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Identifying the domains of dynamic instability for inhomogeneous shell systems under periodic loads

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The paper outlines an approach to identifying the principal dynamic-instability domain for systems composed of shells of revolution with different shapes under axisymmetric periodic loading. The original problem is reduced to one-dimensional eigenvalue problems with respect to the meridional coordinate. Results of calculations for a specific shell system are presented

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References

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

    MATH  Google Scholar 

  2. A. T. Vasilenko, Ya. M. Grigorenko, and P. N. Cherin’ko, ”Dynamic stability of orthotropic shells of revolution with variable stiffness,” Dokl. AN USSR, Ser. A, No. 10, 28–31 (1984).

  3. A. T. Vasilenko and P. N. Cherin’ko, “Parametric vibrations of composite shells of revolution,” in: Dynamics of Structural Members, Vol. 9 of the 12-volume series Mechanics of Composite Materials [in Russian], A.S.K., Kyiv (1999).

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

    Google Scholar 

  5. A. A. Efimov, “Parametric vibrations and stability of underwater main oil pipelines,” Izv. VUZov, Neft’ i Gas, No. 2, 123–126 (2008).

  6. Von L. Collatz, Eigenvalue Problems with Engineering Applications [in German], Akad. Verlagsges., Leipzig (1963).

    Google Scholar 

  7. E. R. Kol’man, ”Stability of a conical shell dynamically loaded by uniform pressure,” Izv. VUZov, Mashinostroenie, No. 4, 60–65 (1968).

  8. V. A. Krys’ko and T. V. Shchekaturova, ”Chaotic vibrations of conical shells,” Izv. RAN, Mekh. Tverd. Tela, No. 4, 140–150 (2004).

  9. V. A. Krys’ko and I. V. Kravtsova, ”Stochastic vibrations of flexible axisymmetric spherical shells movably hinged at the edge,” Izv. VUZov, Mashinostroenie, No. 1, 11–20 (2004).

  10. I. I. Pertusheva, ”Dynamic-instability domains for a laminated cylindrical elastic shell,” in: Numerical Methods of Solving Problems of Elasticity and Plasticity [in Russian], Novosibirsk (2005), pp. 218–223.

  11. Handbook of Strength, Stability, and Vibrations [in Russian], Vol. 3, Mashinostroenie, Moscow (1988).

  12. J. Awrejcewicz and V. A. Krys’ko, Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells, Springer, Berlin (2003).

    Book  MATH  Google Scholar 

  13. J. Awrejcewicz, L. Kurpa, and O. Mazur, ”Research of stability and nonlinear vibrations by R-functions method,” in: Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems, Lodz (2009), pp. 179–189.

  14. E. Bespalova and G. Urusova, ”Vibration of highly inhomogeneous shells of revolution under static loading,” J. Mech. Mater. Struct., 3, No. 7, 1299–1313 (2008).

    Article  Google Scholar 

  15. E. Bespalova and G. Urusova, ”Vibrations of statically loaded shells of revolution subject to transverse shears and reduction,” Int. Appl. Mech., 46, No. 3, 279–286 (2010).

    Article  ADS  Google Scholar 

  16. B. Kh. Eshmatov, “Nonlinear vibrations and dynamic stability of a viscoelastic circular cylindrical shell with shear strain and inertia of rotation taken into account,” Appl. Math. Mech., 45, No. 3, 421–434 (2009).

    Google Scholar 

  17. B. Kh. Eshmatov and D. A. Khodyaev, ”Dynamic stability of a viscoelastic plate with concentrated mass,” Int. Appl. Mech., 44, No. 2, 109–118 (2008).

    Article  MATH  Google Scholar 

  18. P. S. Koval’chuk and L. A. Kruk, ”Nonlinear parametric vibrations of orthotropic cylindrical shells interacting with a pulsating fluid flow,” Int. Appl. Mech., 45, No. 9, 1007–1015 (2009).

    Article  ADS  Google Scholar 

  19. L. V. Kurpa and O. S. Mazur, ”Parametric vibrations of orthotropic plates with complex shape,” Int. Appl. Mech., 46, No. 4, 438–449 (2010).

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  21. Li Jing-Jing, Cheng Chang-Jun, and Zhang Neng-Hui, ”Dynamic stability of viscoelastic plates with finite deformation and shear effects,” J. of Shanghai University (English Edition), 6, No. 2, 115–124 (2002).

    Article  Google Scholar 

  22. T. Y. Ng ane K. Y. Lam, ”Dynamic stability analysis of cross-ply laminated cylindrical shells using different thin shell theories,” Acta Mech., 134, No. 3–4, 147–167 (1999).

    Google Scholar 

  23. J. Tani, ”Dynamic instability of truncated conical shells under periodic axial load,” Int. J. Solids Struct., 10, No. 2, 169–176 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhang We, ”Analysis of global dynamics in a parametrically excited thin plate,” Acta Mech. Sin., 17, No. 1, 71–85 (2001).

    Article  ADS  Google Scholar 

  25. Zhou Cheng-ti and Wang Lie-dong, Nonlinear theory of dynamic stability for laminated composite cylindrical shells,” Appl. Math. Mech., 22, No. 1, 53–62 (2001).

    Article  Google Scholar 

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Correspondence to E. I. Bespalova.

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Translated from Prikladnaya Mekhanika, Vol. 47, No. 2, pp. 96–106, March 2011.

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Bespalova, E.I., Urusova, G.P. Identifying the domains of dynamic instability for inhomogeneous shell systems under periodic loads. Int Appl Mech 47, 186–194 (2011). https://doi.org/10.1007/s10778-011-0452-3

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  • DOI: https://doi.org/10.1007/s10778-011-0452-3

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