An analytical solution versus half space BEM formulation for acoustic radiation and scattering from a rigid sphere

Soenarko, Benjamin; Setiadikarunia, Daniel

doi:10.1088/1742-6596/776/1/012065

Cited by 4 publications

(8 citation statements)

References 9 publications

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“…Equation ( 11) is derived using the impedance boundary condition (7) and equation ( 9) by adopting R t = 21, corresponding to the high-frequency limit condition for the free surface, and R b = 1, prescribing the rigid-wall condition.…”

Section: Doubly-bounded Domainsmentioning

confidence: 99%

Investigation of acoustic radiation from a sphere vibrating on the free surface of a finite depth water using a boundary element method

Üstündağ,

Uğurlu,

Ergin

2023

Proceedings of the Institution of Mechanical Engineers, Part M:

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In this study, a boundary element method (BEM) is applied to investigate acoustic radiation from a sphere vibrating in pulsating mode on the free surface of finite or infinite depth water. Effect of the free surface is introduced by employing a half-space Green’s function. A modified version of the Helmholtz integral equation (HIE) is used to calculate acoustic radiation from the sphere vibrating in pulsating mode on the free surface. Free-terms of the HIE are calculated using two different forms of integrals and “dummy” boundary elements. Moreover, to simulate finite depth fluid medium, a chain image-source method is used to derive a waveguide Green’s function. To demonstrate applicability of the method presented, calculated acoustic pressures are compared with those by finite element method (FEM) and analytical calculations. Additionally, the effects of submergence depth and vibration frequency on acoustic radiation are investigated for infinitely deep water together with those of water depth and field point distance on acoustic radiation for finite water depth medium. The calculations show that there is a good agreement between BEM, FEM and analytical solutions. Also, it is observed that field point distance significantly affects the convergence behavior of waveguide Green’s function. Furthermore, it is noted that submergence depth, domain depth and vibration frequency have pronounce influence on radiated pressure amplitude and pressure field pattern.

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Section: Doubly-bounded Domainsmentioning

confidence: 99%

Investigation of acoustic radiation from a sphere vibrating on the free surface of a finite depth water using a boundary element method

Üstündağ,

Uğurlu,

Ergin

2023

Proceedings of the Institution of Mechanical Engineers, Part M:

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“…In the first case study, it is assumed that the sphere is placed at a finite depth from a free surface as shown in Figure 11(a). In order to validate the numerical predictions, the pressure field is computed with the analytical solution proposed by Soenarko and Setiadikarunia [26] as follows…”

Section: Pulsating Sphere In Half-spacementioning

confidence: 99%

“…However, Guo et al [25] studied the vibro-acoustic response behavior of submerged, pre-stressed finite length cylindrical shells. For spherical geometry, Soenarko and Setiadikarunia [26] derived analytical formulations for half-space radiation and scattering problems, for pulsating sphere and rigid sphere, respectively, using the method of images. Qu et al [27] developed a semi-analytical mathematical model to investigate the structural and acoustic responses of a coupled propeller-shafting and submarine hull under different propeller excitation forces.…”

Section: Introductionmentioning

confidence: 99%

“…In the first case, the sphere is considered pulsating near a free surface (perfectly reflecting plane) and the free surface effect is included using the single image-source in the BEM formulation. The acoustic radiation pressure values obtained are compared with the analytical solutions of Soenarko and Setiadikarunia [26] and a very good comparison is obtained between the results. In the second case, the sphere is modeled as pulsating near a perfectly reflecting (rigid) or absorbing (soft) impedance plane, using extremely small and large acoustic admittance values, respectively, in the solutions.…”

Section: Introductionmentioning

confidence: 99%

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Acoustic radiation from a sphere pulsating near an impedance plane using a boundary integral equation method

Üstündağ

Yildizdag

Uğurlu

et al. 2022

Mathematics and Mechanics of Solids

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In this study, a boundary integral equation method is proposed for investigating acoustic pressure radiation from a sphere pulsating near a free surface or an impedance plane. The half-space and free-space problems are investigated for the acoustic radiation of pulsating sphere. The effects of free surface and impedance boundaries are introduced into the mathematical model by employing three different half-space Green’s functions, respectively. These Green’s functions are derived, respectively, using the single image-source method, multiple equivalent-source method, and complex equivalent-source method. Green’s functions are implemented into the boundary element (BE) formulation. The surface of the pulsating sphere is discretized with linear and quadratic BEs, and the Combined Helmholtz Integral Equation Formulation (CHIEF) is employed to overcome the non-uniqueness problem. Four different case studies are considered for the sphere pulsating near a free surface or an impedance plane. The first case study involves the sphere pulsating near a free surface (perfectly reflective) and the single image-source method is used in the boundary element method (BEM) formulation. In the second case study, the sphere is assumed as pulsating near a perfectly reflecting and perfectly absorbing impedance planes, respectively. The multiple equivalent-source method is employed for the perfectly reflecting plane, but the multiple equivalent-source method and complex equivalent-source methods for the perfectly absorbing plane. The third case study involves a general impedance plane, and all the methods are employed, respectively, in the BE formulation. The final case study assumes a general impedance plane forming a perpendicular incidence and the complex equivalent-source method is used in this particular case. It is observed that there is a very good comparison between the results obtained from all these methods.

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“…Sua aplicação também ocorre no estudo da reflexão ou absorção de uma pluma contaminante de um contorno dito impenetrável, sem fluxo. Outra aplicação de grande importância está ligada ao estudo e contenção da propagação do som ao ar livre, onde barreiras acústicas são modeladas como corpos sem espessura e neste caso, sua aplicação no contexto do MEC revela grande adequação e eficiência [9]. Na literatura referente ao MEC, o Método das Imagens foi apresentado inicialmente abordando problemas de potencial [10].…”

Section: O Método Das Imagensunclassified

Solução de problemas de potencial em meios semi-infinitos bidimensionais através do Método dos Elementos de Contorno

Loeffler¹,

Coutinho²,

Lara³

2021

Blucher Physics Proceedings

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O presente trabalho apresenta a formulação e os princípios matemáticos que compõem o modelo do Método dos Elementos de Contorno para a abordagem de problemas bidimensionais com meios infinitos e semi-infinitos, incluindo as particularidades referentes à definição das variáveis pertinentes, às características das soluções fundamentais nestes casos e o comportamento das variáveis primais em pontos infinitamente distantes. Os aspectos relacionados à discretização e às questões numéricas também são abordados, através da solução de dois problemas particulares envolvendo semi-planos.

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An analytical solution versus half space BEM formulation for acoustic radiation and scattering from a rigid sphere

Cited by 4 publications

References 9 publications

Investigation of acoustic radiation from a sphere vibrating on the free surface of a finite depth water using a boundary element method

Investigation of acoustic radiation from a sphere vibrating on the free surface of a finite depth water using a boundary element method

Acoustic radiation from a sphere pulsating near an impedance plane using a boundary integral equation method

Solução de problemas de potencial em meios semi-infinitos bidimensionais através do Método dos Elementos de Contorno

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