Almost Complete Transmission of Low Frequency Waves in a Locally Damaged Elastic Waveguide

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Almost Complete Transmission of Low Frequency Waves in a Locally Damaged Elastic Waveguide. / Nazarov, S. A.

In: Journal of Mathematical Sciences (United States), Vol. 244, No. 3, 01.01.2020, p. 451-496.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{3f2ff36bf6004a56bc26302cd3a07911,

title = "Almost Complete Transmission of Low Frequency Waves in a Locally Damaged Elastic Waveguide",

abstract = "It is established that low frequency waves in a symmetric orthotropic elastic waveguide pass almost without distortion through a local perturbation of the straight cylinder, i.e., the reflection coefficient is small and the transmission coefficient slightly differs from 1. The results are obtained by the asymptotic analysis of low frequency waves and the corresponding scattering matrix. The formal asymptotic analysis is also performed for an anisotropic elastic waveguide with asymmetric cross-section, but since the canonical system of Jordan chains for the corresponding operator pencil is too complicated, the known results of the theory of perturbations of nonselfadjoint operators provide asymptotic formulas only under additional elastic and geometric symmetry conditions. We define the polarization matrix and prove its main properties.",

author = "Nazarov, {S. A.}",

year = "2020",

month = jan,

day = "1",

doi = "10.1007/s10958-019-04629-8",

language = "English",

volume = "244",

pages = "451--496",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - Almost Complete Transmission of Low Frequency Waves in a Locally Damaged Elastic Waveguide

AU - Nazarov, S. A.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - It is established that low frequency waves in a symmetric orthotropic elastic waveguide pass almost without distortion through a local perturbation of the straight cylinder, i.e., the reflection coefficient is small and the transmission coefficient slightly differs from 1. The results are obtained by the asymptotic analysis of low frequency waves and the corresponding scattering matrix. The formal asymptotic analysis is also performed for an anisotropic elastic waveguide with asymmetric cross-section, but since the canonical system of Jordan chains for the corresponding operator pencil is too complicated, the known results of the theory of perturbations of nonselfadjoint operators provide asymptotic formulas only under additional elastic and geometric symmetry conditions. We define the polarization matrix and prove its main properties.

AB - It is established that low frequency waves in a symmetric orthotropic elastic waveguide pass almost without distortion through a local perturbation of the straight cylinder, i.e., the reflection coefficient is small and the transmission coefficient slightly differs from 1. The results are obtained by the asymptotic analysis of low frequency waves and the corresponding scattering matrix. The formal asymptotic analysis is also performed for an anisotropic elastic waveguide with asymmetric cross-section, but since the canonical system of Jordan chains for the corresponding operator pencil is too complicated, the known results of the theory of perturbations of nonselfadjoint operators provide asymptotic formulas only under additional elastic and geometric symmetry conditions. We define the polarization matrix and prove its main properties.

UR - http://www.scopus.com/inward/record.url?scp=85076921849&partnerID=8YFLogxK

U2 - 10.1007/s10958-019-04629-8

DO - 10.1007/s10958-019-04629-8

M3 - Article

AN - SCOPUS:85076921849

VL - 244

SP - 451

EP - 496

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -

ID: 60873596