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On symmetric wedge mode of an elastic solid

Part of: Waves Equations of mathematical physics and other areas of application Elastic materials

Published online by Cambridge University Press:  11 January 2021

ALEXANDER NAZAROV Open the ORCID record for ALEXANDER NAZAROV [Opens in a new window] ,
SERGEY NAZAROV  and
GERMAN ZAVOROKHIN
ALEXANDER NAZAROV
Affiliation:
Department of Mathematics and Mechanics, St.Petersburg State University, Universitetskii Prospect, 28, 198504, St.Petersburg, Russia, emails: al.il.nazarov@gmail.com; srgnazarov@yahoo.co.uk St.Petersburg Department of the Steklov Mathematical Institute, Fontanka, 27, 191023, St.Petersburg, Russia, email: zavorokhin@pdmi.ras.ru
SERGEY NAZAROV
Affiliation:
Department of Mathematics and Mechanics, St.Petersburg State University, Universitetskii Prospect, 28, 198504, St.Petersburg, Russia, emails: al.il.nazarov@gmail.com; srgnazarov@yahoo.co.uk Institute for Problems in Mechanical Engineering of RAS, Bol’shoy Prospekt V.O., 61, St. Petersburg, 199178, Russia
GERMAN ZAVOROKHIN
Affiliation:
St.Petersburg Department of the Steklov Mathematical Institute, Fontanka, 27, 191023, St.Petersburg, Russia, email: zavorokhin@pdmi.ras.ru
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Abstract

The existence of a symmetric mode in an elastic solid wedge for all admissible values of the Poisson ratio and arbitrary interior angles close to π has been proven.

Keywords

Wedge wavesguided acoustic waveslocalised solutionsdiscrete spectrum

MSC classification

Primary: 35Q74: PDEs in connection with mechanics of deformable solids
Secondary: 74B05: Classical linear elasticity 74J99: None of the above, but in this section
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 2 , April 2022 , pp. 201 - 223
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

Dedicated to Professor V.M. Babich on the occasion of his 90th anniversary, with admiration

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