An annular superposition integral for axisymmetric radiators.

Area of Science:

• Acoustics
• Computational Physics
• Wave Propagation

Background:

• Calculating nearfield pressure is crucial in acoustics.
• Existing methods like Rayleigh-Sommerfeld and generalized King integrals can be computationally intensive.
• Axisymmetric radiators are common in various acoustic applications.

Purpose of the Study:

• To derive a faster integral expression for computing nearfield pressure for axisymmetric radiators.
• To compare the computational efficiency and accuracy of the new method against existing techniques.
• To investigate the impact of apodization functions on the wave field's spectral content.

Main Methods:

• Developed a novel integral expression replacing annular sums with a double integral.
• Applied the method to plane circular pistons with continuous wave and pulsed excitations.
• Analyzed various apodization schemes, including polynomial and smooth piston functions.
• Performed quantitative error and time comparisons with Rayleigh-Sommerfeld and generalized King integrals.

Main Results:

• The new annular superposition method converges significantly faster than traditional integrals.
• Achieved speed-ups of at least 4x over point-source methods and 3x over the generalized King integral.
• Demonstrated comparable accuracy across various error tolerances.
• Explored the influence of apodization on the spectral content of the acoustic wave field.

Conclusions:

• The derived integral expression provides a computationally efficient alternative for nearfield pressure calculations.
• The method offers significant speed advantages without compromising accuracy.
• It is applicable to various excitation types and apodization functions for axisymmetric radiators.