A formulation based on the Fourier transform and generalized functions, and implemented with a fast Fourier transform, is developed to solve a classic acoustics problem: radiation from an unbaffled cylinder with flat endcaps. The endcaps as well as the cylindrical surface have a specified modal vibration pattern, and the problem is solved using the sum of two independent formulations based on the Fourier transform: (1) a vibrating cylinder with rigid endcaps and (2) a rigid cylindrical tube with vibrating diaphragms at its ends. The resulting nearfield solution correctly models the diffraction effects generated at the sharp ends of the cylinder. Calculation of the farfield radiated pressure follows directly from the nearfield solutions with a slight modification to the standard formulas. Results from the formulations are validated with a boundary element simulation and show excellent agreement with errors of less than 1%.
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