TY - JOUR

T1 - Acoustic radiation from a sphere pulsating near an impedance plane using a boundary integral equation method

AU - Üstündağ, Burak

AU - Yildizdag, M. Erden

AU - Uğurlu, Bahadır

AU - Ergin, Ahmet

N1 - Publisher Copyright:
© The Author(s) 2022.

PY - 2022/10

Y1 - 2022/10

N2 - 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.

AB - 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.

KW - Acoustic radiation

KW - boundary element method

KW - Combined Helmholtz Integral Equation Formulation method

KW - half-space Green’s functions

KW - Helmholtz integral equation

UR - http://www.scopus.com/inward/record.url?scp=85128257901&partnerID=8YFLogxK

U2 - 10.1177/10812865221085196

DO - 10.1177/10812865221085196

M3 - Article

AN - SCOPUS:85128257901

SN - 1081-2865

VL - 27

SP - 1913

EP - 1929

JO - Mathematics and Mechanics of Solids

JF - Mathematics and Mechanics of Solids

IS - 10

ER -