### Abstract

Original language | English |
---|---|

Article number | 095202 |

Journal | Journal of Physics A-mathematical and Theoretical |

Volume | 51 |

Issue number | 9 |

Number of pages | 16 |

ISSN | 1751-8113 |

DOIs | |

Publication status | Published - 2018 |

### Keywords

- Flexural waves
- Perturbation techniques
- Scattering
- Short-range potentials

### Cite this

*Journal of Physics A-mathematical and Theoretical*,

*51*(9), [095202]. https://doi.org/10.1088/1751-8121/aaa810

}

*Journal of Physics A-mathematical and Theoretical*, vol. 51, no. 9, 095202. https://doi.org/10.1088/1751-8121/aaa810

**Scattering of flexural waves in Euler-Bernoulli beams by short-range potentials : Paper.** / Christiansen, Peter Leth; Iermakova, Sofia V.; Gaididei, Yuri B.; Sørensen, Mads Peter.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Scattering of flexural waves in Euler-Bernoulli beams by short-range potentials

T2 - Paper

AU - Christiansen, Peter Leth

AU - Iermakova, Sofia V.

AU - Gaididei, Yuri B.

AU - Sørensen, Mads Peter

PY - 2018

Y1 - 2018

N2 - Time-harmonic flexural waves on a beam and on two elastically coupled beams with short-range localized imperfections in the mass distribution and in the position dependant coupling are considered. Thus scattering of an incident wave solution to the Euler-Bernoulli equation by a Dirac delta function and its derivative up to order three is studied, and the possible physical interpretations are outlined. Reflected, transmitted and evanescent waves exist, and their scattering data are determined. For δ(x) and δ'(x), the scattering problem is solved by standard integration. For δ"(x) and δ"'(x), the standard integration procedure does not work and solutions are obtained by regularization. In the latter case the scatterer is in general nontransparent and only partially penetrable at discrete resonances. The first few of these as well as their scattering data are determined numerically.

AB - Time-harmonic flexural waves on a beam and on two elastically coupled beams with short-range localized imperfections in the mass distribution and in the position dependant coupling are considered. Thus scattering of an incident wave solution to the Euler-Bernoulli equation by a Dirac delta function and its derivative up to order three is studied, and the possible physical interpretations are outlined. Reflected, transmitted and evanescent waves exist, and their scattering data are determined. For δ(x) and δ'(x), the scattering problem is solved by standard integration. For δ"(x) and δ"'(x), the standard integration procedure does not work and solutions are obtained by regularization. In the latter case the scatterer is in general nontransparent and only partially penetrable at discrete resonances. The first few of these as well as their scattering data are determined numerically.

KW - Flexural waves

KW - Perturbation techniques

KW - Scattering

KW - Short-range potentials

U2 - 10.1088/1751-8121/aaa810

DO - 10.1088/1751-8121/aaa810

M3 - Journal article

VL - 51

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 9

M1 - 095202

ER -