Isogeometric vibration analysis of functionally graded material pre-twisted blades with three-dimensional theory

In this paper, the free vibration characteristics of a rotating functionally graded material (FGM) pre-twisted blades are investigated by the isogeometric method based on the three-dimensional (3D) theory. The effects of Coriolis force, centrifugal softening, and centrifugal rigidity of the FGM pre-twisted blades are considered in this vibration analysis model. The material properties of the FGM pre-twisted blades are assumed to change continuously along thickness direction. It is easy to satisfy the weak form requirements of the vibration control equation of the FGM pre-twisted blades by using the NURBS functions. Then, the dynamic equation of the pre-twisted rotating blades can be derived by using the Hamilton's variational principle. Finally, a standard eigenvalue equation is obtained through discretizing equations and expanding dimensions. Numerical examples showed that the current formulation has fast convergency and good accuracy. Additionally, the influence of installation angle, pre-twisted angle, variable cross-section, material properties and rotating speed on the vibration characteristics of the FGM pre-twisted blades under rotating conditions is explored in detail. The work can also shed some new lights on the vibration behaviors of pre-twisted blades composite materials.