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Application of a symbolic method of integration to the three-dimensional equations of the dynamics of a transversally isotropic slab

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Literature Cited

  1. 1.

    V. G. Babadzhanyan, A. K. Galin'sh, and A. B. Sachenkov, “The method of initial functions of V. Z. Vlasov,” Prikl. Mekh.,11, No. 1, 15–21 (1975).

  2. 2.

    V. Z. Vlasov, “A method of initial functions in problems of elasticity theory,” Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 7, 49–69 (1955).

  3. 3.

    N. A. Kil'chevskii, “Generalization of contemporary shell theory,” Prikl. Mat. Mekh.,2, No. 4, 427–438 (1939).

  4. 4.

    M. Kutser and U. Nigul, “Application of the symbolic method of A. I. Lur'e in plate dynamics for deformations symmetric with respect to the middle surface,” Izv. Akad. Nauk ÉstSSR, Ser. Fiz. Mat. Tekh. Nauk,14, No. 3, 385–392 (1965).

  5. 5.

    S. G. Lekhnitskii, “Elastic equilibrium of a transversally isotropic layer and a thick plate,” Prikl. Mat. Mekh.,26, No. 4, 687–696 (1962).

  6. 6.

    A. I. Lur'e, “The theory of thick plates,” Prikl. Mat. Mekh.,6, Nos. 2–3, 151–168 (1942).

  7. 7.

    A. Myannil and U. Nigul, “Stress states of an elastic plate on the propagation of a sinusoidal flexural wave,” Izv. Akad. Nauk ÉstSSR, Ser. Fiz. Mat. Tekh. Nauk,12, No. 3, 273–283 (1963).

  8. 8.

    U. Nigul, “Application of A. I. Lur'e's symbolic method in the three-dimensional theory of elastic plate dynamics,” Izv. Akad. Nauk ÉstSSR, Ser. Fiz. Mat. Tekh. Nauk,12, No. 2, 146–155 (1963).

  9. 9.

    U. Nigul, “The roots of Lamb's equation for the deformation of a plate antisymmetric with respect to the middle surface,” Izv. Akad. Nauk ÉstSSR, Ser. Fiz. Mat. Tekh. Nauk,12, No. 3, 284–293 (1963).

  10. 10.

    I. T. Selezov, “Investigations of the transverse vibrations of a plate,” Prikl. Mekh.,6, No. 3, 319–327 (1960).

  11. 11.

    I. T. Selezov and Yu. G. Krivonos, “Investigations, based on refined theories, of longitudinal waves in a plate,” Prikl. Mekh.,9, No. 11, 56–63 (1973).

  12. 12.

    R. D. Mindlin, “Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates,” J. Appl. Mech.,18, No. 1, 31–38 (1951).

  13. 13.

    D. R. Westbrook, “Symbolic approach to dynamical problems in plates,” J. Acoust. Soc. Amer.,44, No. 4, 1083–1092 (1968).

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Additional information

Kazan' State University. Translated from Prikladnaya Mekhanika, Vol. 12, No. 9, pp. 24–29, September, 1976.

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Babadzhanyan, V.G., Galin'sh, A.K. Application of a symbolic method of integration to the three-dimensional equations of the dynamics of a transversally isotropic slab. Soviet Applied Mechanics 12, 893–897 (1976). https://doi.org/10.1007/BF00884731

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Keywords

  • Symbolic Method
  • Isotropic Slab