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Parametric vibrations of orthotropic plates with complex shape

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The paper proposes a method to study the parametric vibrations of orthotropic plates with complex shape. The method is based on the R-function theory and variational methods. Dynamic-instability domains and amplitude–frequency responses for plates with complex geometry and different types of boundary conditions are plotted

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References

  1. S. A. Ambartsumyan, Theory of Anisotropic Plates, Technomic, Stamford (1987).

    Google Scholar 

  2. V. V. Bolotin, The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco, CA (1964).

    MATH  Google Scholar 

  3. N. N. Bogolyubov and Y. A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York (1962).

    Google Scholar 

  4. A. S. Vol’mir, Nonlinear Dynamics of Plates and Shells [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  5. S. G. Lekhnitskii, Anisotropic Plates, Gordon and Breach, New York (1968).

    Google Scholar 

  6. V. D. Kubenko and P. S. Koval’chuk, “Nonlinear problems of the vibration of thin shells (review),” Int. Appl. Mech., 34, No. 8, 703–728 (1998).

    Article  MathSciNet  Google Scholar 

  7. V. D. Kubenko, P. S. Koval’chuk, and T. S. Krasnopol’skaya, Nonlinear Interaction of Flexural Vibration Modes of Cylindrical Shells [in Russian], Naukova Dumka, Kyiv (1984).

    Google Scholar 

  8. L. V. Kurpa and O. S. Masur, “Studying the nonlinear vibrations of statically compressed plates,” Int. Appl. Mech., 42, No. 12, 1421–1432 (2006).

    Article  Google Scholar 

  9. O. S. Masur, “Determining dynamic-instability domains for plates of complex geometry,” Vest. Nats. Tekhn. Univ. “KhPI,” 32, 112–118 (2006).

    Google Scholar 

  10. N. W. McLachlan, Theory and Application of Mathieu Functions, Dover, New York (1964).

    MATH  Google Scholar 

  11. I. G. Malkin, Some Problems in the Theory of Nonlinear Oscillations [in Russian], Gostekhizdat, Moscow (1965).

    Google Scholar 

  12. A. A. Martynyuk, Technical Stability in Dynamics [in Russian], Tekhnika, Kyiv (1973).

    Google Scholar 

  13. S. G. Mikhlin, Variational Methods in Mathematical Physics, Pergamon Press, Oxford (1964).

    MATH  Google Scholar 

  14. V. L. Rvachev and L. V. Kurpa, R-Functions in Plate Problems [in Russian], Naukova Dumka, Kyiv (1987).

    Google Scholar 

  15. G. Schmidt, Parametric Vibrations [in German], DVW, Berlin (1975).

    Google Scholar 

  16. J. Awrejcewicz and A. V. Krys’ko, ”Analysis of complex parametric vibrations of plates and shells using Bubnov–Galerkin approach,” Appl. Mech., 73, 495–504 (2003).

    Article  MATH  Google Scholar 

  17. M. Ganapathi, B. P. Patel, P. Boise, and M. Touratier, ”Non-linear dynamic stability characteristics of elastic plates subjected to periodic in-plane load,” Int. J. Non-linear. Mech., 35, 467–480 (2000).

    Article  MATH  Google Scholar 

  18. J. M. Hutt, “Dynamic stability of plates by finite elements?” J. Eng. Mech. Div., 879–890 (1971).

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Correspondence to L. V. Kurpa.

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Translated from Prikladnaya Mekhanika, Vol. 46, No. 4, pp. 83–95, April 2010.

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Kurpa, L.V., Mazur, O.S. Parametric vibrations of orthotropic plates with complex shape. Int Appl Mech 46, 438–449 (2010). https://doi.org/10.1007/s10778-010-0326-0

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  • DOI: https://doi.org/10.1007/s10778-010-0326-0

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