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Natural vibrations of thin conical panels of variable thickness

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A numerical analytical approach is proposed to study the natural vibrations of thin isotropic conical shells with varying thickness. The approach is based on the spline-approximation of unknown functions. Open shells (panels) with different boundary conditions are considered. The effect of variable thickness on the dynamic characteristics is analyzed

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References

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

    Google Scholar 

  2. Ya. M. Grigorenko and A. T. Vasilenko, Theory of Shells with Variable Stiffness, Vol. 4 of the series Methods of Shell Design [in Russian], Naukova Dumka, Kyiv (1981).

    Google Scholar 

  3. Ya. M. Grigorenko and A. P. Mukoed, Computer-Aided Solution of Linear and Nonlinear Problems of Shell Theory [in Ukrainian], Lubid’, Kyiv (1992).

  4. Yu. S. Zav’yalov, Yu. I. Kvasov, and V. L. Miroshnichenko, Spline-Function Methods [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  5. I. A. Birger and Ya. G. Panovko (eds.), Strength, Stability, and Vibration [in Russian], Vol. 3 of the three-volume Handbook, Mashinostroenie, Moscow (1968).

  6. V. D. Budak, A. Ya. Grigorenko, and S. V. Puzyrov, “Solution describing the natural vibrations of rectangular shallow shells with varying thickness,” Int. Appl. Mech., 43, No. 4, 432–441 (2007).

    Article  Google Scholar 

  7. Ya. M. Grigorenko and O. A. Avramenko, “Studying the stress–strain state of closed nonthin orthotropic conical shells of variable thickness,” Int. Appl. Mech., 44, No. 6, 635–661 (2008).

    Article  Google Scholar 

  8. Ya. M. Grigorenko and S. N. Yaremchenko, “Influence of orthotropy on displacements and stresses in nonthin cylindrical shells with elliptic cross section,” Int. Appl. Mech., 43, No. 6, 82–92 (2007).

    Article  Google Scholar 

  9. A. Ya. Grigorenko and N. P. Yaremchenko, “Stress–strain state of shallow shells with rectangular planform and varying thickness: Refined formulation,” Int. Appl. Mech., 43, No. 10, 1132–1141 (2007).

    Article  Google Scholar 

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine, 03057

    A. Ya. Grigorenko & S. A. Mal’tsev

Authors
  1. A. Ya. Grigorenko
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  2. S. A. Mal’tsev
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Correspondence to S. A. Mal’tsev.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 45, No. 11, pp. 90–100, November 2009.

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Grigorenko, A.Y., Mal’tsev, S.A. Natural vibrations of thin conical panels of variable thickness. Int Appl Mech 45, 1221–1231 (2009). https://doi.org/10.1007/s10778-010-0262-z

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  • DOI: https://doi.org/10.1007/s10778-010-0262-z

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