A method for approximating high frequency sound radiation-The plane projection Rayleigh integral.

Area of Science:

• Acoustics
• Computational Mechanics
• Numerical Analysis

Background:

• Calculating sound radiation from vibrating surfaces often requires computationally intensive integral-based numerical methods.
• High frequencies necessitate increased discretization, leading to significant computational burdens.
• There is a need for approximation methods that balance computational efficiency with high precision.

Purpose of the Study:

• To introduce and evaluate a novel approximation method, the plane projection Rayleigh integral (PPRI).
• To assess the PPRI's accuracy and computational efficiency compared to existing methods.
• To analyze the PPRI's performance concerning surface curvature, frequency, and distance.

Main Methods:

• The plane projection Rayleigh integral (PPRI) method approximates sound radiation by applying the Rayleigh integral to a 2D virtual plane.
• Performance evaluation involved comparison with the visible element Rayleigh integral and the high frequency boundary element method (HFBEM).
• Analytical solutions for breathing and oscillating spheres served as benchmarks for accuracy assessment.

Main Results:

• The PPRI method demonstrated superior accuracy compared to the visible element Rayleigh integral and HFBEM.
• Error decreased with larger radii and higher frequencies, achieving below 1% error at significantly smaller Helmholtz numbers than HFBEM.
• The PPRI required the least computational time among the evaluated methods.

Conclusions:

• The PPRI method effectively achieves both high precision and computational efficiency in sound radiation calculations.
• This method presents a valuable alternative for scenarios requiring accurate acoustic predictions with reduced computational cost.
• The PPRI's performance is particularly advantageous at higher frequencies and for surfaces with larger radii of curvature.