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Asymptotic analysis of nonlinear dynamics of simply supported cylindrical shells

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Abstract

Donnell equations are used to simulate free nonlinear oscillations of cylindrical shells with imperfections. The expansion, which consists of two conjugate modes and axisymmetric one, is used to analyze shell oscillations. Amplitudes of the axisymmetric motions are assumed significantly smaller, than the conjugate modes amplitudes. Nonlinear normal vibrations mode, which is determined by shell imperfections, is analyzed. The stability and bifurcations of this mode are studied by the multiple scales method. It is discovered that stable quasiperiodic motions appear at the bifurcations points.

The forced oscillations of circular cylindrical shells in the case of two internal resonances and the principle resonance are analyzed too. The multiple scales method is used to obtain the system of six modulation equations. The method for stability analysis of standing waves is suggested. The continuation algorithm is used to analyze fixed points of the system of the modulation equations.

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Authors and Affiliations

  1. Department of Gas and Fluid Mechanics, Faculty of Physics and Engineering, National Technical University “KhPI”, Frunze St.21, Kharkov, 61002, Ukraine

    K. V. Avramov

  2. Department of Applied Mathematics, National Technical University “KhPI”, Frunze St.21, Kharkov, 61002, Ukraine

    Yu. V. Mikhlin & E. Kurilov

Authors
  1. K. V. Avramov
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  2. Yu. V. Mikhlin
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  3. E. Kurilov
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Correspondence to K. V. Avramov.

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Avramov, K.V., Mikhlin, Y.V. & Kurilov, E. Asymptotic analysis of nonlinear dynamics of simply supported cylindrical shells. Nonlinear Dyn 47, 331–352 (2007). https://doi.org/10.1007/s11071-006-9032-1

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  • DOI: https://doi.org/10.1007/s11071-006-9032-1

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