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

Результат исследований: Научные публикации в периодических изданияхстатья

1 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)451-496
Число страниц46
ЖурналJournal of Mathematical Sciences (United States)
Том244
Номер выпуска3
DOI
СостояниеОпубликовано - 1 янв 2020

Предметные области Scopus

  • Теория вероятности и статистика
  • Математика (все)
  • Прикладная математика

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