A probabilistic analysis for vibration of rotating beams with uncertain parameters

In this paper, the material properties, sectional properties, rotating speed and the boundary condition of beam are treated as random variable. A Ritz method is used to derive the eigenvalues equation of the rotating beam with uncertain parameters. A matrix perturbation technique is employed to obtain probabilistic characters of the natural frequencies and vibration modes for free vibration. The sensitivity analysis is performed to study the influence of parametric changes on the variation of nature frequencies. The effects of variation in material propertied, rotating speed and the joint stiffness on the deterministic part of natural frequencies and vibration modes, the covariance and the coefficient of variance (COV) for the nature frequencies are investigated. A numerical example is studied by the present method and the Monte Carlo simulation to establish the validity of the present method.