A Fourier transform formulation for radiation from an unbaffled cylinder

Area of Science:

• Acoustics
• Computational physics
• Applied mathematics

Background:

• Acoustic radiation from unbaffled cylinders with flat endcaps is a complex problem.
• Accurate modeling is crucial for understanding sound propagation and designing acoustic systems.

Purpose of the Study:

• To develop a robust formulation for predicting acoustic radiation from unbaffled cylinders with flat endcaps.
• To implement the formulation using fast Fourier transform (FFT) for efficient computation.

Main Methods:

• A novel formulation based on the Fourier transform and generalized functions was developed.
• The problem was solved by summing two independent formulations: a vibrating cylinder with rigid endcaps and a rigid tube with vibrating diaphragms.
• Fast Fourier Transform (FFT) was employed for efficient implementation.

Main Results:

• The formulation accurately models nearfield acoustic radiation, including diffraction effects at the cylinder ends.
• Farfield radiated pressure calculations were derived with minor modifications to standard formulas.
• Validation with boundary element simulations showed excellent agreement, with errors below 1%.

Conclusions:

• The proposed Fourier transform-based method provides an accurate and efficient solution for acoustic radiation from unbaffled cylinders with flat endcaps.
• The approach correctly accounts for diffraction phenomena at the cylinder extremities.
• The validated results demonstrate the efficacy of the method for acoustics research and engineering applications.