The probabilistic approach for rotating Timoshenko beams

Abstract

A stochastic modal analysis is developed for reliability studies of rotating beams with uncertain material and sectional properties, uncertain geometric parameters, and random rotating speed. The formulation of the stochastic modal analysis is based on mean-centered second-order perturbation technique and nonlinear eigenvalue analysis. A consistent linearization of the fully geometrically nonlinear beam theory and the virtual work principle are used to derive the governing equations of a rotating Timoshenko beam, and a power series method is employed for the nonlinear eigenvalue analysis to obtain the natural frequencies and vibration modes for free vibration. The effects of variations in material and sectional properties, geometric parameters, and rotating speed on variation in natural frequency are investigated. A sensitivity analysis is performed to identify the important factors on the variation of frequency responses. Here, a definition of resonant failure of a rotating beam is introduced and considered as the limit-state function in the reliability assessment of the rotating beams. To establish the validity of the present probabilistic approach, numerical examples with results obtained by using the Monte Carlo method are given for comparison.