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.
Highlights
During the past decade, many researchers have focused on the vibration characteristics of stationary and rotating functionally graded beams employing various methods of analysis
Variation in taper ratios affects the frequency parameters of the beam
The frequency parameters are observed to increase with an increase in hub radius
Summary
Many researchers have focused on the vibration characteristics of stationary and rotating functionally graded beams employing various methods of analysis. The present study is aimed at studying the free vibration characteristics of functionally graded double-tapered rotating cantilever beam with symmetric cross section. The design as well as analysis and estimation of dynamic characteristics of these structures is very difficult. Centrifugal inertia force due to rotation is one of the critical factors in evaluating the dynamic characteristics of the rotating structures. Many researchers have investigated the dynamic characteristics of the homogeneous rotating beams in the past. Tsai et al (2011) investigated the free vibrations for inclined Euler beam rotating at constant angular speed using the co-rotational finite element method combined with floating frame method. The equations of motion were derived in terms of an inertial global coordinate system using
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