This paper deals with the problems of free vibration, buckling, and dynamic stability of rotating pre-twisted functionally graded carbon nanotube reinforced composite (FG-CNTRC) imperfect beams in thermal environment. The imperfect beam contains different modes of geometric imperfections such as sine, global, and local modes, and it is restrained by an elastic root. Three types of CNTs distributions including FG-X, UD, and FG-O distributions are considered and the material is temperature-dependent. First, bending–bending coupled governing equations are established through the Hamilton’s principle based on the Euler–Bernoulli beam theory. By setting different parameters, the governing equations can solve the problems of free vibration, buckling, and dynamic stability of the beam. Then, the differential quadrature method (DQM) is employed to get the discrete equations and numerical solutions of the natural frequency, critical buckling load, and instability region. Finally, parametric studies are carried out to present the effects of hub radius, rotating speed, material properties, geometric imperfections, and rigidity of the elastic root on the natural frequencies, critical buckling load, and instability regions. Results show that the elastic root and imperfection mode have obvious influence on the instability regions.

本文讨论了在热环境下旋转的预扭曲功能梯度碳纳米管增强复合材料（FG-CNTRC）不完全梁的自由振动，屈曲和动态稳定性问题。不完善的梁包含不同的几何缺陷模式，例如正弦，整体和局部模式，并且受弹性根约束。考虑了三种类型的CNT分布，包括FG-X，UD和FG-O分布，并且该材料取决于温度。首先，基于欧拉-伯努利梁理论，通过汉密尔顿原理建立弯曲-弯曲耦合控制方程。通过设置不同的参数，控制方程可以解决梁的自由振动，屈曲和动态稳定性问题。然后，采用微分求积法（DQM）得到固有频率，临界屈曲载荷和不稳定性区域的离散方程和数值解。最后，进行参数研究以显示轮毂半径，旋转速度，材料特性，几何缺陷和弹性根部的刚性对固有频率，临界屈曲载荷和不稳定性区域的影响。结果表明，弹性根和缺陷模式对不稳定性区域具有明显的影响。固有频率，临界屈曲载荷和不稳定性区域上的弹性根的刚度和刚度。结果表明，弹性根和缺陷模式对不稳定性区域具有明显的影响。固有频率，临界屈曲载荷和不稳定性区域上的弹性根的刚度和刚度。结果表明，弹性根和缺陷模式对不稳定性区域具有明显的影响。