Eigenvalue analysis for acoustic problem in 3D by boundary element method with the block Sakurai–Sugiura method

Gao, Haifeng; Matsumoto, Toshiro; Takahashi, Tōru; Isakari, Hiroshi

doi:10.1016/j.enganabound.2013.03.015

Cited by 32 publications

(17 citation statements)

References 31 publications

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“…In the numerical eigenvalue analysis of the interior Dirichlet problem, the contour integral path C is defined as a circle with γ ¼ ð5:1; 0Þ; ρ ¼ 2:0 and the parameters in the block SS method are set as N ¼ 200; K ¼ 4; L ¼ 15 and δ ¼ 10 À 12 . Discussions about the choices of these parameters can be found in [30,43]. Numerical eigenvalues are given in Table 3 where both the CBIE and the combined formulation are employed.…”

Section: The Interior Of the Unit Spherementioning

confidence: 99%

“…The conversion is achieved by solving a set of linear systems of equations, for instance the standard boundary element systems of equations in the BEM eigenvalue analysis. CIM has already been applied to solve nonlinear eigenproblems formulated by the acoustic BEM [30,31] and the method of fundamental solution (MFS) [32], and also nonlinear eigenproblems of vibro-acoustic simulations formulated by a coupled finite and boundary element approach [33]. In this paper, a CIM approach called the block Sakurai-Sugiura (SS) method [28] is employed.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Is the Burton–Miller formulation really free of fictitious eigenfrequencies?

Zheng

Chen

Gao

et al. 2015

Engineering Analysis with Boundary Elements

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Section: The Interior Of the Unit Spherementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Is the Burton–Miller formulation really free of fictitious eigenfrequencies?

Zheng

Chen

Gao

et al. 2015

Engineering Analysis with Boundary Elements

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“…For instance, the method proposed by Asakura et al . has been applied to solve acoustic eigenvalue problems in References and to conduct the band structure analysis of phononic crystals in Reference . Kimeswenger et al .…”

Section: Introductionmentioning

confidence: 99%

“…So far, the contour integral methods have already been applied to solve some nonlinear eigenvalue problems in engineering applications. For instance, the method proposed by Asakura et al [35] has been applied to solve acoustic eigenvalue problems in References [39][40][41] and to conduct the band structure analysis of phononic crystals in Reference [42]. Kimeswenger et al [43] analyzed the approximation of a fluid-structure interaction eigenvalue problem and used Beyn's method [36] for the numerical solution of the discretized nonlinear eigenvalue problem.In addition to the frequency-dependent coefficient matrices, some other inherent shortcomings also exist in the acoustic BEM.…”

mentioning

confidence: 99%

Coupled FE–BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain

Zheng

Zhang

et al. 2016

Numerical Meth Engineering

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Summary For thin elastic structures submerged in heavy fluid, e.g., water, a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies. Therefore, the eigenanalysis of the fluid–structure interaction system is necessary. In this paper, a coupled finite element and boundary element (FE–BE) method is developed for the numerical eigenanalysis of the fluid–structure interaction problems. The structure is modeled by the finite element method. The compressibility of the fluid is taken into consideration, and hence the Helmholtz equation is employed as the governing equation and solved by the boundary element method (BEM). The resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method. Adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest. The Burton–Miller formulation is applied to tackle the fictitious eigenfrequency problem of the BEM, and the optimal choice of its coupling parameter is investigated for the coupled FE–BE method. Numerical examples are given and discussed to demonstrate the effectiveness and accuracy of the developed FE–BE method. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Recently, Wang et al investigated approximation functions such as RBF (radial basis functions) and TPS (thin plate spline functions) in the dual reciprocity BEM for accurate acoustic eigenvalue analysis [16]. Gao et al presented accurate solutions for eigenvalue analysis of three-dimensional acoustic cavities using BEM with the block Sakurai-Sugiura method [17].…”

Section: Introductionmentioning

confidence: 99%

Application of Nondimensional Dynamic Influence Function Method for Eigenmode Analysis of Two-Dimensional Acoustic Cavities

Kang

Atluri

2014

Advances in Mechanical Engineering

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This paper establishes an improved NDIF method for the eigenvalue extraction of two-dimensional acoustic cavities with arbitrary shapes. The NDIF method, which was introduced by the authors in 1999, gives highly accurate eigenvalues despite employing a small number of nodes. However, it needs the inefficient procedure of calculating the singularity of a system matrix in the frequency range of interest for extracting eigenvalues and mode shapes. The paper proposes a practical approach for overcoming the inefficient procedure by making the final system matrix equation of the NDIF method into a form of algebraic eigenvalue problem. The solution quality of the proposed method is investigated by obtaining the eigenvalues and mode shapes of a circular, a rectangular, and an arbitrarily shaped cavity.

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Eigenvalue analysis for acoustic problem in 3D by boundary element method with the block Sakurai–Sugiura method

Cited by 32 publications

References 31 publications

Is the Burton–Miller formulation really free of fictitious eigenfrequencies?

Is the Burton–Miller formulation really free of fictitious eigenfrequencies?

Coupled FE–BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain

Application of Nondimensional Dynamic Influence Function Method for Eigenmode Analysis of Two-Dimensional Acoustic Cavities

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