Method of initial-value transformation for obtaining approximate analytic periods of a class of nonlinear oscillators

LI Yin-shan;LI Shu-ji e

Journal of Vibration and Shock ›› 2010, Vol. 29 ›› Issue (8) : 99-102.

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PDF(1107 KB)
Journal of Vibration and Shock ›› 2010, Vol. 29 ›› Issue (8) : 99-102.
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Method of initial-value transformation for obtaining approximate analytic periods of a class of nonlinear oscillators

  • LI Yin-shan1; LI Shu-ji e2
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Abstract

The periodic solutions of a class of nonlinear oscillators can be expressed in the forms of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as a set of non-linear algebraic equations with frequency, central offset and amplitudes as the independent variables by using Ritz-Galerkin method. But the set of equations is incomplete. The key is that considering initial -value transformation, supplementary equations. were added and a set of non-linear algebraic equations with angular frequencies and amplitudes as the independent variables was constituted completely. As examples, six asymmetric periodic solutions bifurcating about a nonlinear differential equation arising in general relativity were solved by using the method of initial-value transformation. Amplitude-frequency curves and central offset-frequency curves of the asymmetrical vibration systems were derived. In addition, the drift phenomenon of natural angular frequency was discovered.

Key words

method of initial-value transformation / asymmetric vibration / bifurcation / central offset-frequency curves / drift of natural angular frequency

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LI Yin-shan;LI Shu-ji e. Method of initial-value transformation for obtaining approximate analytic periods of a class of nonlinear oscillators[J]. Journal of Vibration and Shock, 2010, 29(8): 99-102
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