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Spectral Analysis Of Elastic Waveguides

Year 2020, Volume: 13 Issue: 1, 43 - 54, 30.06.2020
https://doi.org/10.20854/bujse.738083

Abstract

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.

Elastik Dalga Klavuzlarının Spektral Analizi

Year 2020, Volume: 13 Issue: 1, 43 - 54, 30.06.2020
https://doi.org/10.20854/bujse.738083

Abstract

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

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.
There are 21 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mahir Hasansoy

Publication Date June 30, 2020
Published in Issue Year 2020 Volume: 13 Issue: 1

Cite

APA Hasansoy, M. (2020). Spectral Analysis Of Elastic Waveguides. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 13(1), 43-54. https://doi.org/10.20854/bujse.738083
AMA Hasansoy M. Spectral Analysis Of Elastic Waveguides. BUJSE. June 2020;13(1):43-54. doi:10.20854/bujse.738083
Chicago Hasansoy, Mahir. “Spectral Analysis Of Elastic Waveguides”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 13, no. 1 (June 2020): 43-54. https://doi.org/10.20854/bujse.738083.
EndNote Hasansoy M (June 1, 2020) Spectral Analysis Of Elastic Waveguides. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 13 1 43–54.
IEEE M. Hasansoy, “Spectral Analysis Of Elastic Waveguides”, BUJSE, vol. 13, no. 1, pp. 43–54, 2020, doi: 10.20854/bujse.738083.
ISNAD Hasansoy, Mahir. “Spectral Analysis Of Elastic Waveguides”. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 13/1 (June 2020), 43-54. https://doi.org/10.20854/bujse.738083.
JAMA Hasansoy M. Spectral Analysis Of Elastic Waveguides. BUJSE. 2020;13:43–54.
MLA Hasansoy, Mahir. “Spectral Analysis Of Elastic Waveguides”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 13, no. 1, 2020, pp. 43-54, doi:10.20854/bujse.738083.
Vancouver Hasansoy M. Spectral Analysis Of Elastic Waveguides. BUJSE. 2020;13(1):43-54.