Dynamic Analysis Of Flexible Rotating Beam System With Extended Members

With the progress of today’s technology, flexible manipulator technology is widely used in industrial production and aernspace engineering. At the same time in order to be able to get a larger space for the activities but their own space is very small, whth flexible components of the flexible manipulator system have been used widely and replace the tradional arm system. The dynamic behavior very complicated of the flexible manipulator system with the extension member because of its time-varying and flexible. In this paper, absolute nodal coordinate formulation is applied to establish the dynamic model of the flexible rotating beam system with extensional members, and the dynamic characteristics of those mechanisms are analyzed. The main works of this paper are as follow:(1) Based on the absolute node coordinate method, the absolute position vector, node coordinates of any point of the Euler-Bernoulli beam element in the absolute coordinate sytem are described The shape function matrix, mass matrix, the generalized stiffness matrix and the elastic force of the beam element are calculated,then establish the the dynamic equation of the bcam element.(2) According to the absolute node coordinale formulation, a variable length Euler-Bernoulli beam element is adopted for the axial extension cantilever bearn,and its kinetic equation is cstabli shed by using the virtual work principle. The same results are obtained by calculation,its instructions that the variable length beam element model proposed in this papar correct.Then the tip deflection response of the free-vibrated cantilever beam are analyzed under different structural parameters (elastic modulus, density), different spreading rules (constant speed, uniform accelcration) land different stretchirng speeds. The results show that the smaller the stretching speed, the higher the elastic modulus, the lighter the mthe higher the transverse vibration frequency of the end of the cantilever beam.(3) The dynamic characteristics of the system which contain axially extending cantilever beam and the rotating flexible beam are studied. Based on the theory of absolute nodal coordinate method, the dynamic equation of the cantilever beam and the rotating flexible beam system is established by introducing the Lagrangian multiplier. The dynamic response of the system with axial extension cantilever and rotating flexible beam is obtained by the method called Newmark -β .With different spreading rules(constant speed, uniform acceleration),the dynamic response of the cantilever beam with different elastic modulus and the rotating flexible beam which in the system are discussed. The results show that the acceleration of the extension cantilever beam have a great influence on the absolute displacement in the vertical direction of end of the rotating beam, and also have effect on the tip transverse displacement in the satellite coordinate system of the rotating beam. And when the cantilever beam is stretched uniformly,its own deflection is smaller than the deflection of the cantilever beam when its uniform acceleration stretch.