Boundary Element Modeling of Sound Attenuation in Acoustically Lined Curved Pipes

2019 ◽  
Vol 27 (03) ◽  
pp. 1850046
Author(s):  
A. Saide Sarıgül
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Analytical Solution ◽  
Boundary Element ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Sound Attenuation ◽  
Acoustic Behavior ◽  
Curved Pipes ◽  
Helmholtz Integral

The results of a modeling study for the numerical solution of the interior surface Helmholtz integral for acoustically lined curved pipes with rectangular cross-section are presented. The solution of the Helmholtz integral equation is calculated by using the boundary element method (BEM). The sound attenuation spectra of different possible models with regard to the lining on the boundaries are compared with the analytical solution. The acoustic behavior of different models is discussed and the features of the model that gives more accurate results are presented.

BOUNDARY ELEMENT SOLUTION OF A BODY'S EXTERIOR ACOUSTIC FIELD NEAR ITS INTERNAL EIGENVALUES

1993 ◽  
Vol 01 (03) ◽  
pp. 335-353 ◽  
Author(s):  
R. A. MARSCHALL
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Singular Value ◽  
Practical Implementation ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Value Decomposition ◽  
Element Method ◽  
Helmholtz Integral

A relatively straightforward Boundary Element Method (BEM) for the numerical solution of the exterior Helmholtz problem is specified in a tutorial fashion. The algorithm employs the Combined Helmholtz Integral Equation Formulation (CHIEF) and then Singular Value Decomposition (SVD) to solve the resulting system. Its accuracy and convergence characteristics are examined, and compared to the simplest boundary element method for exterior acoustics, the Helmholtz Integral Equation Formulation or HIEF. Boundary element and auxiliary (CHIEF) point requirements to obtain BEM solutions of a desired accuracy are described. This particular CHIEF algorithm is found to largely avoid the numerical difficulties of the HIEF technique while retaining theoretical and practical implementation simplicity.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

A Novel Displacement Gradient Boundary Element Method for Elastic Stress Analysis With High Accuracy

1988 ◽  
Vol 55 (4) ◽  
pp. 786-794 ◽  
Author(s):  
H. Okada ◽  
H. Rajiyah ◽  
S. N. Atluri
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Numerical Differentiation ◽  
Boundary Integral ◽  
Displacement Gradient ◽  
Direct Integral ◽  
Displacement Boundary ◽  
Element Method

The boundary element method (BEM) in current usage, is based on the displacement boundary integral equation. The current practice of computing stresses in the BEM involves the use of a two-tier approach: (i) numerical differentiation of the displacement field at the boundary, and (ii) analytical differentiation of the displacement integral equation at the source point in the interior. A new direct integral equation for the displacement gradient is proposed here, to obviate this two-tier approach. The new direct boundary integral equation for displacement gradients has a lower order singularity than in the standard formulation, and is quite tractable from a numerical view point. Numerical results are presented to illustrate the advantages of the present approach.

STABILITY ANALYSIS OF A COLLOCATION METHOD FOR SOLVING THE RETARDED POTENTIAL INTEGRAL EQUATION

2005 ◽  
Vol 13 (02) ◽  
pp. 287-299 ◽  
Author(s):  
P. J. HARRIS ◽  
H. WANG ◽  
R. CHAKRABARTI ◽  
D. HENWOOD
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Stability Analysis ◽  
Boundary Element Method ◽  
Numerical Solution ◽  
Boundary Element ◽  
Collocation Method ◽  
Stability Problem ◽  
Numerical Scheme ◽  
Type Boundary

This paper deals with the numerical solution of the retarded potential integral equation using a collocation type boundary element method. This method is widely used in practice but often suffers from stability problems. The purpose of the paper is to carry out a stability analysis of the numerical scheme and examine how any instability arises. This paper will then propose a method for overcoming this stability problem. A comparison with an exact solution demonstrates that the approach proposed here is effective for the case of a sphere.

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