Shin Murakami

Dynamic Response and Stability of a Rotating Asymmetric Shaft Mounted on a Flexible Base

This paper presents the dynamic response and stability of an asymmetric rotating shaft supported by a flexible base near the major critical speed and the secondary critical speed. In this system, the base is movable only in a direction transversal to the shaft. In the theoretical analysis, taking into account the effects of damping, the unstable vibrations near the major critical speed are mainly considered, and also the behavior of the forced oscillations near the major and secondary critical speeds is investigated. From the theoretical analysis, the unstable region is found to be divided into at most six subregions which depend on the mass of the base, the stiffness of the base, and the asymmetry of the shaft. In addition, the resonance curves near unstable subregions are calculated. It is found that there exist two shapes of resonance curves. In experiments, five types of response curves, which contained n unstable subregion (n = 1, 2, ¨, 5) near the major critical speed, were obtained by changing the mass of the base. It was ascertained that the theoretical results for the behavior near the major critical speed agreed quantitatively with the experimental results.

Autoparametric Responses of an Elastic Structure Carrying a Cylindrical Tank (1st Report, Influence of Liquid Levels on Resonance Curves)

鉛 直励振 を受ける弾性構造物 と 円筒容器内ス ロッシングの非線形連成振動* (第1報,液 位による共振曲線の変化) 池 田 隆*1, 村 上 新*1 Autoparametric Responses of an Elastic Structure Carrying a Cylindrical Tank (1st Report, Influence of Liquid Levels on Resonance Curves) Takashi IKEDA*2 and Shin MURAKAMI *2 Department of Electronic and Control Systems Engineering, Shimane University, 1060 Nishikawatsu-cho, Matsue-shi, Shimane, 690-8504 Japan The nonlinear vibrations of an elastic structure carrying a liquid-filled cylindrical tank are examined. Modal equations goveming the coupled motions of the structure and liquid sloshing are derived when the structure is subjected to a vertical sinusoidal excitation and when the natural frequency of the structure is equal to twice the natural frequency of the first axisymmetric mode of sloshing. This system behaves as an autoparametric system. Then, van der Pols method is applied to the modal equations to determine the theoretical resonance curves. This demonstrates that the resonance curve for the liquid sloshing changes from a soft spring type to a hard spring type as the liquid level decreases. The structures resonance curve has a flat shape for an appropriate liquid level. In experiments the theoretical resonance curves were quantitatively in agreement with the experimental results.

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.

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.