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S.A. Nazarov, "Asymptotics of the Frequencies of Elastic Waves Trapped by a Small Crack in a Cylindrical Waveguide," Mech. Solids. 45 (6), 856-864 (2010)
Year 2010 Volume 45 Number 6 Pages 856-864
DOI 10.3103/S0025654410060099
Title Asymptotics of the Frequencies of Elastic Waves Trapped by a Small Crack in a Cylindrical Waveguide
Author(s) S.A. Nazarov (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr-t 61, V.O., St.&nsbp;Petersburg, 199178 Russia, srgnazarov@yahoo.co.uk)
Abstract An asymptotics of frequencies of waves trapped in a space waveguide with a partially clamped lateral surface and a crack of a small diameter O(h) is obtained. The corresponding eigenvalue is located at a distance O(h6) from the first threshold of the continuous spectrum.
Keywords elastic waveguide, crack, trapped wave, eigenvalue asymptotics
References
1.  V. V. Novozhilov, "On the Foundations of a Theory of Equilibrium Cracks in Elastic Solids," Prikl. Mat. Mekh. 33 (5), 797-812 (1969) [J. Appl. Math. Mech. (Engl. Transl.) 33 (5), 777-790 (1969)].
2.  V. V. Novozhilov and L. I. Slepyan, "Some Problems and Achievements in Fracture Mechanics," Vestinik AN SSSR, No. 9, 96-111 (1987).
3.  N. F. Morozov and V. V. Novozhilov, "Some Problems of Structural Fracture Mechanics," Fiz.-Khim. Mekh. Mat. 24 (1), 21-26 (1988) [Mater. Sci. (Engl. Transl.) 24 (1), 18-22 (1988)].
4.  S. A. Nazarov, Asymptotic Theory of Thin Plates and Rods. Vol. 1: Dimension Reduction and Integral Estimates (Nauchnaya Kniga, Novosibirsk, 2001) [in Russian].
5.  V. A. Kondrat'ev and O. A. Oleinik, "Boundary-Value Problems for the System of Elasticity Theory in Unbounded Domains. Korn's Inequalities," Uspekhi Mat. Nauk 43 (5), 55-98 (1988) [Russ. Math. Surv. (Engl. transl.) 43 (5), 65-119 (1988)].
6.  A.-S. Bonnet-Bendhia and F. Starling, "Guided Waves by Electromagnetic Gratings and Non-Uniqueness Examples for the Diffraction Problem," Math. Models Mech. Appl. Sci. 17 (5), 305-338 (1994).
7.  A.-S. Bonnet-Bendhia, J. Duterte, and P. Joly, "Mathematical Analysis of Elastic Surface Waves in Topographic Waveguides," Math. Models Mech. Appl. Sci. 9 (5), 755-798 (1999).
8.  C. M. Linton and P. McIver, "Embedded Trapped Modes in Water Waves and Acoustics," Wave Motion 45 (1), 16-29 (2007).
9.  S. A. Nazarov, "Properties of Spectra of Boundary Value Problems in Cylindrical and Quasicylindrical Domain," in Sobolev Spaces in Mathematics II. International Mathematical Series. Vol. 9: Applications in Analysis and Partial Differential Equations. Ed. by V. Maz'ya (Springer, New York, 2008), pp. 261-309.
10.  M. S. Birman and M. Z. Solomjak, Spectral Theory of Self-Adjoint Operators in Hilbert Space (Izd-vo LGU, Leningrad, 1980; Reidel, Dortrecht, 1987).
11.  V. A. Kondratiev, "Boundary-Value Problems for Elliptic Equations in Domains with Conical or Angular Points," Trudy Moskov. Mat. Obshch. 16, 219-292 (1967) [Trans. Moscow Math. Soc. (Engl. Transl.) 16, 227-313 (1967)].
12.  M. S. Agranovich and M. I. Vishik, "Elliptic Problems with a Parameter and Parabolic Problems of General Type," Uspekhi Mat. Nauk 19 (3), 53-161 (1964) [Russ. Math. Surv. (Engl. transl.) 19 (3), 53-157 (1964)].
13.  S. A. Nazarov, "Variational and Asymptotic Methods for Finding Eigenvalues below the Continuous Spectrum Threshold," Sibirsk. Mat. Zh. 51 (5), 1086-1101 (2010) [Siberian Math. J. (Engl. Transl.) 51 (5), 866-878 (2010)].
14.  S. A. Nazarov and B. A. Plamenevsky, Elliptic Problems in Domains with Piecewise Smooth Boundaries (Nauka, Moscow, 1991; Walter de Gruyter, Berlin, New York, 1994).
15.  I. S. Zorin, A. B. Movchan, and S. A. Nazarov, "Use of the Elastic Polarisation Tensor in Problems of Crack Mechanics," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 6, 128-134 (1988) [Mech. Solids (Engl. Transl.) 23 (6), 120-126 (1988)].
16.  S. A. Nazarov, "Damage Tensor and Measures. I. Asymptotic Analysis of Anisotropic Media with Defects," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 113-124 (2000) [Mech. Solids (Engl. Transl.) 35 (3), 96-105 (2000)].
17.  V. G. Maz'ya and B. A. Plamenevsky, "On Coefficients in Asymptotics of Solutions of Elliptic Boundary-Value Problems in a Domain with Conic Points," Math. Nachr. 76, 29-60 (1977).
18.  W. G. Mazja, S. A. Nasarow, and B. A. Plamenewski, Asymptotische Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten, Vol. 1 (Akademie Verlag, Berlin, 1991).
19.  S. A. Nazarov, "On the 3D Formulation for the Novozhilov Criterion for Quasi-Static Fracture," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 118-127 (2006) [Mech. Solids (Engl. Transl.) 41 (2), 93-100 (2006)].
20.  M. Bach, S. A. Nazarov, and W. L. Wendland, "Stable Propagation on a Model Crack in an Isotropic Elastic Space. Comparison of the Irwin and the Griffith Approaches," in Problemi Attuali dell'Analisi e della Fisica Matematica (Aracne, Rome, 2000), pp. 167-189.
Received 12 August 2010
Link to Fulltext http://www.springerlink.com/content/2378415677x18207/
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