### Abstract

The question concerning the uniqueness of the solution to the problem of the acoustic diffraction by an immersed and isolated thin infinite plate with a finite scatterer is studied. It is shown that, to provide the uniqueness of the solution, the conditions at the scatterer must lead to an energy inequality for a source-free field, which determines the absence of the energy-carrying field components at infinity. A formula that generalizes the Sommerfeld formula is obtained and is used to prove the uniqueness of the solution to the problem of diffraction by a plate immersed in an acoustic medium. For the problem of diffraction of a flexural wave by an irregularity of the plate, the uniqueness theorem is proved only for the case of a fixed or hinged edge. When boundary conditions of a general form are imposed on the scatterer in an isolated plate, the uniqueness of the solution is generally lost, which is also corroborated by an example.

Original language | English |
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Pages (from-to) | 3-9 |

Number of pages | 7 |

Journal | Acoustical Physics |

Volume | 47 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2001 |

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### Scopus subject areas

- Acoustics and Ultrasonics

### Cite this

*Acoustical Physics*,

*47*(1), 3-9. https://doi.org/10.1134/1.1340071

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*Acoustical Physics*, vol. 47, no. 1, pp. 3-9. https://doi.org/10.1134/1.1340071

**On the uniqueness of the problem of acoustic diffraction by an infinite plate with local irregularities.** / Andronov, I. V.; Belinskiǐ, B. P.

Research output

TY - JOUR

T1 - On the uniqueness of the problem of acoustic diffraction by an infinite plate with local irregularities

AU - Andronov, I. V.

AU - Belinskiǐ, B. P.

PY - 2001/1/1

Y1 - 2001/1/1

N2 - The question concerning the uniqueness of the solution to the problem of the acoustic diffraction by an immersed and isolated thin infinite plate with a finite scatterer is studied. It is shown that, to provide the uniqueness of the solution, the conditions at the scatterer must lead to an energy inequality for a source-free field, which determines the absence of the energy-carrying field components at infinity. A formula that generalizes the Sommerfeld formula is obtained and is used to prove the uniqueness of the solution to the problem of diffraction by a plate immersed in an acoustic medium. For the problem of diffraction of a flexural wave by an irregularity of the plate, the uniqueness theorem is proved only for the case of a fixed or hinged edge. When boundary conditions of a general form are imposed on the scatterer in an isolated plate, the uniqueness of the solution is generally lost, which is also corroborated by an example.

AB - The question concerning the uniqueness of the solution to the problem of the acoustic diffraction by an immersed and isolated thin infinite plate with a finite scatterer is studied. It is shown that, to provide the uniqueness of the solution, the conditions at the scatterer must lead to an energy inequality for a source-free field, which determines the absence of the energy-carrying field components at infinity. A formula that generalizes the Sommerfeld formula is obtained and is used to prove the uniqueness of the solution to the problem of diffraction by a plate immersed in an acoustic medium. For the problem of diffraction of a flexural wave by an irregularity of the plate, the uniqueness theorem is proved only for the case of a fixed or hinged edge. When boundary conditions of a general form are imposed on the scatterer in an isolated plate, the uniqueness of the solution is generally lost, which is also corroborated by an example.

UR - http://www.scopus.com/inward/record.url?scp=0035529736&partnerID=8YFLogxK

U2 - 10.1134/1.1340071

DO - 10.1134/1.1340071

M3 - Article

AN - SCOPUS:0035529736

VL - 47

SP - 3

EP - 9

JO - Acoustical Physics

JF - Acoustical Physics

SN - 1063-7710

IS - 1

ER -