Vibration and Buckling Analyses of Rotating Axially Functionally Graded Nonuniform Beams

Purpose In this paper, free vibration and buckling characteristics of axially functionally graded, tapered and rotating Euler-Bernoulli and Timoshenko beams with different end conditions are studied. Effects of several parameters are investigated. Methods Tapered beam structural equations and functionally graded material formulations are considered both for the Euler-Bernoulli and the Timoshenko Beam Theories. Material properties of the beam such as elastic modulus, shear modulus, material density are assumed to change continuously in the longitudinal direction as a function of volume fraction and according to a simple power law. Finite Element Method is used to carry out the vibratory and stability characteristic analyses. A two-noded beam element with different degrees of freedom for different beam theories is considered for the solution. Results Effects of several parameters, i.e., rotational speed, hub radius, material properties, power law index parameter, taper ratios, slenderness ratio and boundary conditions are investigated and are displayed in several figures and tables in different combinations. Conclusion Comparisons with the results available in open literature are provided to validate the present procedure. The results reveal that the mentioned parameters have significant effects on the natural frequencies and critical loads of FG tapered beams. Detailed comments are made about the nature of vibratory and stability characteristics in the scope of varying parameters.