Vibration of a Shaft Passing through a Critical Speed : 2nd Report, Approximate Equations

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This paper deals with a vibrational problem which occurs during passage through a critical speed. An exact solution for the problem has been obtained assuming that the angular velocity of the external force increases linearly with time and the system has no damping. This solution, however, contains Fresnel integrals and these integrals prevent us from understanding characteristics of the transient vibration. In this paper, we derive approximate equations from the exact solution by using the series and the asymptotic expanssion for Fresnel integral. These approximate equations show that the transient vibration is divided into three domains of τ and also show characteristics of the amplitude, the phase angle and the angular velocity of vibration in each domain.
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