Sensitivity of the dynamic behaviour of random rotating Timoshenko beams to system parameter changes

Abstract

A computational procedure has been developed to evaluate the influence of the random parameter changes to the dynamic behaviour of rotating Timoshenko beams. Based on the mean-centred second-order perturbation technique and non-linear eigenvalue analysis, the stochastic modal analysis is developed for stochastic sensitivity measures of rotating beams with uncertain material and sectional properties, uncertain geometric parameters and a random rotating velocity. A consistent linearization of the fully geometrically non-linear 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 non-linear eigenvalue analysis to obtain the natural frequencies and vibration modes. A sensitivity analysis is performed to identify the important factors influencing the variation in frequency responses. To establish the validity of the present probabilistic approach, numerical examples with results obtained by using the Monte Carlo method are given for comparison.