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

Paper

Peter Leth Christiansen, Sofia V. Iermakova, Yuri B. Gaididei, Mads Peter Sørensen*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

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.
Original languageEnglish
Article number095202
JournalJournal of Physics A-mathematical and Theoretical
Volume51
Issue number9
Number of pages16
ISSN1751-8113
DOIs
Publication statusPublished - 2018

Keywords

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

Cite this

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title = "Scattering of flexural waves in Euler-Bernoulli beams by short-range potentials: Paper",
abstract = "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.",
keywords = "Flexural waves, Perturbation techniques, Scattering, Short-range potentials",
author = "Christiansen, {Peter Leth} and Iermakova, {Sofia V.} and Gaididei, {Yuri B.} and S{\o}rensen, {Mads Peter}",
year = "2018",
doi = "10.1088/1751-8121/aaa810",
language = "English",
volume = "51",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing",
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}

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.

In: Journal of Physics A-mathematical and Theoretical, Vol. 51, No. 9, 095202, 2018.

Research output: Contribution to journalJournal articleResearchpeer-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

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