### Abstract

The scattering of arbitrary elastic waves by a circular crack in a tranversely isotropic solid is investigated. The symmetry axis of the solid and the normal to the crack are parallel. The problem is first divided into a symmetric and an antisymmetric part with respect to the plane of the crack. A Fourier-Hankel representation for the scattered field is then assumed and some manipulations using the conditions in the plane of the crack lead to an integral equation for the normal crack opening displacement for the symmetric part and two coupled integral equations for the tangential components of the crack opening displacement for the antisymmetric part. The crack opening displacements are expanded in series of Legendre functions which fulfil the correct edge conditions and the integral equations are projected on the same set of Legendre functions. The far field is calculated with the stationary phase method. Numerical results are given for crack opening displacements for incident quasi P and SV plane waves and compared with corresponding results for an isotropic solid.

Original language | English (US) |
---|---|

Pages (from-to) | 285-300 |

Number of pages | 16 |

Journal | Wave Motion |

Volume | 15 |

Issue number | 3 |

DOIs | |

State | Published - 1992 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics

### Cite this

*Wave Motion*,

*15*(3), 285-300. https://doi.org/10.1016/0165-2125(92)90012-Q

**Elastic wave scattering by a circular crack in a transversely isotropic solid.** / Kundu, Tribikram; Boström, A.

Research output: Contribution to journal › Article

*Wave Motion*, vol. 15, no. 3, pp. 285-300. https://doi.org/10.1016/0165-2125(92)90012-Q

}

TY - JOUR

T1 - Elastic wave scattering by a circular crack in a transversely isotropic solid

AU - Kundu, Tribikram

AU - Boström, A.

PY - 1992

Y1 - 1992

N2 - The scattering of arbitrary elastic waves by a circular crack in a tranversely isotropic solid is investigated. The symmetry axis of the solid and the normal to the crack are parallel. The problem is first divided into a symmetric and an antisymmetric part with respect to the plane of the crack. A Fourier-Hankel representation for the scattered field is then assumed and some manipulations using the conditions in the plane of the crack lead to an integral equation for the normal crack opening displacement for the symmetric part and two coupled integral equations for the tangential components of the crack opening displacement for the antisymmetric part. The crack opening displacements are expanded in series of Legendre functions which fulfil the correct edge conditions and the integral equations are projected on the same set of Legendre functions. The far field is calculated with the stationary phase method. Numerical results are given for crack opening displacements for incident quasi P and SV plane waves and compared with corresponding results for an isotropic solid.

AB - The scattering of arbitrary elastic waves by a circular crack in a tranversely isotropic solid is investigated. The symmetry axis of the solid and the normal to the crack are parallel. The problem is first divided into a symmetric and an antisymmetric part with respect to the plane of the crack. A Fourier-Hankel representation for the scattered field is then assumed and some manipulations using the conditions in the plane of the crack lead to an integral equation for the normal crack opening displacement for the symmetric part and two coupled integral equations for the tangential components of the crack opening displacement for the antisymmetric part. The crack opening displacements are expanded in series of Legendre functions which fulfil the correct edge conditions and the integral equations are projected on the same set of Legendre functions. The far field is calculated with the stationary phase method. Numerical results are given for crack opening displacements for incident quasi P and SV plane waves and compared with corresponding results for an isotropic solid.

UR - http://www.scopus.com/inward/record.url?scp=38249014715&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249014715&partnerID=8YFLogxK

U2 - 10.1016/0165-2125(92)90012-Q

DO - 10.1016/0165-2125(92)90012-Q

M3 - Article

AN - SCOPUS:38249014715

VL - 15

SP - 285

EP - 300

JO - Wave Motion

JF - Wave Motion

SN - 0165-2125

IS - 3

ER -