Higher-order stability analysis of a rotating BDFG tapered beam with time-varying velocity

Abstract

In this paper, dynamic stability analysis is carried out for a rotating tapered cantilever beam made of bi-directional functionally graded (BDFG) materials with time-dependent rotating velocity. Rayleigh-Ritz method is employed to obtain the eigenfrequencies and mode shapes of the beam. Hamilton’s principle and the Galerkin method are adopted to establish the equation of motion with periodic coefficients. Dynamic instability problem due to the periodic rotating velocity is solved by Bolotin’s method with higher-order approximation. Both the sub-harmonic and harmonic parametric instability regions are investigated. Floquet theory is applied to verify the dynamic instability boundaries. The results indicate that the typical first-order approximate Bolotin’s method cannot meet the accuracy requirements of dynamic instability analysis for rotating BDFG tapered beam, and a second-order approximation is needed to improve computation accuracy. The effects of mean rotating velocity, hub radius, dynamic amplitude factor, material FG indexes and taper ratio on the natural frequencies and dynamic instability characteristics of the rotating BDFG tapered beam are discussed under different parameters.