Enviar artigo por via de e-mail Elastic Waves Trapped by Semi-Infinite Strip with Clamped Lateral Sides and a Curved or Broken End
- Autores: Nazarov S.1
-
Afiliações:
- Institute for Problems in Mechanical Engineering RAS
- Edição: Volume 87, Nº 2 (2023)
- Páginas: 265-279
- Seção: Articles
- URL: https://journals.rcsi.science/0032-8235/article/view/138857
- DOI: https://doi.org/10.31857/S0032823523020108
- EDN: https://elibrary.ru/TZWXRA
- ID: 138857
Citar
Acesso aberto
Acesso está concedido
Somente assinantes
Resumo
We show several geometric conditions of trapping elastic waves by homogeneous isotropic strip with one or two fixed lateral sides and arbitrarily curved end. Shapes of the resonator are found that support any given in advance number of linearly independent trapped modes.
Sobre autores
S. Nazarov
Institute for Problems in Mechanical Engineering RAS
Autor responsável pela correspondência
Email: srgnazarov@yahoo.co.uk
Russia, Saint-Petersburg
Bibliografia
- Nazarov S.A. Two-dimensional asymptotic models of thin cylindruical elastic gaskets// Diff. Eqns., 2022, vol. 58, no. 12, pp. 1651–1667.
- Ladyzhenskaya O.A. The boundary value problems of mathematical physics // Appl. Math. Sci., 1985, vol. 49.
- Fichera G. Existence Theorems in the Theory of Elasticity. Handbuch der Physic. Berlin: Springer, 1972.
- Birman M.Sh., Solomyak M.Z. Spectral Theory of Selfadjoint Operators in Hilbert Space Dordrecht: Reidel, 1987.
- Kamotskii I.V., Nazarov S.A. On eigenfunctions localized in a neighborhood of the lateral surface of a thin domain // J. Math. Sci., 2000, vol. 101, no. 2, pp. 2941–2974.
- Kondrat’ev V.A. Boundary problems for elliptic equations in domains with conical or angular points // Trans. Moscow Math. Soc., 1967, vol. 16, pp. 227–313.
- Nazarov S.A., Plamenevsky B.A. Elliptic Problems in Domains with Piecewise Smooth Boundaries. Berlin; N.Y.: Walter de Gruyter, 1994.
- Nazarov S.A. The polynomial property of self-adjoint elliptic boundary-value problems and the algebraic description of their attributes // Russ. Math. Surv., 1999, vol. 54, no. 5, pp. 947–1014.
- Kamotskii I.V., Nazarov S.A. Exponentially decreasing solutions of the problem of diffraction by a rigid periodic boundary // Math. Notes, 2003, vol. 73, no. 1–2, pp. 129–131.
- Nazarov S.A. Variational and asymptotic methods for finding eigenvalues below the continuous spectrum threshold // Sib. Math. J., 2010, vol. 51, no. 5, pp. 866–878.
- Molchanov S., Vainberg B. Scattering solutions in networks of thin fibers: small diameter asymptotics // Comm. Math. Phys., 2007, vol. 273, no. 2, pp. 533–559.
- Grieser D. Spectra of graph neighborhoods and scattering // Proc. London Math. Soc., 2008, vol. 97, no. 3, pp. 718–752.
- Nazarov S.A. Threshold resonances and virtual levels in the spectrum of cylindrical and periodic waveguides // Math. Izv., 2020, vol. 84, no. 6, pp. 1105–1180.
- Maz’ya V., Nazarov S., Plamenevskij B. Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. Vol. 1 & 2. Basel: Birkhäuser Verlag, 2000.
- Nazarov S.A. Asymptotic Theory of Thin Plates and Rods. Dimension Reduction and Integral Bounds. Novosibirsk: Nauch. Kniga, 2002. (in Russian)
- Nazarov S.A. Elastic waves trapped by a homogeneous anisotropic semicylinder // Sb. Math., 2013, vol. 204, no. 11, pp. 1639–1670.
- Nazarov S.A. The localization for eigenfunctions of the Dirichlet problem in thin polyhedra near the vertices // Sib. Math. J., 2013, vol. 54, no. 3, pp. 517–532.
- Babich V.M., Buldyrev V.S. Asymptotic Methods in Short-wavelength Diffraction Theory. Alpha Science Int., 2009.
- Mikhlin S.G. Variational Methods in Mathematical Physics.N.Y.: Pergamon, 1964.
- Campbell A., Nazarov S.A., Sweers G.H. Spectra of two-dimensional models for thin plates with sharp edges // SIAM J. Math. Anal., 2010, vol. 42, no. 6, pp. 3020–3044.
Arquivos suplementares
