Spectral Analysis Of Elastic Waveguides

Year 2020, Volume: 13 Issue: 1, 43 - 54, 30.06.2020

Mahir Hasansoy

https://doi.org/10.20854/bujse.738083

https://izlik.org/JA92EY29XN

Abstract

Elastik Dalga Klavuzlarının Spektral Analizi

https://izlik.org/JA92EY29XN

Abstract

Elastik Dalga klavuzlarının operatör modelleri oluşturulmuş ve spektral yapısı araştırmıştır.
Dalga klavuzlarının kesitlerinin sonlu ve sonsuz olduğu durumlar ele alınmıştır

Keywords

Özdeğer , Spektrum , DaLga Klavuzu

References

• 1. R. A. Adams, J. J. F. Fournier, Sobolev spaces, Academic Press, 2002.
• 2. V. M. Babich, On a class of topographic waveguides, Algebra i Analiz , 22, (2010), no. 1, 98-107.
• 3. M. S. Birman, M. Z. Solomyak, Spectral theory of self-adjoint operators in Hilbert space, D.Reidel Publishing Company, 1997.
• 4. M. S. Birman, M. Z. Solomyak, Quantitive analysis in Sobolev imbedding theorems and applications to spectral theory, Translations of Mathematical Monographs, series 2, vol.114, American Mathematical Society, Providence, RI, 1980.
• 5. J. Bognar Indefinite inner product spaces, Springer-Verlag, New York, 1974.
• 6. A. S. Bonnet-Ben Dhia, J. Duterte, P. Joly,Mathematical Analysis of elastic surface waves in topographic waveguides, Mathematical Models and Methods in Applied Sciences, 9, No. 5 (1999) 755-798.
• 7. N. Colakoglu, M. Hasanov, B. U. Uzun, Eigenvalues of two parameter Polynomial operator pencils of waveguide type, Integral Equations Operator Theory, 56 (2006) 381-400..
• 8. J. Duterte, P. Joly, A numerical method for surface waves in a cylindrically perturbed elastic half-space. Part 1: Construction and analysis, SIAM J. Appl. Math. 59, No. 5, (1999) pp. 1599-1635.
• 9. I.~Gohberg, M.~Krein, Introduction to the theory of linear nonselfadjoint operators in Hilbert space, American Mathematical Society, Providence, R.I., 1969.
• 10. M.~Hasanov, On the spectrum of a weak classof operator pencils of waveguide type, Mathematische Nachrichten , 279 (2006) 843-853.
• 11. M.~Hasanov, The spectra of two-parameter quadratic operator pencils, Mathematical and Computer Modelling { 54}, (2011) 742-755.
• 12. C. O. Horgan, Korn's inequalities and their applications in continuum mechanics, SIAM Review, 37, No. 4 (1995) 491-511.
• 13. D. Jakobson, M. Levitin, N. Nadirashvili, I. Polterovich, Spectral problems with mixed Dirichlet-Neumann boundary conditions: Isospectrality and beyond, \emph{Journal of Computational and Applied Mathematics, Volume {194}, Issue 1, (2006), 141-155.
• 14. I. V. Kamotskii, A. P. Kiselev, An energy approach to the proof of the existence of Rayleigh waves in an anisotropic elastic half-space, J. Appl. Math. Mech. {73} (2009), no. 4, 464-470.
• 15. I. V. Kamotskii, On a surface wave traveling along the edge of an elastic wedge, St. Petersburg Math. J.{20} (2009), no. 1, 59-63.
• 16. T.~Kato, Perturbation theory for linear operators, \emph{Springer- Verlag, Berlin, 1995.
• 17. A.~G.~Kostyuchenko, M.~B.~Orazov, The problem of oscillations of an elastic half cylinder and related selfadjoint quadratic pencils, Journal of Soviet Mathematics,, 33, (1986) 1025--1065.}
• 18. M.~G.~Krein, H.~Langer, On some mathematical principles in the linear theory of damped oscillations of continua. I, II, Integral Equations Operator Theory {1} (1978), no. 3, 364--399, no. 4, 539--566.
• 19. A.~S.~Markus, Introduction to the spectral theory of polynomial operator pencils, Translations of Mathematical Monographs, vol.71, American Mathematical Society, Providence, RI, 1988.
• 20. J. Miklowitz, , The theory of elastic waves and waveguides, North-Holland, 1978.
• 21. A.~Zilbergleit, Y.~Kopilevich, Spectral theory of guided waves, \emph{Institute of Physics Publishing, Bristol,, 1996.