Helmholtz-Kirchhoff integral formula for predicting the acoustic pressure from a radiator including irregular surface

2019 ◽  
Vol 146 (4) ◽  
pp. 3074-3074 ◽  
Author(s):  
Kyounghun Been ◽  
Junsu Lee ◽  
Wonkyu Moon
Keyword(s):  
Acoustic Pressure ◽  
Integral Formula ◽  
Irregular Surface ◽  
Kirchhoff Integral

scholarly journals A COMPARISON OF TRANSIENT INFINITE ELEMENTS AND TRANSIENT KIRCHHOFF INTEGRAL METHODS FOR FAR FIELD ACOUSTIC ANALYSIS

2013 ◽  
Vol 21 (02) ◽  
pp. 1350006 ◽  
Author(s):  
TIMOTHY F. WALSH ◽  
ANDREA JONES ◽  
MANOJ BHARDWAJ ◽  
CLARK DOHRMANN ◽  
GARTH REESE ◽  
...  
Keyword(s):  
Acoustic Pressure ◽  
Acoustic Analysis ◽  
System Stability ◽  
Far Field ◽  
Element Analysis ◽  
Infinite Element ◽  
Infinite Elements ◽  
Integral Methods ◽  
Element Approach ◽  
Kirchhoff Integral

Finite element analysis of transient acoustic phenomena on unbounded exterior domains is very common in engineering analysis. In these problems there is a common need to compute the acoustic pressure at points outside of the acoustic mesh, since meshing to points of interest is impractical in many scenarios. In aeroacoustic calculations, for example, the acoustic pressure may be required at tens or hundreds of meters from the structure. In these cases, a method is needed for post-processing the acoustic results to compute the response at far-field points. In this paper, we compare two methods for computing far-field acoustic pressures, one derived directly from the infinite element solution, and the other from the transient version of the Kirchhoff integral. We show that the infinite element approach alleviates the large storage requirements that are typical of Kirchhoff integral and related procedures, and also does not suffer from loss of accuracy that is an inherent part of computing numerical derivatives in the Kirchhoff integral. In order to further speed up and streamline the process of computing the acoustic response at points outside of the mesh, we also address the nonlinear iterative procedure needed for locating parametric coordinates within the host infinite element of far-field points, the parallelization of the overall process, linear solver requirements, and system stability considerations.

One‐way versions of the Kirchhoff Integral

Geophysics ◽  
1989 ◽  
Vol 54 (4) ◽  
pp. 460-467 ◽  
Author(s):  
A. J. Berkhout ◽  
C. P. A. Wapenaar
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Wave Field ◽  
Green's Function ◽  
Green's Functions ◽  
Acoustic Pressure ◽  
Green’S Functions ◽  
Absorbing Boundary Conditions ◽  
Multiple Reflections ◽  
Kirchhoff Integral

The conventional Kirchhoff integral, based on the two‐way wave equation, states how the acoustic pressure at a point A inside a closed surface S can be calculated when the acoustic wave field is known on S. In its general form, the integrand consists of two terms: one term contains the gradient of a Green’s function and the acoustic pressure; the other term contains a Green’s function and the gradient of the acoustic pressure. The integrand can be simplified by choosing reflecting boundary conditions for the two‐way Green’s functions in such a way that either the first term or the second term vanishes on S. This conventional approach to deriving Rayleigh‐type integrals has practical value only for media with small contrasts, so that the two‐way Green’s functions do not contain significant multiple reflections. We present a modified approach for simplifying the integrand of the Kirchhoff integral by choosing absorbing boundary conditions for the one‐way Green’s functions. The resulting Rayleigh‐type integrals are the theoretical basis for true amplitude one‐way wave‐field extrapolation techniques in inhomogeneous media with significant contrasts.

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

2019 ◽  
Vol 105 (5) ◽  
pp. 827-837
Author(s):  
Kyounghun Been ◽  
Wonkyu Moon
Keyword(s):  
Finite Element Method ◽  
Acoustic Pressure ◽  
The Finite Element Method ◽  
Integration Process ◽  
Rigorous Derivation ◽  
Irregular Surfaces ◽  
Pressure Distributions ◽  
Surface Integration ◽  
Kirchhoff Integral ◽  
Integral Solutions

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.

