Dynamical behavior of a spinning tapered Rayleigh beam subjected to an axial load

Abstract

As a first attempt, the vibration and stability analysis of a spinning tapered beam subjected to an axial load are investigated. The radius of the cross-section of the beam is assumed to vary exponentially in the longitudinal direction. The tapered beam is modeled in Rayleigh beam assumption with rotary inertia, eccentricity, and gyroscopic effects. Based on the Hamilton principle, the governing equations of motion of the spinning tapered beam with an axial force are obtained. Also, a Galerkin discretization scheme is employed to obtain the natural frequency and critical divergence rotating speeds of the system. As a result, the instability thresholds and stability evolution of the system are acquired. Furthermore, a detailed parametric study is conducted to evaluate the effects of the slenderness ratio, taper parameter, axial load, and eccentricity ratio on the dynamical behavior of the system. The results show that the natural frequency and critical divergence rotating speed of the tapered beam are larger than those of the circular-section beam. In addition, the axial load, taper parameter, and eccentricity are the key factors that influence the stability of the system.