V.2 No 1

59

On complex resonance vibration systems calculation

References

1.      Skudrzyk, E. Simple and complex vibratory systems. Mir, Moscow, 1971, 557 pp. (Russian; from edition: Skudrzyk, E. Simple and complex vibratory systems. The Pennsylvania State University Press, University Park and London, 1968)

2.      Grebennikov, E.A. Introduction to the resonance systems theory. Moscow State University, 1987, 174 pp. (Russian)

3.      Kuhta, K.Ya., Boyko, A.G. and Garmash, N.Z. Investigation of complex continouosly-discrete systems. Naukova Dumka, Kyev, 1981, 270 pp. (Russian)

4.      Volkenshtein, M.V., Eliashkevitch, M.A. and Stepanov, B.I. Molecules oscillations, vol. 1: Geometry and mechanics of molecules oscillations. The State Publishing of Technical and Theoretical Literature, Moscow – Leningrad, 1949, 600 pp. (Russian)

5.      Slater, J.C. Insulators, semiconductors and metals. Mir, Moscow, 1969, 647 pp. (Russian; from edition: Slater, J.C. Insulators, semiconductors and metals. In: Quantum theory of molecules and solids, vol.3. McGraw Hill Book Company, New York – St. Lous – San Francisco – Toronto – London – Sydney, 1967).

6.      Blakemore, J.S. Solid state physics. Metallurgia, Moscow, 1972, 488 pp. (Russian; from edition: Blakemore, J.S. Solid state physics. W.B. Saunders Company, Philadelphia – London – Toronto, 1970)

7.      Born, M. and Hypper-Meyer, M. Dynamical theory of lattice. The Principal Editorial for Technical and Theoretical Literature, Moscow – Leningrad, 1938, 364 pp. (Russian, translated from German).

8.      Mikhailov, I.G., Soloviev, V.A. and Sirnikov, Yu.P. Foundations of molecular acoustics. Nauka, Moscow, 1964, 514 pp. (Russian)

9.      Thouless, D.J. The quantum mechanics of many-body systems. Publishing for Foreign Literature, Moscow, 1963 (Russian; from edition: Thouless, D.J. The quantum mechanics of many-body systems. Academic Press, New York – London,1961)

10.  Chernous’ko, F.L., Akulenko, L.D. and Soloviev, B.N. Control of oscillations. Nauka, Moscow, 1980, 383 pp. (Russian).

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12.  Atkinson, F.V. Discrete and continuous boundary problems. Mir, Moscow, 1968, 750 pp. (Russian; from edition: Atkinson, F.V. Discrete and continuous boundary problems. Academic Press, new York – London, 1964)

13.  Palis, J. and de Melo, J.W. Geometric theory of dynamical systems. Mir, Moscow, 1986, 302 pp. (Russian; from edition: J. Palis and J.W. de Melo. Geometric theory of dynamical systems. Springer-Verlag, New York – Heidelberg – Berlin, 1982) .

14.  Reiscig, R., Sansone, G. and Conti, R. Qualitative theory of nonlinear differential equations. Nauka, Moscow, 1974, 318 pp. (Russian; from edition: Reiscig, R., Sansone, G. and Conti, R. Qualitative theorie nichtlinearer differentialleichungen. Edizioni cremonese, Roma, 1963)

15.  Mitropolsky, Yu.A. and Homa, G.P. Mathematical background of nonlinear mechanics asymptotic methods. Naukova Dumka, Kyev, 1983, 215 pp. (Russian)

16.  Cherepennikov, V.B. Functional parameters method in the ordinary differential equations theory. Nauka, Novosibirsk, 1983 (Russian)

17.  Giacagrilia, G.E.O. Perturbation methods in non-linear systems. Nauka, Moscow, 1979, 320 pp. (Russian; from edition: Giacagrilia, G.E.O. Perturbation methods in non-linear systems. Springer-Verlag, New York – Heidelberg – Berlin, 1972)

18.  Dymentberg, M.F. Nonlinear stochastic problems of mechanical vibrations. Nauka, Moscow, 1980, 368 pp. (Russian)

19.  Banerjee, P.K. and Butterfield, R. Boundary element methods in engineering science. Mir, Moscow, 1984, 494 pp. (Russian; from edition: Banerjee, P.K. and Butterfield, R. Boundary element methods in engineering science. McGraw hill Book Company Ltd., London – New York – Sydney – Tokyo – Toronto, 1981)

20.  Karavashkin, S.B. 'Exact analytic solutions of vibrations of infinite 1-D elastic lines with lumped parameters', IJMEE, 30 (2), (2002), 138-154.

21.  Karavashkin, S.B. 'Exact analytical solution for 1D elastic homogeneous finite lumped line vibration', Materials, technologies, tools (National Academy of Sciences of Belarus), 4 (4), (1999), 5-13

22.  Karavashkin, S.B. Some features of the forced vibrations modelling for 1D homogeneous elastic lumped lines. Materials, Technologies, Tools. The Journal of National Academy of Sciences of Belarus, 5 (2000), 3, 15-23

23.  Karavashkin, S.B. The features of inclined force action on 1D homogeneous elastic lumped line and correspondig modernisation of the wave equation. arXiv (Los Alamos), #math-ph/0006028

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