A quasi-3D dynamic model for free vibration analysis of rotating pre-twisted functionally graded blades

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. ? 2021 Elsevier Ltd. All rights reserved.