Technical Memorandum 527249322-2

Rayleigh’s integral equations applied to the radiation of sound in two- and three-dimensional spaces
Publication date
2026-03-04
Document type
Bericht
Author
Organisational unit
Language
English
DDC Class
534 Schall und verwandte Schwingungen
530 Physik
621 Angewandte Physik
Keyword
Active structural acoustic control
Structural vibration
Near-field Acoustical Holography
Rayleigh integral
Radiation of sound
Sound intensity
Free-field Green's function
Simply supported plate
Abstract
When Nearfield Acoustical Holography (NAH) is used as a sensor principle for Active Structural Acoustic Control (ASAC), details for the implementation of NAH needs to be understood. Therefore, simple planar radiation models are necessary to work with known solutions and to synthesize input data. The first step involves deriving Rayleigh’s integrals in two dimensions. The three-dimensional solution follows thereafter. Findings presented in the literature are used to compare the results derived here for the three-dimensional case.
Description
Rayleigh’s integral equations are popular when dealing with harmonic sound radiation. This is because implementing these integral equations is comparatively straightforward, no numerical finite or boundary element model is required, and they enable the generation of sound fields that possess a high degree of physical interpretability for practical applications. In engineering, it is practical to first reduce sound radiation problems to two dimensions.
Version
Author's original
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Open access