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

Abstract

Background: 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. Material and Method: 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. Results: 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. Conclusions: 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.

Quasi-3D beam models for the computation of eigenfrequencies of functionally graded beams with arbitrary boundary conditions

“…Maganti and Nullari [27] investigated the free vibration analysis of pre-twisted rotating FG beams by using Rayleigh-Ritz method. The same authors [28] studied the flapwise bending vibration analysis of functionally graded rotating double-tapered beams. Free vibration of FG Timoshenko beams with through-width delamination have been investigated by Li and Fan [29].…”

Free vibration analysis of functionally graded double-tapered beam rotating in thermal environment considering geometric nonlinearity, shear deformability, and Coriolis effect

“…Apart from this, the free vibration behaviors of rotating FGM tapered beams in ambient condition are reported in Maganti and Nalluri. 36,37 But, in those literatures, the mathematical model was based on Euler-Bernoulli beam theory compared to the present study being developed on an improved mathematical model involving Timoshenko beam theory, as explained in the following paragraph.…”

The nonlinear thermomechanical vibration of a functionally graded beam on Winkler-Pasternak foundation

“…Maganti et Nalluri [13] considered the deformation variables to determine flapwise bending of rotating functionally graded double tapered beam attached to a rigid hub. The equations of motions are derived using hybrid deformation variables employing Lagrange's approach and Rayliegh-Ritz method is used to evaluate the frequencies of the beam.…”