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Reconsideration on Helmholtz-Kirchhoff Integral Solutions for Boundary Points in Radiation Problems

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The Helmholtz-Kirchhoff integral (HKI) formula is very useful when designing transducers because it can be used to predict the acoustic pressure of a radiator at any position given only the acoustic pressure and velocity of the source. Many studies have been carried out to determine how to predict the acoustic pressure distributions generated by radiator sources using the HKI formula and boundary conditions. However, if the surface integration process includes radiator edges or vertices, then it is difficult to predict a consistent acoustic pressure distribution accurately, and the precise HKI formula to solve this problem and rigorous derivation are not known. In this article, to overcome these limitations, a formulation of the HKI for the boundary is proposed. This formulation is based on intuitive considerations and proven mathematically. Using the proposed expression of the HKI formula for the boundary, the acoustic pressures radiated by irregular surfaces were calculated and compared with the distributions obtained by the finite element method and theoretically exact solutions. The results obtained with the proposed formulation of the HKI were confirmed to be more accurate than those of the conventional HKI formula.
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Document Type: Research Article

Publication date: September 1, 2019

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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