The semi-opened elastic waveguide structure formed by a layer which is rigidly fixed on the one hand and is linked to a half-space on another hand is considered. The characteristic equation for the waveguide modes of such structure is constructed. Solutions of the characteristic equation are investigated. Existence conditions of the waveguide modes for concrete elastic media are obtained. Graphics of dependences of wave numbers on frequency are provided.
собственные колебания, метод переопределенной граничной задачи, eigen oscillations, over-determined boundary value problem method
1. B.E. Pobedrya, Mehanika kompozicionnyh materialov. Izd-vo Mosk. un-ta, Moskva, 1984. 336 s.
2. R. Kristensen, Vvedenie v mehaniku kompozitov. Mir, Moskva, 1982. 334 s.
3. N.A. Alfutov, P.A. Zinov'ev, B.G. Popov, Raschet mnogosloynyh plastin i obolochek iz kompozicionnyh materialov. Mashinostroenie, Moskva, 1984. 446 s.
4. V.V. Vasil'ev, Mehanika konstrukciy iz kompozicionnyh materialov. Mashinostroenie, Moskva, 1988. 272 s.
5. V.I. Korolev, Sloistye anizotropnye plastinki i obolochki iz armirovannyh plastmass. Mashinostroenie, Moskva, 1965. 272 s.
6. I.E. Pleschinskaya, N.B. Pleschinskiy, Vestnik Kazan. tehnol. un-ta, №11, 147-153 (2010).
7. I.E. Pleschinskaya, N.B. Pleschinskiy, D.N. Tumakov, Vestnik Kazan. tehnol. un-ta, №18, 111-115 (2011).
8. V.L. Kipot', D.N. Tumakov, Georesursy, 1, 33-35 (2009).
9. V.L. Kipot', D.N. Tumakov, E.V. Eronina, Georesursy, 6, 2-6 (2011).
10. G.I. Petrashen', Osnovy matematicheskoy teorii rasprostraneniya uprugih voln. Voprosy dinamicheskoy teorii rasprostraneniya seysmicheskih voln. Vyp. XVIII. Nauka, Leningrad, 1978. 248 s.
11. N.S. Bahvalov, G.P. Panasenko, Osrednenie processov v periodicheskih sredah. Matematicheskie zadachi mehaniki kompozicionnyh materialov. Nauka, Moskva, 1984. 352 s.
12. I.E. Pleschinskaya, N.B. Pleschinskiy, Uchenye zapiski Kazan. gos. un-ta, 147, 3, 4-32 (2005).
13. D.N. Tumakov, Sobstvennye kolebaniya dvuh sopryazhennyh polos. Preprint PMF-06-04. Kazansk. matem. ob-vo, Kazan', 2006.26 s.
14. D.N. Tumakov, Raspredelenie energii v ploskom uprugom volnovode. Preprint PMF-06-02. Kazansk. matem. ob-vo, Kazan', 2006. 30 s.
15. K.N. Vdovina, N.B. Pleschinskiy, D.N. Tumakov, Izvestiya vysshih uchebnyh zavedeniy. Matematika, №9, 69-75 (2008).