Stability analysis of spinning liquid-filled cylinders with exponentially varying cross section

Abstract

In this paper, the stability analysis of a spinning liquid-filled cylinder with exponentially varying cross sections is carried out. Based on the spinning Euler–Bernoulli beam theory, the governing equation for vibration of the spinning cylinder is formulated by using Hamilton's principle. The relative perturbation motion equation of the rotating fluid is derived using the composition theorem of acceleration. Combined with the flow boundary conditions, the fluid forces exerted on the cylinder are obtained. Using the analytical method, the characteristic frequency equation of the system is determined. The stability of the considered system is determined by eigenvalue analysis. The accuracy of the proposed model is validated by comparing it with the existing data in the literature. Finally, a detailed parameter study is conducted to demonstrate the effects of mass ratio, cavity ratio, taper parameter, thickness ratio, and axial position on the vibration and stability of the system. The results show that these parameters play an important role in the instability, natural frequency, and critical spinning speed of the spinning taper cylinder partially filled with liquid.