Numerical Analysis of Structure Acoustic Radiation Based on Wave Superposition Method

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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An Indirect Boundary Element Method for Computing Sound Field

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.476-478.1173 ◽

2012 ◽

Vol 476-478 ◽

pp. 1173-1177

Author(s):

Sheng Yao Gao ◽

De Shi Wang

Keyword(s):

Integral Equation ◽

Boundary Element Method ◽

Boundary Element ◽

Acoustic Field ◽

Boundary Surface ◽

Sound Field ◽

Boundary Integral ◽

Superposition Method ◽

Wave Superposition ◽

Element Method

Computing sound field from an arbitrary radiator is of interest in acoustics, with many significant applications, one that includes the design of classical projectors and the noise prediction of underwater vehicle. 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. In this paper, the theoretical backgrounds to the direct boundary element method and the wave superposition method are presented. The wave superposition method does not solve the Kirchoff-Helmholtz integral equation directly. In the approach a lumped parameter model is estabiled from spatially averaged quantities, and 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. Then the sound field over the of a pulsating sphere is calculated. Finally, comparison between the analytical and numerical results is given, and the speed of solution is investigated. The results show that the agreement between the results from the above numerical methods is excellent. The wave superposition method requires fewer elements and hence is faster, which do not need as high a mesh density as traditionally associated with BEM.

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Reconstruction of vibro-acoustic field in half-space based on wave superposition method using dual surface measurement

2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications (SPAWDA) ◽

10.1109/spawda.2011.6167223 ◽

2011 ◽

Cited By ~ 1

Author(s):

Chao Sun ◽

Yuan-an He ◽

Yue-chan Liu ◽

Da-jing Shang

Keyword(s):

Half Space ◽

Acoustic Field ◽

Surface Measurement ◽

Superposition Method ◽

Wave Superposition

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Acoustical feature extraction of rotating machinery with combined wave superposition and blind source separation

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/0954406jmes189 ◽

2006 ◽

Vol 220 (9) ◽

pp. 1423-1431 ◽

Cited By ~ 8

Author(s):

W F Xue ◽

J Chen ◽

J Q Li ◽

X F Liu

Keyword(s):

Fault Diagnosis ◽

Blind Source Separation ◽

Acoustic Radiation ◽

Microphone Array ◽

Source Separation ◽

Point Sources ◽

Superposition Method ◽

Sound Sources ◽

Reconstruction Process ◽

Wave Superposition

As the result of vibration emission in air, machine sound signal carries affluent information about the working condition of machine and it can be used to make mechanical fault diagnosis. The fundamental problems with fault diagnosis are the estimation of the number of sound sources and the localization of sound sources. The wave superposition can be employed to identify and locate sound sources, which is based on the idea that an acoustic radiator can be approximated and represented by the sum of the fields due to a finite number of interior point sources. But, in practice, a large number of measurements must be used in order to achieve a desired resolution, which makes the reconstruction process very time-consuming and expensive. In this paper, a combined wave superposition method has been developed reconstruct to acoustic radiation from machine acoustical signals. This method combines the advantages of both the wave superposition and Helmholtz equationleast squares methods, and it allows for reconstruction of the acoustic field from an arbitrary object with relatively few measurements, thus significantly enhancing the reconstruction efficiency. After sound source localization, the blind source separation (BSS) is proposed to extract acoustical feature from the mixed measuring sound signals. In a semi-anechoic chamber, a cross-planar microphone array, which consists of 29 microphones, was successfully applied to obtain the two-dimensional mapping of the sound sources. The location, the sound pressure, and the properties in frequency domain of the sound sources can be found through this method precisely. The experimental results demonstrate that the methods presented can potentially become an acoustical diagnosis tool.

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Wave Superposition Method Applied to Calculate the Radiation Sound Power from a Thin Plate

Journal of Physics Conference Series ◽

10.1088/1742-6596/1325/1/012122 ◽

2019 ◽

Vol 1325 ◽

pp. 012122

Author(s):

Yong-yong Zhu ◽

Jing-hui Peng ◽

Bao Liu

Keyword(s):

Thin Plate ◽

Superposition Method ◽

Sound Power ◽

Wave Superposition

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Location Optimization of Monopole Equivalent Sources in Wave Superposition Method

The International Journal of Acoustics and Vibration ◽

10.20855/ijav.2018.23.21467 ◽

2018 ◽

Vol 23 (2) ◽

Author(s):

Shaowei Wu ◽

Yang Xiang

Keyword(s):

Superposition Method ◽

Location Optimization ◽

Wave Superposition ◽

Equivalent Sources

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Wave Superposition Method Applied To Calculate the Radiation Sound Power of a Stiffened Plate

Journal of Physics Conference Series ◽

10.1088/1742-6596/1549/5/052072 ◽

2020 ◽

Vol 1549 ◽

pp. 052072

Author(s):

Yongyong Zhu ◽

Bao Liu ◽

Kai Zhang

Keyword(s):

Superposition Method ◽

Sound Power ◽

Stiffened Plate ◽

Wave Superposition

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Review: The Use of Equivalent Source Method in Computational Acoustics

Journal of Computational Acoustics ◽

10.1142/s0218396x16300012 ◽

2017 ◽

Vol 25 (01) ◽

pp. 1630001 ◽

Cited By ~ 18

Author(s):

Seongkyu Lee

Keyword(s):

Boundary Surface ◽

Optimal Number ◽

Method Of Fundamental Solutions ◽

Attractive Alternative ◽

Superposition Method ◽

Numerical Instability ◽

Equivalent Source ◽

Source Method ◽

Equivalent Sources ◽

Equivalent Source Method

This paper reviews the equivalent source method (ESM), an attractive alternative to the standard boundary element method (BEM). The ESM has been developed under different names: method of fundamental solutions, wave superposition method, equivalent source method, etc. However, regardless of the method name, the basic concept is very similar; that is to use auxiliary points called equivalent sources to reconstruct the acoustic pressure for radiation or scattering problems. The strength of the equivalent sources are then determined via various approaches such that the boundary conditions on the boundary surface are satisfied. This paper reviews several frequency-domain and time-domain ESMs. There are several distinct advantages in these types of methods: (1) the method is a meshless approach so that it is easy and simple to implement; (2) it does not have a numerical singularity problem that occurs in the BEM; (3) the number of equivalent sources can be fewer than the number of surface collocation points so that the matrix size is reduced and a fast computation is achieved for large problems. The main issue of the ESM is that there is no rule to find out the optimal number and position of equivalent sources. In addition, the ESM suffers from the numerical instability that is associated with the ill-conditioned matrix. Some guidelines have been suggested in terms of finding the number and position of the sources, and several numerical techniques have been developed to resolve the numerical instability. This paper reviews the common theories, numerical issues and challenges of the ESM, and it summarizes recent developments and applications of the ESM to aircraft noise.

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