Vibration and Stability Analysis of a Spinning Hollow Functionally Graded Beam with Exponentially Varying Cross-Section

Abstract

This paper presents an analytical investigation of the whirl characteristics and flexural instability of a spinning functionally graded (FG) hollow beam with exponentially varying cross-section. Applying Rayleigh beam theory, the governing equation of motion of the spinning beam with eccentricity is formulated via the Hamilton principle. The dimensionless whirl frequency equation is obtained for the FG beam with pinned–pinned end supports. On the basis of the obtained model, the whirl frequency, critical spinning speed, and stability conditions of the system are studied. Also, the effects of the main parameters on the whirl characteristics and stability of the system are evaluated. Results show that the unbalanced mass is the main source of system instability. It is also shown that the whirl frequency, critical spinning speed, and stability boundaries of the system are strongly dependent on the slenderness ratio, taper parameter, gradient index, hollow ratio, and eccentricity effects.