A semi-analytical approach for radiation and scattering problems with circular boundaries

Chen, J.T.; Chen, C.T.; Chen, P.Y.; Chen, I.L.

doi:10.1016/j.cma.2007.02.004

Cited by 48 publications

(27 citation statements)

References 16 publications

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“…Furthermore, since standard finite elements are used in the VIEM, it is easier and more convenient to handle multiple nonsmooth anisotropic inclusions. Therefore, the formulations developed in this paper in conjunction with other useful methods [18,19] can be used to calculate the dynamic stress intensity factors and other quantities of practical interest in realistic models of materials containing strong heterogeneities.…”

Section: Discussionmentioning

confidence: 99%

SH Wave Scattering Problems for Multiple Orthotropic Elliptical Inclusions

Lee

Han

Ahn

2013

Advances in Mechanical Engineering

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A volume integral equation method (VIEM) is applied for the effective analysis of elastic wave scattering problems in unbounded solids containing general anisotropic inclusions. It should be noted that this numerical method does not require use of Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is necessary for the analysis. This new method can also be applied to general two-dimensional elastodynamic problems involving arbitrary shapes and numbers of anisotropic inclusions. A detailed analysis of SH wave scattering problems is developed for an unbounded isotropic matrix containing multiple orthotropic elliptical inclusions. Numerical results are presented for the displacement fields at the interfaces of the inclusions in a broad frequency range of practical interest. Through the analysis of plane elastodynamic problems in an unbounded isotropic matrix with multiple orthotropic elliptical inclusions, it is established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing general anisotropic inclusions of arbitrary shapes.

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Section: Discussionmentioning

confidence: 99%

SH Wave Scattering Problems for Multiple Orthotropic Elliptical Inclusions

Lee

Han

Ahn

2013

Advances in Mechanical Engineering

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“…Recently, Chen et al [10][11][12][13] developed the null-field integral equation in conjunction with the degenerate kernel to solve many engineering problems. They claimed that their approach is one kind of semianalytical approaches as the error comes from truncating the terms of Fourier series.…”

Section: Introductionmentioning

confidence: 99%

“…If the boundary element method (BEM) is used, Cauchy principal value or finite part concept is required to calculate the singular or hypersingular inteqrals [17]. An idea using the null-field integral formulation but collocating on the real boundary without singularity is proposed by Chen et al [10][11][12][13]. Five advantages, mesh-free generation, well-posed model, free of calculating principal value (the singular or hypersingular integrals are transformed into series summability by introducing degenerate kernels and Fourier series), elimination of boundary-layer effect, and exponential convergence, are obtained.…”

Section: Introductionmentioning

confidence: 99%

Scattering of sound from point sources by multiple circular cylinders using addition theorem and superposition technique

Chen

Lee

Lin

et al. 2011

Numer. Methods Partial Differential Eq.

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In this study, we use the addition theorem and superposition technique to solve the scattering problem with multiple circular cylinders arising from point sound sources. Using the superposition technique, the problem can be decomposed into two individual parts. One is the free-space fundamental solution. The other is a typical boundary value problem (BVP) with specified boundary conditions derived from the addition theorem by translating the fundamental solution. Following the success of null-field boundary integral formulation to solve the typical BVP of the Helmholtz equation with Fourier densities, the second-part solution is easily obtained after collocating the observation point exactly on the real boundary and matching the boundary condition. The total solution is obtained by superimposing the two parts which are the fundamental solution and the semianalytical solution of the Helmholtz problem. An example was demonstrated to validate the present approach. The parameter study of size and spacing between cylinders are addressed. The results are well compared with the available theoretical solutions and experimental data.

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“…The similar technique is used in the case of Neumann's boundary condition. The description of this technique with more details can be found in [36] and in the literature presented here.…”

Section: Waveguides With Non-singular Boundarymentioning

confidence: 99%

“…This admits of applying very effective meshless numerical techniques to solve (3), (4): the MFS, the boundary knot method [35], the boundary integral method [36].…”

Section: Introductionmentioning

confidence: 99%

The Methods of External Excitation for Analysis of Arbitrarily-Shaped Hollow Conducting Waveguides

Reutskiy¹

2008

PIER

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Abstract-A new numerical technique is proposed for analyzing arbitrary shaped hollow waveguides.The method is based on mathematically modelling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. The results of the numerical experiments justifying the method are presented. The method is validated by circular waveguide, rectangular waveguide an equilateral triangular waveguide. We apply the method for multi connected domains and for waveguides with boundary singularities like the Lshaped waveguide. Good agreements between the simulated and the published results have been obtained. The method does not generate spurious eigenfrequencies.

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A semi-analytical approach for radiation and scattering problems with circular boundaries

Cited by 48 publications

References 16 publications

SH Wave Scattering Problems for Multiple Orthotropic Elliptical Inclusions

SH Wave Scattering Problems for Multiple Orthotropic Elliptical Inclusions

Scattering of sound from point sources by multiple circular cylinders using addition theorem and superposition technique

The Methods of External Excitation for Analysis of Arbitrarily-Shaped Hollow Conducting Waveguides

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