This study provides a quasi-three-dimensional (quasi-3D) dynamic model for rotating pre-twisted functionally graded (FG) blades based on the three-dimensional elasticity shell theory and Carrera unified formulation. The material properties of the pre-twisted FG blades alter continuously in the direction of the thickness. The boundary conditions (clamped-end and free-edge) are realized by utilizing the well-known penalty method. Initial centrifugal stress field due to the high rotating speed is determined by two centrifugal stress solving methods, direct integration of centrifugal forces (DICF) and static analysis under centrifugal forces (SACF). The modified Fourier spectral approach is utilized to construct the displacement variables of the higher-order configurations. Eigenvalue problems are obtained by using the Hamilton's principle on the base of the kinetic, strain, centrifugal potential and boundary potential energy. The results of the theoretical model display a good agreement with the reference data and FEM results. Parametric studies are then performed to assess the applicability of the centrifugal stress solving methods and investigate the effects of the centrifugal shear stress, rotating speed, pre-twisted angle, penalty factors as well as the volume fraction index on the vibration characteristics of the pre-twisted FG blades. It is expected that the quasi-3D solutions for the rotating pre-twisted FG blades will serve as benchmarks in future researches.

这项研究基于三维弹性壳理论和Carrera统一公式，为旋转预扭曲功能梯度（FG）叶片提供了一个准三维（quasi-3D）动力学模型。预扭曲的FG叶片的材料特性沿厚度方向连续变化。边界条件（钳端和自由边缘）是通过使用众所周知的罚分法实现的。高转速引起的初始离心应力场由两种离心应力求解方法确定，即离心力的直接积分（DICF）和离心力下的静态分析（SACF）。改进的傅立叶谱方法用于构造高阶结构的位移变量。特征值问题是通过使用汉密尔顿算子获得的 的原理基于动能，应变，离心势和边界势能。理论模型的结果与参考数据和有限元结果具有很好的一致性。然后进行参数研究，以评估离心应力求解方法的适用性，并研究离心切应力，转速，预扭转角，罚因子以及体积分数指数对预应力振动特性的影响。扭曲的FG刀片。预计用于旋转预扭曲FG叶片的准3D解决方案将作为未来研究的基准。然后进行参数研究，以评估离心应力求解方法的适用性，并研究离心切应力，转速，预扭转角，罚因子以及体积分数指数对预应力振动特性的影响。扭曲的FG刀片。预计用于旋转预扭曲FG叶片的准3D解决方案将作为未来研究的基准。然后进行参数研究，以评估离心应力求解方法的适用性，并研究离心切应力，转速，预扭转角，罚因子以及体积分数指数对预应力振动特性的影响。扭曲的FG刀片。预计用于旋转预扭曲FG叶片的准3D解决方案将作为未来研究的基准。