Geometrically nonlinear vibration analysis of rotating pre-twisted shell blades with a high rotating speed

A geometrically nonlinear dynamic model is developed for the vibration analysis of rotational pre-twisted shell-type blades with a high rotating speed. The present model is based on the Carrera unified formulation and 3-D elasticity shell theory considering the geometrical non-linearities. In using the assumed-modes method to produce an approximate solution, the displacement variables of the non-self-adjoint structure are constructed by a linear combination of the modified Fourier series. The solving process contains two stages. For the first stage, a prior large deflection analysis is carried out for the rotational pre-twisted shell-type blades subjected to a high centrifugal load. An iteration technique based on the Newton-Raphson method is employed to solve the nonlinear steady equilibrium equations that are derived by using the principle of virtual work. In the second solving stage, Hamilton's principle is employed for the derivation of the nonlinear governing equations of motion, which are linearized and solved on the basis of the equilibrium operating condition. Two representative numerical examples are pre-sented and discussed, which include the rotating twisted plates and twisted cylindrical shells with different radii of curvature. Comprehensive comparisons and verifications with the previously published data demonstrate that the developed formulation has excellent convergence properties and the capabilities of accurately predicting the vibration characteristics of the high-speed rotating pre-twisted shell-type blades. The influences of the rotational speed, hub-radius ratio, pre-twisted and presetting angles on the vibration characteristics of the shell-type blades are investigated. Meanwhile, the ranges of applicability of the linear and nonlinear models are assessed for the dynamic analysis of high-speed rotating shell-type blades.