Dynamic Characteristics Analysis Of Rotating Curved Beams And Shells Based On Absolute Nodal Coordinate Method

Many rotating machines,such as wind turbine blades,helicopter rotors,Aeroengine Blades and steam turbine generator blades,belong to the system of flexible blades consolidated on rigid rotating base.Considering the size of blade aspect ratio and the curvature change of blade surface,the above system can be simplified as a rotating central rigid body-flexible curved beam or shell model.Dynamic analysis.Because of the strong centrifugal force produced by the rotating blade and the complex coupling effect between the flexible blade and the rotating rigid base,and the coupling between the large-scale motion and the elastic deformation of the blade,the conventional dynamic model can not solve the complex coupling effect mentioned above and the non-linear dynamic characteristics of the rotating blade in order to analyze the dynamic characteristics of the rotating blade.For this kind of problem,it is necessary to develop a dynamic model based on the non-linear finite element method.Considering the above engineering background and research significance,the dynamic equations of rotating curved beam and shell are established based on absolute node coordinate method,and the corresponding dynamic characteristics are analyzed.The main research work and achievements of this paper are as follows:Based on the absolute nodal coordinate method and Green-Lagrange strain tensor,ANCF curved beam element and ANCF thin shell element are derived by geometrically accurate analysis.On the basis of virtual work principle,the dynamic equation of rotating central rigid body-flexible curved beam is established,and the dynamic equation of rotating central rigid cylinder-thin shell is established according to Hamilton principle.The correctness of the model is verified by several static examples.Considering the boundary conditions of rotating curved beams and shells,the constrained equations are transformed into constrained equations.By Lagrange multiplier method,the constrained equations are substituted into the dynamic equations of the model,and the dynamic equations in the form of Index-3 are composed of the constrained equations.The solving algorithms of the equations are summarized and pointed out.Based on the rotating central rigid body-flexible curved beam dynamic equation,the corresponding dynamic solution software is developed,and the influence of initial curvature and concentrated mass on the end deformation of the rotating curved beam is analyzed.The rotating curved beam is equivalent to the form of non-rotating curved beam plus centrifugal force by Darumbell principle.The perturbation equation of the system is obtained by linear perturbation processing.The static equilibrium state of the system is obtained by quasi-static method.The frequency steering and mode switching of the rotating curved beam are studied and analyzed in the perturbation equation.Based on the dynamic equation of rotating rigid cylinder-flexible shell,the difference of dynamic response between rotating thin plate and thin shell is analyzed.The perturbation equation of the rotating shell is obtained by the D'Alembert principle and the linear perturbation treatment.The effects of thickness-length ratio and rotating angular velocity on the natural circular frequency of the thin plate are mainly studied.Finally,the frequency steering and mode switching of rotating thin plate are analyzed.