scholarly journals Methods for Speeding Up the Boundary Element Solution of Acoustic Radiation Problems

1992 ◽  
Vol 114 (3) ◽  
pp. 374-380 ◽  
Author(s):  
S. M. Kirkup ◽  
D. J. Henwood
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Helmholtz Equation ◽  
Boundary Element ◽  
Linear Systems ◽  
Acoustic Radiation ◽  
Integral Operators ◽  
Test Problems ◽  
Element Solution ◽  
Integral Equation Formulation

Methods for speeding up the boundary element solution of acoustic radiation problems are considered. The methods are based on solving the integral equation formulation of Burton and Miller for the exterior Helmholtz equation over a range of frequencies simultaneously. Methods for speeding up the computation of the discrete forms of the integral operators and the solution of the linear systems that arise in the boundary element method are considered. A particular implementation of speedup methods is described. Results from the application of this to test problems are given.

Application of the Boundary Element Method to Acoustic Cavity Response and Muffler Analysis

1987 ◽  
Vol 109 (1) ◽  
pp. 15-21 ◽  
Author(s):  
A. F. Seybert ◽  
C. Y. R. Cheng
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Transmission Loss ◽  
Radiation Condition ◽  
Boundary Integral ◽  
Exterior Problems ◽  
Integral Equation Formulation ◽  
Element Method

This paper is concerned with the application of the Boundary Element Method (BEM) to interior acoustics problems governed by the reduced wave (Helmholtz) differential equation. The development of an integral equation valid at the boundary of the interior region follows a similar formulation for exterior problems, except for interior problems the Sommerfeld radiation condition is not invoked. The boundary integral equation for interior problems does not suffer from the nonuniqueness difficulty associated with the boundary integral equation formulation for exterior problems. The boundary integral equation, once obtained, is solved for a specific geometry using quadratic isoparametric surface elements. A simplification for axisymmetric cavities and boundary conditions permits the solution to be obtained using line elements on the generator of the cavity. The present formulation includes the case where a node may be placed at a position on the boundary where there is not a unique tangent plane (e.g., at an edge or a corner point). The BEM capability is demonstrated for two types of classical interior axisymmetric problems: the acoustic response of a cavity and the transmission loss of a muffler. For the cavity response comparison data are provided by an analytical solution. For the muffler problem the BEM solution is compared to data obtained by a finite element method analysis.

Analytic Method on Vibrate Induced Noise of Engine Block

2011 ◽  
Vol 308-310 ◽  
pp. 21-26
Author(s):  
Guang Ze Zheng ◽  
Kazuhide Ohta
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Acoustic Radiation ◽  
Engine Block ◽  
Analytic Method ◽  
Mean Square ◽  
Integral Equation Formulation ◽  
Block Based ◽  
Singular Matrices ◽  
Engine Development

Numerical prediction of the acoustic radiation of vibrating engine block is conventionally based on the boundary element method (BEM). This approach yields good predictions, provided that the dynamic behavior of engine block is well established. However, interior resonances may lead to singular matrices and nonunique solution. To avoid the problems with interior resonances and singular matrices, this paper introduced the combined Helmholtz integral equation formulation method (CHIEF METHOD). The numerical experiment shows the performance of CHIEF METHOD and then we use this method to estimate the acoustic radiation of engine block. Based on spatially mean square velocity and acoustic radiation efficiency of vibrating engine block, a simplified analytic method is presented in this paper, by which the vibrate induced noise can be predicted in the early design process of engine development.

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.

scholarly journals The Boundary Element Method in Acoustics: A Survey

2019 ◽  
Vol 9 (8) ◽  
pp. 1642 ◽  
Author(s):  
Kirkup
Keyword(s):  
Integral Equation ◽  
Computational Complexity ◽  
Boundary Element Method ◽  
Inverse Problems ◽  
Boundary Element ◽  
Integral Operators ◽  
Boundary Integral ◽  
Boundary Element Methods ◽  
Software Library ◽  
Element Method

The boundary element method (BEM) in the context of acoustics or Helmholtz problems is reviewed in this paper. The basis of the BEM is initially developed for Laplace’s equation. The boundary integral equation formulations for the standard interior and exterior acoustic problems are stated and the boundary element methods are derived through collocation. It is shown how interior modal analysis can be carried out via the boundary element method. Further extensions in the BEM in acoustics are also reviewed, including half-space problems and modelling the acoustic field surrounding thin screens. Current research in linking the boundary element method to other methods in order to solve coupled vibro-acoustic and aero-acoustic problems and methods for solving inverse problems via the BEM are surveyed. Applications of the BEM in each area of acoustics are referenced. The computational complexity of the problem is considered and methods for improving its general efficiency are reviewed. The significant maintenance issues of the standard exterior acoustic solution are considered, in particular the weighting parameter in combined formulations such as Burton and Miller’s equation. The commonality of the integral operators across formulations and hence the potential for development of a software library approach is emphasised.

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.

Sign in / Sign up

Export Citation Format

Share Document