Modelling and analysis of the dynamic behavior of inhomogeneous continuum containing a circular inclusion

Hei, Baoping; Yang, Zeng-Quan; Sun, Baitao; Yao, Wang

doi:10.1016/j.apm.2015.03.015

Cited by 31 publications

(8 citation statements)

References 24 publications

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“…Subsequently, Liu et al [3] studied SH-waves' scattering and dynamic stress concentration by interface cylindrical elastic inclusion. Recently, Hei [4] modelled and analyzed the dynamic behavior of an inhomogeneous continuum containing a circular inclusion, while Mcarthur et al [5] discussed a circular inclusion with circumferentially inhomogeneous imperfect interface in harmonic materials. Further, Jiang [6] studied a shallow circular inclusion's dynamic response under incident SH-waves in a radially inhomogeneous half-space and analyzed it applying complex function theory and the multipolar coordinate system.…”

Section: Introductionmentioning

confidence: 99%

Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion

2019

Advances in Mathematical Physics

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This paper focuses on analyzing SH-wave scattering around a circular nanoinclusion using the complex variable function method. The surface elasticity theory is employed in the analysis to account for the interface effect at the nanoscale. Considering the interface effect, the boundary condition is given, and the infinite algebraic equations are established to solve the unknown coefficients of the scattered and refracted wave solutions. The analytic solutions of the stress field are obtained by using the orthogonality of trigonometric function. Finally, the dynamic stress concentration factor and the radial stress of a circular nanoinclusion are analyzed with some numerical results. The numerical results show that the interface effect weakens the dynamic stress concentration but enhances the radial stress around the nanoinclusion; further, we prove that the analytic solutions are correct.

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Section: Introductionmentioning

confidence: 99%

Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion

2019

Advances in Mathematical Physics

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“…Lee and Amornwongpaibun 18 employed the wave function expansion method in the elliptical coordinates and elliptical cosine half‐range expansion method to offer an analytical solution to the problem of the scattering around the semi‐elliptical hill on half‐space and found that the existence of an elliptical hill causes complicated effects on ground motion. Hei et al 19 presented a universal approach of solving the dynamic stress concentration around a circular inclusion in two‐dimensional inhomogeneous medium based on the complex function theory. The inhomogeneity of medium is considered in the calculation process, which expands the research of complex medium.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of the different types of elliptic cylindrical inclusions subjected to plane SH‐wave scattering

Tao

Luo

et al. 2022

Math Methods in App Sciences

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The complex boundary of the elliptical inclusion rendered it difficult to solve the problem of wave scattering. In this study, the steady‐state response was analyzed using the wave function expansion method. Subsequently, the Ricker wavelet was employed as the transient disturbance, and Fourier transform was used to determine the distribution of transient dynamic stress concentration around the elliptical inclusion. The effects of wave number, elliptical axial ratio, and difference in material properties on the distribution of the dynamic stress concentration around the elliptical inclusion were evaluated. The numerical results revealed that the dynamic stress concentration always appeared at both ends of the major axis and minor axis of the elliptical inclusion, and the difference in material properties between the inclusion and medium influenced the variations in the dynamic stress concentration factor with the wave number and elliptical axial ratio.

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“…Lee and Amornwongpaibun 18 employed the wave function expansion method in the elliptical coordinates and elliptical cosine half-range expansion method to offer an analytical solution to the problem of the scattering around the semi-elliptical hill on half-space, and found that the existence of an elliptical hill causes complicated effects on ground motion. Hei et al 19 presented a universal approach of solving the dynamic stress concentration around a circular inclusion in two-dimensional inhomogeneous medium based on the complex function theory. The inhomogeneity of medium is considered in the calculation process, which expands the research of complex medium.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of the different-types elliptic cylindrical inclusions subjected to plane SH-wave scattering

Tao

Luo

et al. 2022

Preprint

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The complex boundary of the elliptical inclusion rendered it difficult to solve the problem of wave scattering. In this study, the steady-state response was analyzed using the wave function expansion method. Subsequently, the Ricker wavelet was employed as the transient disturbance and Fourier transform was used to determine the distribution of transient dynamic stress concentration around the elliptical inclusion. The effects of wave number, elliptical axial ratio and difference in material properties on the distribution of the dynamic stress concentration around the elliptical inclusion were evaluated. The numerical results revealed that the dynamic stress concentration always appeared at both ends of the major axis and minor axis of the elliptical inclusion, and the difference in material properties between the inclusion and medium influenced the variations in the dynamic stress concentration factor with the wave number and elliptical axial ratio.

show abstract

Modelling and analysis of the dynamic behavior of inhomogeneous continuum containing a circular inclusion

Cited by 31 publications

References 24 publications

Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion

Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion

Dynamic analysis of the different types of elliptic cylindrical inclusions subjected to plane SH‐wave scattering

Dynamic analysis of the different-types elliptic cylindrical inclusions subjected to plane SH-wave scattering

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