Extension of Poincare’s Nonlinear Oscillation Theory to Continuum Mechanics(I)-Basic Theory and Method

Huo Lin-chun; Li Li

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Huo Lin-chun, Li Li. Extension of Poincare’s Nonlinear Oscillation Theory to Continuum Mechanics(I)-Basic Theory and Method[J]. Applied Mathematics and Mechanics, 1987, 8(1): 1-9.

Citation:

Huo Lin-chun, Li Li. Extension of Poincare’s Nonlinear Oscillation Theory to Continuum Mechanics(I)-Basic Theory and Method[J]. Applied Mathematics and Mechanics, 1987, 8(1): 1-9.

Citation:

Huo Lin-chun, Li Li. Extension of Poincare’s Nonlinear Oscillation Theory to Continuum Mechanics(I)-Basic Theory and Method[J]. Applied Mathematics and Mechanics, 1987, 8(1): 1-9.

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Extension of Poincare’s Nonlinear Oscillation Theory to Continuum Mechanics(I)-Basic Theory and Method

Huo Lin-chun,
Li Li

Tianjin University, Tianjin

Received Date: 1985-10-25
Publish Date: 1987-01-15

Abstract

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 non-resonance.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(6)

References

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