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Extension of poincare's nonlinear oscillation theory to continuum mechanics (I)—Basic theory and method

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Abstract

In this paper we extend Poincaré's nonlinear oscillation theory of discrete system to continuum mechanics. First we investigate the existence conditions of periodic solution for linear continuum system in the states of resonance and nonresonance. By applying the results of linear theory, we prove that the main conclusion of Poincaré's nonlinear oscillation theory can be extended to continuum mechanics. Besides, in this paper a new method is suggested to calculate the periodic solution in the states of both resonance and nonresonance by means of the direct perturbation of partial differential equation and weighted integration.

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References

  1. Poincaré,Les méthodes nouvelles de mécanique celest, Paris (1892).

  2. Malkin, I.G.,Some Problems in the Theory of Nonlinear Oscillation, GITTL Moscow (1956). (in Russian)

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Authors and Affiliations

  1. Tianjin University, Tianjin

    Huo Lin-chun & Li Li

Authors
  1. Huo Lin-chun
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  2. Li Li
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Projects Supported by the Science Fund of the Chinese Academy of Sciences.

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Lin-chun, H., Li, L. Extension of poincare's nonlinear oscillation theory to continuum mechanics (I)—Basic theory and method. Appl Math Mech 8, 1–10 (1987). https://doi.org/10.1007/BF02014493

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  • DOI: https://doi.org/10.1007/BF02014493

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