Nonstationary vibration of a rotating shaft with nonlinear spring characteristics during acceleration through a major critical speed. A discussion by the asymptotic method and the FFT method.

Abstract

Nonstationary vibrations of a rotating shaft with nonlinear spring characteristics are investigated. Firstly we obtain the first-order approximate solution by the asymptotic method, paying attention to the nonlinear components in the polar coordinate expression, and clarify that only the isotropic nonlinear component influences this solution. Next, we propose the complex-FFT method where nonstationary vibration wave data obtained from numerical integration of the equations of motion are treated as complex numbers. By this method, we can extract the desired vibration component and obtain its amplitude variation curve. Comparing these curves and those of the asymptotic method, we show that the curve obtained by the asymptotic method has comparatively large quantitative error. In addition, we clarify that the anisotropic nonlinear components which do not appear in the first approximate solution of the asymptotic method cause higher-order vibration components in the nonstationary wave.