Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Free vibrations of three-layered and transversely isotropic spherical shells

  • 22 Accesses

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

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

  2. 2.

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

  3. 3.

    J. P. Wilkinson and A. Kalnins, “On nonsymmetric dynamic problems of elastic spherical shells,” Trans. ASME, Ser. E, J. Appl. Mech.,32, No. 3, 525–532 (1965).

  4. 4.

    R. B. Rikards and G. A. Teters, Stability of Shells Made Out of Composite Materials [in Russian], Riga (1974).

  5. 5.

    G. Bateman and A. Erdelyi, Higher Transcendental Functions. Hypergeometric Function, Legendre Functions [Russian translation], Moscow (1965).

  6. 6.

    A. D. Lizarev, V. U. Ognev, and N. B. Rostanina, “The associated Legendre functions of arbitrary complex order,” Zh. Vychisl. Mat. Mat. Fiz.,15, No. 2, 496–501 (1975).

  7. 7.

    A. D. Lizarev and N. B. Rostanina, “Eigenfrequencies of vibrations of very thin spherical shells,” in: Calculation of Spatial Structures [in Russian], No. 18, Moscow (1979), pp. 139–153.

  8. 8.

    B. L. Pelekh, Shell Theory with Finite Shear Strength [in Russian], Kiev (1973).

  9. 9.

    B. L. Pelekh, “Some problems of the development of the theory and computational methods of anisotropic shells and plates with low shear strength,” Mekh. Polim., No. 2, 284–296 (1975).

  10. 10.

    A. A. Khachatryan, “The stability and vibrations of a transversely Isotropic spherical shell,” Izv. Akad. Nauk Arm. SSR, Ser. Fiz.-Mat. Nauk,13, No. 4, 19–28 (1960).

  11. 11.

    P. R. Ghosh, “Vibrations of nonhomogeneous spherically aelotropic spherical shell,” Indian J. Phys.,42, No. 5, 296–304 (1968).

  12. 12.

    C. V. Ramakrishnan and A. H. Shah, “Vibration of an aelotropic spherical shell,” J. Acoust. Soc. Am.,47, No. 5, Part 2, 1366–1374 (1970).

  13. 13.

    A. L. Gol'denveizer, “Approximate methods of investigation of free vibrations of thin shells,” Prikl. Mat. Mekh.,41, No. 6, 1079–1094 (1977).

  14. 14.

    A. L. Gol'denveizer, V. B. Lidskii, and P. E. Tovstik, Free Vibrations of Thin Elastic Shells [in Russian], Moscow (1979).

  15. 15.

    A. D. Lizarev and N. B. Rostanina, “Investigation of the vibrations of spherical shells of the Timoshenko type by the method of separation of the frequency spectrum,” in: The Dynamics of Spatial Structures [in Russian], Kiev (1978), pp. 40–43.

  16. 16.

    O. V. Luzhin, “The problem of free vibrations of a thin spherical shell,” Stroit. Mekh. Raschet Sooruzhenii, 32–36 (1961).

Download references

Author information

Additional information

Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 669–675, July–August, 1980.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lizarev, A.D., Rostanina, N.B. Free vibrations of three-layered and transversely isotropic spherical shells. Mech Compos Mater 16, 464–469 (1981). https://doi.org/10.1007/BF00604865

Download citation

Keywords

  • Free Vibration
  • Spherical Shell
  • Isotropic Spherical Shell