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An approach to the investigation of free vibrations of elastic structural elements

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Literature Cited

  1. Ya. M. Grigorenko, E. I. Bespalova, A. B. Kitaigorodskii, and A. I. Shinkar', Free Vibrations of Elements of Shell Structures [in Russian], Naukova Dumka, Kiev (1986).

    Google Scholar 

  2. Ya. M. Grigorenko and A. T. Vasilenko, Theory of Variable-Stiffness Shells, (Methods for the Analysis of Shells, fifth printing, Vol. 4) [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  3. L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis, Interscience, New York (1958).

    Google Scholar 

  4. V. F. Kirichenko and V. A. Krys'ko, “Method of variational iterations in the theory of plates and foundation of the method,” Prikl. Mekh.,16, No. 4, 71–76 (1981).

    Google Scholar 

  5. L. Collatz, Eigenwertprobleme und ihre numerische Behandlung, Chelsea, New York (1948).

    Google Scholar 

  6. S. G. Lekhnitskii, Theory of Elasticity of Anisotropic Bodies [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  7. V. V. Novozhilov, Theory of Thin Shells [in Russian], Sudostroenie, Leningrad (1962).

    Google Scholar 

  8. B. L. Pelekh, Theory of Shells with finite Shear Stiffness [in Russian], Naukova Dumka, Kiev (1973).

    Google Scholar 

  9. N. A. Krasnosel'skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, et al., Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  10. V. G. Prokopov, E. I. Bespalova, and Yu. V. Sherenkovskii, “A new method for the mathematical investigation of transport processes,” Prom. Teplotekh.,1, No. 2, 33–41 (1979).

    Google Scholar 

  11. V. G. Prokopov, E. I. Bespalova, Yu. V. Sherenkovskii, and D. G. Blinov, “Investigation of heat-transfer processes in regions of complex configuration with arbitrary boundary conditions,” Prom. Teplotekh.,4, No. 3, 44–49 (1982).

    Google Scholar 

  12. V. G. Prokopov, E. I. Bespalova, and Yu. V. Sherenkovskii, “Method of reduction to the ordinary differential equations of L. V. Kantorovich and a general method for the solution of multidimensional heat-transfer problems,” Inzh.-Fiz. Zh.,42, No. 6, 1007–1013 (1982).

    Google Scholar 

  13. G. Strang, Linear Algebra and Its Applications, 2nd Ed., Academic Press, New York (1980).

    Google Scholar 

  14. D. R. Hartree, The Calculation of Atomic Structures, Wiley, New York (1957).

    Google Scholar 

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Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 1, pp. 43–48, January, 1988.

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Bespalova, E.I. An approach to the investigation of free vibrations of elastic structural elements. Soviet Applied Mechanics 24, 37–41 (1988). https://doi.org/10.1007/BF00885072

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