A FORMULATION OF THE BOUNDARY ELEMENT METHOD FOR ACOUSTIC RADIATION AND SCATTERING FROM TWO-DIMENSIONAL STRUCTURES

2007 ◽  
Vol 15 (03) ◽  
pp. 333-352 ◽  
Author(s):  
Z.-S. CHEN ◽  
H. WAUBKE
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Integral Equations ◽  
Half Space ◽  
Singular Integrals ◽  
Acoustic Radiation ◽  
Ground Surface ◽  
Green Functions ◽  
Two Dimensional ◽  
Element Method

A code for the boundary element method (BEM) for two-dimensional acoustic radiation and scattering problems is developed. To overcome the singularity problem of the integral equations at characteristic frequencies, the Burton–Miller method is employed in the formulation. The integral equations are then discretized by using the two-nodal constant elements and a collocation procedure. The hyper and weakly singular integrals in each element containing the collocation points are computed analytically and numerically respectively (stark singularity does not appear). In outdoor acoustic, the ground surface can be seen occasionally as an infinite surface with a given constant impedance. In this case the ground surface can either be discretized by using finite and infinite boundary elements or simulated by using the Green functions for impedance half space. The method to compute such Green functions presented in Ref. 1, is improved and used in the code. A formulation of the infinite boundary element is proposed. The two BEM approaches for the impedance half space problems are tested by means of examples and the agreement is found to be good.

Removing Non-Uniqueness in Symmetric Galerkin Boundary Element Method for Elastostatic Neumann Problems and its Application to Half-Space Problems

2020 ◽  
Vol 36 (6) ◽  
pp. 749-761
Author(s):  
Y. -Y. Ko
Keyword(s):  
Boundary Element Method ◽  
Rigid Body ◽  
Boundary Element ◽  
Integral Equations ◽  
Half Space ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Neumann Problems ◽  
Galerkin Boundary Element Method ◽  
Element Method

ABSTRACTWhen the Symmetric Galerkin boundary element method (SGBEM) based on full-space elastostatic fundamental solutions is used to solve Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid-body-motion terms involved. Several methods that have been used to remove the non-uniqueness, including additional point support, eigen decomposition, regularization of a singular system and modified boundary integral equations, were introduced to amend SGBEM, and were verified to eliminate the rigid body motions in the solutions of full-space exterior Neumann problems. Because half-space problems are common in geotechnical engineering practice and they are usually Neumann problems, typical half-space problems were also analyzed using the amended SGBEM with a truncated free surface mesh. However, various levels of errors showed for all the methods of removing non-uniqueness investigated. Among them, the modified boundary integral equations based on the Fredholm’s theory is relatively preferable for its accurate results inside and near the loaded area, especially where the deformation varies significantly.

A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

2020 ◽  
pp. 1475472X2097838
Author(s):  
Bassem Barhoumi ◽  
Jamel Bessrour
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Singular Integrals ◽  
Acoustic Radiation ◽  
Normal Derivative ◽  
Boundary Integral ◽  
Meridian Plane ◽  
Mean Flow ◽  
Transform Method ◽  
Element Method

This paper presents a new numerical analysis approach based on an improved Modal Boundary Element Method (MBEM) formulation for axisymmetric acoustic radiation and propagation problems in a uniform mean flow of arbitrary direction. It is based on the homogeneous Modal Convected Helmholtz Equation (MCHE) and its convected Green’s kernel using a Fourier transform method. In order to simplify the flow terms, a general modal boundary integral solution is formulated explicitly according to two new operators such as the particular and convected kernels. Through the use of modified operators, the improved MBEM approach with flow takes a convective form of the general MBEM approach and has a similar form of the nonflow MBEM formulation. The reference and reduced Helmholtz Integral Equations (HIEs) are implicitly taken into account a new nonreflecting Sommerfeld condition to solve far field axisymmetric regions in a uniform mean flow. For isolating the singular integrations, the modal convected Green’s kernel and its modified normal derivative are performed partly analytically in terms of Laplace coefficients and partly numerically in terms of Fourier coefficients. These coefficients are computed by recursion schemes and Gauss-Legendre quadrature standard formulae. Specifically, standard forms of the free term and its convected angle resulting from the singular integrals can be expressed only in terms of real angles in meridian plane. To demonstrate the application of the improved MBEM formulation, three exterior acoustic case studies are considered. These verification cases are based on new analytic formulations for axisymmetric acoustic sources, such as axisymmetric monopole, axial and radial dipole sources in the presence of an arbitrary uniform mean flow. Directivity plots obtained using the proposed technique are compared with the analytical results.

