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Estimates of upper and lower bounds and the density of the eigenfrequencies of three-layer and transversely isotropic spherical shells

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Literature cited

  1. É. I. Grigolyuk and F. A. Kogan, “The contemporary state of the theory of multilayer shells,” Prikl. Mekh.,8, No. 6, 5–17(1972).

    Google Scholar 

  2. V. V. Bolotin and Yu. N. Novikov, The Mechanics of Multilayer Structures [in Russian], Moscow (1980).

  3. A. D. Lizarev and N. B. Rostanina, “The equations of free vibrations of nonmildly sloping three-layer spherical shells,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 142–148 (1978).

    Google Scholar 

  4. A. D. Lizarev and N. B. Rostanina, “Free vibrations of three-layer and transversely isotropic spherical shells,” Mekh. Komp. Mater., No. 4, 669–675 (1980).

    Google Scholar 

  5. É. I. Grigolyuk and P. P. Chulkov, The Stability and Vibrations of Three-Layer Shells [in Russian], Moscow (1973).

  6. Procedural Recommendations. Calculations and Strength Tests. Method for Calculation of the Eigenfrequencies and Vibration Modes of Three-Layer and Uniform Spherical Shells [in Russian], Moscow (1981).

  7. A. D. Lizarev and N. B. Rostanina, “The eigenfrequencies of fibrations of very thin spherical shells,” in: The Calculation of Three-Dimensional Structures [in Russian], No. 18, Moscow (1979), pp. 139–153.

    Google Scholar 

  8. I. L. Baskin, A. D. Lizarev, and N. B. Rostanina, “Theoretical and empirical eigenfrequency densities of vibrations of nonmildly spherical shells,” in: Transactions of the 10-th Ail-Union Conference on Shell and Plate Theory [in Russian], Vol. 2, Tbilisi (1975), pp. 45–54.

    Google Scholar 

  9. A. D. Lizarev, “The calculation of the logarithmic derivative of the associated Legendre functions,” Zh. Vychisl. Mat. Mat Fiz.,13, No. 6, 1588–1591 (1973).

    Google Scholar 

  10. Tables of the Associated Legendre Functions [in Russian], Library of Mathematical Tables, No. 14, Moscow (1962).

  11. E. W. Hobson, Spherical and Ellipsoidal Harmonics, Chelsea Pub. (1955).

  12. V. V. Bolotin, “General properties of the eigenfrequencies and eigenmodes of elastic systems,” in: Vibrations in Technology [in Russian], Vol 1, Moscow (1978), pp. 166–177.

    Google Scholar 

  13. V. V. Bolotin, “A theory of the eigenfrequency distribution of elastic bodies and its application to problems of random vibrations,” Prikl. Mekh.,8, No. 4, 3–29 (1972).

    Google Scholar 

  14. A. G. Aslanyan and V. B. Lidskii, The Distribution of the Eigenfrequencies of Thin Elastic Shells [in Russian], Moscow (1974).

  15. J. P. D. Wilkinson, “Modal densities of certain shallow structural elements,” J. Acoust. Soc. Am.,43, No. 2, pp. 245–251 (1968).

    Google Scholar 

  16. V. E. Khromatov and V. V. Radyukhina, “The eigenfrequency density of the vibrations of three-layer shells,” in: Tr. Mosk. Energ. Inst., No. 459, 108–113 (1980).

    Google Scholar 

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Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 263–270, March–April, 1982

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Lizarev, A.D. Estimates of upper and lower bounds and the density of the eigenfrequencies of three-layer and transversely isotropic spherical shells. Mech Compos Mater 18, 182–188 (1982). https://doi.org/10.1007/BF00604839

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  • DOI: https://doi.org/10.1007/BF00604839

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