Vibration and stability of a spinning functionally graded cylinder in a liquid-filled concentric drum

The vibration and stability of an axially functionally graded (AFG) cylinder with whirl motion in the annular liquid environment are investigated. The model of the performed system is given by the spinning Rayleigh beam assumptions with the rotary inertia and the gyroscopic effects. The fluid forces exerted on the cylinder, as a result of the external fluid, are calculated analytically. The coupled governing equation of motion for the system is developed via Hamilton's principle. The exact and approximate whirl frequency equations are presented for vibration and stability analysis of the AFG cylinder. The validity of the proposed model is confirmed by comparing it with the numerical solutions available in the literature. Detailed parameter discussions are conducted to evaluate the effects of the density ratio, outer-to-inner radius ratio, hollowness ratio, and slenderness ratio on the whirl characteristics and stability of the system. The results show that the whirl characteristics and instability of the AFG cylinder are strongly dependent on the external fluid.