Calculation Of The Natural Frequency Of Rotating Flexible Beam Using The Absolute Nodal Coordinate Formulation

Flexible structures with large range of motion are the typical system in the area of aerospace and machinery. Structural dynamics of the system is an important factor in the system design. For example, helicopter rotor with big range of movement in space, solar panels of satellites and antenna in the process of expand, crawl space manipulator and wind turbines and turbine blades rotating at high speed and so on. Because flexible structures in the bigger range of space movement, generally, have light weight, large deformation characteristics, the overall rigid body movement and deformation are coupling with each other. The deformation of flexible body will have a huge impact to the dynamic behavior of the system. the coupling of deformation and rigid-body movement appears in the same time, is a central feature of flexible multi-body system dynamics. For the above structures, flexible multi-body syatem dynamics must be used as a mechanical model.There are many defects in the traditional flexible multi-body system dynamics, such as the non-linear mass matrix of the system which is generated coupling between the elastic deformation of the flexible body and rigid body displacement which makes it difficult to solve the dynamic equations. The use of discrete flexible beams, such as plate elements and shell elements are non-isoparametric elements, which is difficult in computing the large deformation of flexible systems. The linearization of the dynamic equations of flexible body, which consists with coordinate containing the rotating angular will result in a non-zero strain energy, this means that the kinetic model itself is not accurate. These problems do not exist in the absolute nodal coordinate formulation.Finite element method and continuum mechanics, first introduced in this paper as the theoretical basis of the absolute nodal co-ordinates formulation, are the theoretical basis for the application of the subsequent chapters. Then we study the absolute nodal coordinate method and the difference between the finite element method which shows that, compared to finite element method, using the absolute nodal coordinate method can guarantee the correctness of the physical model. And then we focused on the two-noded, three-dimensional beam element, including how to represent the deformation of the beam cross-section of the movements in space. At last, helicopter blades with wide range of movement in space as the background, model and analyze the rotating flexible cantilever beam, then calculate the natural frequency by the absolute nodal coordinate formulation. The natural frequency becomes larger as the angular velocity turns bigger. Compared to traditional finite element method, the natural frequencies calculated by the absolute nodal coordinate formulation are a little larger.The research shows that the approach proposed in the papaer is valid.