Probabilistic analysis of dynamic stability for a rotating BDFG tapered beam with time-varying velocity and stochastic parameters

Abstract

Taking the randomness of parameters into account, probabilistic dynamic stability analysis is carried out for a rotating tapered beam made of bidirectional functionally graded (BDFG) materials with time-dependent rotation speed. Hamilton’s principle is adopted to establish the equations of motion. The dynamic instability problem due to parametrical excitation is solved by Bolotin’s method with higher-order approximation. Considering parameter uncertainty, the stability-based system reliability model with multiple failure modes is clarified and established for probabilistic analysis. The active learning and Kriging-based system reliability (AK-SYS) method is used to estimate the stability-based system reliability of the rotating beam. In addition, an improved stopping criterion for an active learning procedure is introduced in the application of the AK-SYS method to accelerate iteration. Monte Carlo simulation is employed to verify the accuracy and efficiency of the proposed method. Finally, a numerical example is carried out for a parameter study, and the reliability-based sensitivities are investigated to rank the geometric and working parameters according to their importance to the system failure probability. Some useful information is provided for the design and use of rotating beam structures.