The Discretization Methods of a Rotating Flexible Cantilever Beam
The dynamics of a rotating flexible cantilever beam is investigated by using assumed mode method, finite element method and Bezier curve interpolation method in this paper. The longitudinal deformation and the transverse deformation of the flexible beam are considered and the coupling term of the deformation which is caused by transverse deformation is included in the expression of longitudinal deformation. The assumed mode, finite element and Bezier interpolation are used to discretize the deformation of the flexible beam, and then the dynamics equations are built by Lagrange equation, and a software package for the dynamic simulation of the rotating cantilever beam is developed. Two cases are considered in the simulations. One is the dynamics study which the external rotating torque is known, another one is that a rotating fixed axis flexible beam falls with gravity. According to the simulation results, assumed mode, finite element and Bezier interpolation method can be well used for discretizing the deformation of the flexible beam; the computational efficiency of finite element method is the lowest, and Bezier interpolation method is the highest; the calculation accuracy of the assumed mode method is lower than the Bezier interpolation method.
Chunliang Zhang and Paul P. Lin
J. H. Fan and D. G. Zhang, "The Discretization Methods of a Rotating Flexible Cantilever Beam", Applied Mechanics and Materials, Vols. 226-228, pp. 697-707, 2012