Özet:

In this paper a revised averaging method is presented, that does not need the detuning factor in the solving procedure. Comparison with the traditional averaging method shows that it has the similar solving procedure and the same result as the primary resonance of the traditional averaging method. Then the nonlinear oscillator with only polynomial-type displacement nonlinearity is studied, and the general forms of the first-order approximate solution by this revised averaging method, and by the traditional averaging method for the super-harmonic resonance and sub-harmonic resonance are established. At last, the Duffing oscillator is investigated as an example, and the comparison of the analytical and numerical results proves the validity and simplicity of the presented method.

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