Calculation of acoustic radiation modes by using spherical waves and generalized singular value decomposition.

Area of Science:

• Acoustics
• Computational Mechanics
• Noise Control Engineering

Background:

• Acoustic radiation modes (ARMs) are crucial for noise control due to their sound-power properties.
• Evaluating ARMs for non-regular structures is computationally demanding, typically requiring boundary integral equation (BIE) solutions via the boundary element method (BEM).

Purpose of the Study:

• To develop a computationally efficient method for evaluating acoustic radiation modes (ARMs) for non-regular structures.
• To eliminate the need for solving boundary integral equations (BIEs) in ARM evaluation.

Main Methods:

• The proposed method involves projecting spherical harmonics onto an enclosing surface.
• Generalized singular value decomposition (GSVD) is applied to the projected spherical harmonics.
• This approach bypasses the traditional BIE solution and singular value decomposition (SVD) of the radiation resistance matrix.

Main Results:

• The new procedure successfully eliminates the necessity of solving the boundary integral equation (BIE).
• Computational effort for evaluating ARMs of non-regular structures is potentially reduced significantly.
• The method provides an alternative pathway to obtain radiation modes without direct BIE computation.

Conclusions:

• The proposed method offers a computationally advantageous alternative for determining acoustic radiation modes (ARMs).
• This technique simplifies the evaluation process for complex geometries in noise control engineering.
• Further research can explore the practical implementation and validation of this GSVD-based approach.