Integral equation methods with unique solution for all wavenumbers applied to acoustic radiation

2010 ◽  
Vol 19 (5-7) ◽  
pp. 619-636
Author(s):  
Antoine Lavie ◽  
Alexandre Leblanc
Keyword(s):  
Integral Equation ◽  
Unique Solution ◽  
Acoustic Radiation ◽  
Integral Equation Methods

scholarly journals Integral equation methods with unique solution for all wavenumbers applied to acoustic radiation

2010 ◽  
pp. 619-636
Author(s):  
Antoine Lavie ◽  
Alexandre Leblanc
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Unique Solution ◽  
Characteristic Frequency ◽  
Acoustic Radiation ◽  
Three Dimensional ◽  
Infinite Cylinder ◽  
Integral Equation Methods ◽  
Time Harmonic ◽  
Small Imaginary Part

The acoustic exterior Neumann problem is solved using an easy process based upon the boundary element method and able to eliminate effects of irregular frequencies in time harmonic domain. This technique is performed as follows: (i) two computations are done around the characteristic frequency, decreased and increased by a small imaginary part; (ii) average between pressures at these two frequencies ensures unique solution for all wavenumbers. This method is numerically tested for an infinite cylinder, an axisymmetric cylinder, a sphere and a three-dimensional cat’s eye structure. This work highlights ease and efficiency of the technique under consideration to remove the irregular frequencies effects.

A Comparison of Two Integral Equation Methods for High Subsonic Lifting Flows

1975 ◽  
Vol 26 (1) ◽  
pp. 56-58 ◽  
Author(s):  
D Nixon
Keyword(s):  
Integral Equation ◽  
Unique Solution ◽  
Subsonic Flow ◽  
Integral Equation Methods ◽  
High Subsonic Flow

SummaryA comparison is made of two recently published integral equation methods for calculating the high subsonic flow around lifting and non-lifting aerofoils. It is shown that one method leads to a non-unique solution.

Improved Integral Formulation for Acoustic Radiation Using Integral Equation of Frequency Averaged Quadratic Pressure

2017 ◽  
Vol 25 (01) ◽  
pp. 1750004 ◽  
Author(s):  
Honglin Gao ◽  
Sheng Li
Keyword(s):  
Integral Equation ◽  
Boundary Conditions ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Acoustic Radiation ◽  
Boundary Integral ◽  
Uniqueness Of Solutions ◽  
High Frequencies ◽  
Numerical Examples ◽  
Integral Equation Formulation

This paper is concerned with the problem of obtaining a unique solution for radiation at irregular frequencies when an integral equation of frequency averaged quadratic pressure (FAQP) is used to get robust predictions at medium and high frequencies. It is proved that there is no unique solution of the integral equation of FAQP at irregular frequencies, and existence and uniqueness of solutions under four types of boundary conditions are discussed. A combined energy boundary integral equation formulation (CEBIEF) is presented and proves to be efficient to overcome the nonuniqueness of the integral equation of FAQP. The numerical examples are given to demonstrate the versatility of the CEBIEF method with a proposed function correctly indicating a solution.

scholarly journals Numerical Analysis of Structure Acoustic Radiation Based on Wave Superposition Method

2011 ◽  
Vol 2-3 ◽  
pp. 733-738
Author(s):  
Sheng Yao Gao ◽  
De Shi Wang ◽  
Yi Qun Du
Keyword(s):  
Integral Equation ◽  
Acoustic Field ◽  
Acoustic Radiation ◽  
Boundary Surface ◽  
Impact Factors ◽  
Power Calculation ◽  
Superposition Method ◽  
Sound Power ◽  
Wave Superposition ◽  
Equivalent Sources

To overcome the non-uniqueness of solution at eigenfrequencies in the boundary integral equation method for structural acoustic radiation, wave superposition method is introduced to study the acoustics characteristics including acoustic field reconstruction and sound power calculation. The numerical method is implemented by using the acoustic field from a series of virtual sources which are collocated near the boundary surface to replace the acoustic field of the radiator, namely the principle of equivalent. How to collocate these equivalent sources is not indicated definitely. Once wave superposition method is applied to sound power calculation, it is necessary to evaluate its accuracy and impact factors. In the paper, the basic principle of wave superposition method is described, and then the integral equation is discretized. Also, the impact factors including element numbers, frequency limitation, and distance between virtual source and integral surface are analyzed in the process of calculate the acoustic radiation from the simply supported thin plate under concentrated force. The extensive measures of acoustic field at the thin plate are compared with results obtain using different numerical methods. The results show that: (a) The agreement between the results from the above numerical methods is excellent. The wave superposition method requires fewer elements and hence is faster. But the extensive numerical modeling suggests that as long as the volume velocity matching yields more than adequate accuracy. (b) The equivalent sources should be collocated inside the radiator. And the accuracy of a given Gauss integration formula will decrease as the source approaches the boundary surface. (c) The numerical method is applicable to the acoustic radiation of structure with complicated shape. (d) The method described in this paper can be used to perform effectively sound power calculation, and its application range can be extended on the basis of these conclusions.

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