Flapwise bending vibration analysis of functionally graded rotating double-tapered beams

Abstract

During the past decade, many researchers have focused on the vibration characteristics of stationary and rotating functionally graded beams employing various methods of analysis. Hitherto, the studies have been mainly confined to uniform beams. Hence, the present study is aimed at studying the free vibration characteristics of functionally graded double-tapered rotating cantilever beam with symmetric cross section. This paper presents a method which considers the deformation variables to determine flapwise bending vibrations of rotating functionally graded doubletapered beam attached to a rigid hub. The tapered beam is characterized by continuously variable Young’s modulus along the thickness direction according to a power law. The equations of motions are derived using hybrid deformation variables employing Lagrange’s approach. Rayleigh-Ritz method is used to evaluate the frequencies of the beam. The effect of several parameters such as material composition gradient, taper ratios, hub radius ratio and rotational speed on flapwise bending natural frequencies of tapered beams are investigated. Variation in taper ratios affects the frequency parameters of the beam. The frequency parameters are observed to increase with an increase in hub radius. The power law index has negligible influence on the trend of flapwise bending natural frequencies with an increase in angular speed for different taper ratios.