A Symmetric Galerkin Formulation of the Boundary Element Method for Acoustic Radiation and Scattering

1997 ◽  
Vol 05 (02) ◽  
pp. 219-241 ◽  
Author(s):  
Z. S. Chen ◽  
G. Hofstetter ◽  
H. A. Mang
Keyword(s):  
Boundary Element Method ◽  
Numerical Solution ◽  
Boundary Element ◽  
Integral Equations ◽  
Acoustic Radiation ◽  
Numerical Study ◽  
Three Dimensional ◽  
Galerkin Formulation ◽  
Thin Walled ◽  
Element Method

A symmetric Galerkin formulation of the Boundary Element Method for acoustic radiation and scattering is presented. The basic integral equations for radiation and scattering of sound are derived for structures, which may consist of a combination of a three-dimensional closed part and thin-walled parts. For the numerical solution of these integral equations a Galerkin-type numerical solution scheme is proposed. The evaluation of the weakly-singular and the hypersingular integrals, occurring in this formulation, is addressed briefly. An improved CHIEF-method is employed in order to prevent the singularity of the coefficient matrix of the algebraic system of equations at so-called irregular frequencies. Subsequently, an algorithm for the automatic determination of the number of nodal unknowns at intersections of thin-walled parts of a structure, or of thin-walled parts and the three-dimensional closed part of a structure, is described. The numerical study contains comparisons of analytical solutions for simple academic examples with the numerical results. In addition, a comparison of measured and computed results is presented for a structure, consisting of both a three-dimensional closed part and a thin-walled part.

Application of the Boundary Element Method and Modal Analysis to Tire Acoustics Problems

1993 ◽  
Vol 21 (2) ◽  
pp. 66-90 ◽  
Author(s):  
Y. Nakajima ◽  
Y. Inoue ◽  
H. Ogawa
Keyword(s):  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Acoustic Radiation ◽  
Traffic Noise ◽  
Noise Prediction ◽  
Prediction System ◽  
Tire Noise ◽  
Acoustic Contribution ◽  
Element Method

Abstract Road traffic noise needs to be reduced, because traffic volume is increasing every year. The noise generated from a tire is becoming one of the dominant sources in the total traffic noise because the engine noise is constantly being reduced by the vehicle manufacturers. Although the acoustic intensity measurement technology has been enhanced by the recent developments in digital measurement techniques, repetitive measurements are necessary to find effective ways for noise control. Hence, a simulation method to predict generated noise is required to replace the time-consuming experiments. The boundary element method (BEM) is applied to predict the acoustic radiation caused by the vibration of a tire sidewall and a tire noise prediction system is developed. The BEM requires the geometry and the modal characteristics of a tire which are provided by an experiment or the finite element method (FEM). Since the finite element procedure is applied to the prediction of modal characteristics in a tire noise prediction system, the acoustic pressure can be predicted without any measurements. Furthermore, the acoustic contribution analysis obtained from the post-processing of the predicted results is very helpful to know where and how the design change affects the acoustic radiation. The predictability of this system is verified by measurements and the acoustic contribution analysis is applied to tire noise control.

Explicit Kutta condition for unsteady two-dimensional high-order potential boundary element method

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1080-1081
Author(s):  
Giuseppe Davi ◽  
Rosario M. A. Maretta ◽  
Alberto Milazzo
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
High Order ◽  
Two Dimensional ◽  
Kutta Condition ◽  
Element Method
Sign in / Sign up

Export Citation Format

Share Document