such as corners, have a predictable effect on the characteristic pulse, and hence on the radiation impedance; some of these fundamental relationships are derived in the form of simple theorems.

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