Extended Kirchhoff Integral Formulations for Sound Radiation from Vibrating Cylinders in Motion

1993 ◽  
Vol 115 (3) ◽  
pp. 324-331 ◽  
Author(s):  
S. F. Wu ◽  
Z. Wang
Keyword(s):  
Acoustic Pressure ◽  
Near Field ◽  
Translational Motion ◽  
Sound Radiation ◽  
Forward Direction ◽  
Numerical Results ◽  
Rectilinear Motion ◽  
Dimensionless Frequency ◽  
Translational Speed ◽  
Kirchhoff Integral

This paper presents numerical results of sound radiation from vibrating cylinders in rectilinear motion at constant subsonic speeds by using the extended Kirchhoff integral formulations recently derived by Wu and Akay (1992). In particular, the effects of the interaction between the turbulent stress field and the vibrating surface in motion are examined. Numerical results demonstrate that this interaction is significant in the near-field when the dimensionless frequency ka > 2 and the dimensionless source translational speed M > 0.1. If this interaction is completely neglected, the predicted acoustic pressure is underestimated by as much as 10 to 20 percent in the near field. The effects of this interaction, however, decrease in the far-field. The effects of surface translational motion on the resulting sound radiation are also examined. It is found that the surface translational motion has a significant effect on the resulting sound generation in both near- and far-fields. The amplitude of the acoustic pressure is approximately doubled in the forward direction when ka > 2 and M > 0.2, which corresponds to at least a 5 dB increase in the SPL value.

scholarly journals Using the Kirchhoff integral for approximate calculation of angular characteristics of sound scattering by elastic shells of nonanalytical form

2021 ◽  
pp. 124-129
Author(s):  
С.Л. Ильменков ◽  
А.В. Богородский ◽  
Г.А. Лебедев ◽  
А.В. Троицкий
Keyword(s):  
Integral Formula ◽  
Separation Of Variables ◽  
Analytical Form ◽  
Theory Of Elasticity ◽  
Individual Characteristics ◽  
Physical Parameters ◽  
Sound Scattering ◽  
Elastic Bodies ◽  
Sound Diffraction ◽  
Kirchhoff Integral

Предложен новый приближенный метод расчета угловых характеристик рассеяния звука на упругих телах неаналитической формы при различных геометрических параметрах стыкуемых фрагментов аналитической формы. Метод базируется на использовании интегральной формулы Кирхгофа и известных строгих решениях задач дифракции звука на упругих аналитических телах. Совместное использование методов динамической теории упругости и разделения переменных с помощью потенциалов Дебая и «типа Дебая» позволяет получить решения задач дифракции звука на изотропных оболочках неаналитической формы, составленных из компонентов сфероидальной, цилиндрической и сферической форм. Вычислены и проанализированы угловые характеристики рассеяния при различных волновых размерах, геометрических и физических параметрах оболочек. Применение рассматриваемого метода имеет особенно актуально в диапазонах низких и средних звуковых частот, где упругие тела являются эффективными рассеивателями звука, что повышает вероятность определения их индивидуальных признаков. A new approximate method for calculating the angular characteristics of sound scattering on elastic bodies of non-analytical form for various geometric parameters of the joined fragments of the analytical shape we proposed. The method they based on the use of the Kirchhoff integral formula and well-known rigorous solutions of sound diffraction problems on elastic analytical bodies. The combined use of methods of the dynamic theory of elasticity and separation of variables using Debye potentials and "Debye type" potentials allows us to obtain solutions to problems of sound diffraction on isotropic shells of non-analytical form composed of components of spherical, cylindrical and spherical forms. Angular scattering characteristics are calculated and analyzed for various wave sizes, geometric and physical parameters of the shells are calculated. The application of this method is particularly relevant in the low and medium sound frequency ranges, where elastic bodies are effective sound diffusers, which increases the probability of determining their individual characteristics.

An integral formula for the even part of the texture function or « the apparition of the fπ and fω ghost distributions »

1982 ◽  
Vol 43 (2) ◽  
pp. 189-195 ◽  
Author(s):  
Claude Esling ◽  
Jacques Muller ◽  
Hans-Joachim Bunge
Keyword(s):  
Integral Formula

scholarly journals ON p – q DUALITY AND EXPLICIT SOLUTIONS IN c ≤ 1 2D GRAVITY MODELS

1995 ◽  
Vol 10 (08) ◽  
pp. 1219-1236 ◽  
Author(s):  
S. KHARCHEV ◽  
A. MARSHAKOV
Keyword(s):  
String Theory ◽  
Exact Solutions ◽  
2D Gravity ◽  
Integral Formula ◽  
Integral Representations ◽  
Gravity Models ◽  
Explicit Solutions ◽  
String Equation ◽  
Duality Transformation

We study the role of integral representations in the description of nonperturbative solutions to c ≤ 1 string theory. A generic solution is determined by two functions, W(x) and Q(x), which behave at infinity like xp and xq respectively. The integral formula for arbitrary (p, q) models is derived, which explicitly realizes a duality transformation between (p, q) and (q, p) 2D gravity solutions. We also discuss the exact solutions to the string equation and reduction condition and present several explicit examples.

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