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.

考虑到参数的随机性，对由双向功能梯度（BDFG）材料制成的随时间变化的旋转锥形光束进行了概率动态稳定性分析。采用汉密尔顿原理建立运动方程。通过具有高阶近似的Bolotin方法解决了因参量激励而引起的动态不稳定性问题。考虑参数不确定性，建立并建立了具有多种失效模式的基于稳定性的系统可靠性模型，用于概率分析。主动学习和基于Kriging的系统可靠性（AK-SYS）方法用于估计旋转梁基于稳定性的系统可靠性。此外，在AK-SYS方法的应用中引入了一种改进的主动学习过程停止准则，以加快迭代速度。蒙特卡罗仿真被用来验证该方法的准确性和效率。最后，通过一个数值例子进行了参数研究，并研究了基于可靠性的灵敏度，以根据几何参数和工作参数对系统故障概率的重要性进行排序。为旋转梁结构的设计和使用提供了一些有用的信息。并研究了基于可靠性的敏感性，以根据几何参数和工作参数对系统故障概率的重要性对其进行排名。为旋转梁结构的设计和使用提供了一些有用的信息。并研究了基于可靠性的敏感性，以根据几何参数和工作参数对系统故障概率的重要性对其进行排名。为旋转梁结构的设计和使用提供了一些有用的信息。