### Abstract

The scattering of waves by an infinite elastic plate, which covers an acoustic half-space and is weakened by a crack in the form of an infinitely long cut of finite width with parallel edges is considered. The scattered field is expressed in terms of the solution of an integro-algebraic system of equations on the crack. The logarithmic characteristic of the kernel enables Bubnov's method with a basis containing Chebvshev polynomials of the first kind to be used for the numerical analysis. Particular attention is given to the asymptotic investigation of the scattering diagram and the amplitudes of the surface waves for a narrow crack and a thin plate. A comparison with the well-known model of a point crack enables the range of parameters of the problem where the point model is applicable to be indicated.

Original language | English |
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Pages (from-to) | 195-202 |

Number of pages | 8 |

Journal | Journal of Applied Mathematics and Mechanics |

Volume | 61 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jan 1997 |

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### Scopus subject areas

- Modelling and Simulation
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics

### Cite this

*Journal of Applied Mathematics and Mechanics*,

*61*(2), 195-202. https://doi.org/10.1016/S0021-8928(97)00026-9

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*Journal of Applied Mathematics and Mechanics*, vol. 61, no. 2, pp. 195-202. https://doi.org/10.1016/S0021-8928(97)00026-9

**Scattering of hydoacoustic waves by a narrow crack in an elastic plate.** / Andronov, I. V.; Belinskii, B. P.

Research output

TY - JOUR

T1 - Scattering of hydoacoustic waves by a narrow crack in an elastic plate

AU - Andronov, I. V.

AU - Belinskii, B. P.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - The scattering of waves by an infinite elastic plate, which covers an acoustic half-space and is weakened by a crack in the form of an infinitely long cut of finite width with parallel edges is considered. The scattered field is expressed in terms of the solution of an integro-algebraic system of equations on the crack. The logarithmic characteristic of the kernel enables Bubnov's method with a basis containing Chebvshev polynomials of the first kind to be used for the numerical analysis. Particular attention is given to the asymptotic investigation of the scattering diagram and the amplitudes of the surface waves for a narrow crack and a thin plate. A comparison with the well-known model of a point crack enables the range of parameters of the problem where the point model is applicable to be indicated.

AB - The scattering of waves by an infinite elastic plate, which covers an acoustic half-space and is weakened by a crack in the form of an infinitely long cut of finite width with parallel edges is considered. The scattered field is expressed in terms of the solution of an integro-algebraic system of equations on the crack. The logarithmic characteristic of the kernel enables Bubnov's method with a basis containing Chebvshev polynomials of the first kind to be used for the numerical analysis. Particular attention is given to the asymptotic investigation of the scattering diagram and the amplitudes of the surface waves for a narrow crack and a thin plate. A comparison with the well-known model of a point crack enables the range of parameters of the problem where the point model is applicable to be indicated.

UR - http://www.scopus.com/inward/record.url?scp=0031284118&partnerID=8YFLogxK

U2 - 10.1016/S0021-8928(97)00026-9

DO - 10.1016/S0021-8928(97)00026-9

M3 - Article

AN - SCOPUS:0031284118

VL - 61

SP - 195

EP - 202

JO - Journal of Applied Mathematics and Mechanics

JF - Journal of Applied Mathematics and Mechanics

SN - 0021-8928

IS - 2

ER -