Three-Dimensional Dynamics Analysis of Rotating Functionally Gradient Beams Based on Timoshenko Beam Theory

Abstract

Through the Timoshenko beam theory (TBT), the 3D dynamics of a rotary functional gradient (FG) cantilever beam are investigated. Material capabilities alter continuously throughout the thickness obeying the power law. It is assumed that the Poisson’s ratio does not change. Based on the von Kármán nonlinearity, the governing equation is determined through the Hamilton principle, which includes the Coriolis effects. The couplings among the axial, flapwise and chordwise deformations caused by the usage of the functionally graded materials (FGMs) are revealed. Chebyshev polynomials are utilized to construct trial functions of deformations in the Rayleigh–Ritz method. The centrifugal strengthening effect caused by the rotational motion is described through the nonlinear axial shortening deformations derived from transverse deformations. The influences of the dimensionless angular velocity, FG index and slenderness ratio on vibration characteristics are studied. It is proved that the FG index significantly affects the dynamic response of deformation. For high-frequency external excitation cases, selection of Chebyshev polynomials as trial functions is more stable and effective than other polynomials.