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The subharmonic bifurcation solution of nonlinear Mathieu's equation and Euler dynamic buckling problems

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Abstract

A new approach is presented in this paper on the basis of dynamic systems theory. This paper presents the form of a generic classification of stable response diagrams for the nonlinear Mathieu equation. In addition, a general method is presented for determining the topological type of the response diagram for a given equation. This method has been successfully applied to Euler dynamic buckling problems. Some new results are obtained.

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Authors and Affiliations

  1. Tianjin University, China

    Chen Yushu

  2. University of Guelph, Canada

    W. F. Langford

Authors
  1. Chen Yushu
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  2. W. F. Langford
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Yushu, C., Langford, W.F. The subharmonic bifurcation solution of nonlinear Mathieu's equation and Euler dynamic buckling problems. Acta Mech Sinica 4, 350–362 (1988). https://doi.org/10.1007/BF02486668

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  • DOI: https://doi.org/10.1007/BF02486668

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