Based on the Absolute Nodal Coordinate Formulation %0 Journal Article %D 2017 %J Journal of Shanghai Jiao Tong University %R 10.16183/j.cnki.jsjtu.2017.10.004 %P 1174-1180 %V 51 %N 10 %U {https://xuebao.sjtu.edu.cn/CN/abstract/article_41386.shtml} %8 2017-10-31 %X The boundary features of the variable crosssection beams are taken into consideration and the stiffness matrix is derived based on the nonlinear continuum mechanics. A dynamic model of the beam is established by using the absolute nodal coordinate formulation. The statespace equation of the beam during motion is developed. Based on the Lyapunov theory a criterion of the motion stability of the flexible beams is proposed, and the effects of material properties and variable crosssections are investigated. The results indicate that with a small elastic modulus, the variable crosssection beam shows a better stability than the constant crosssection beam. As the elastic modulus increases, the stability of the constant crosssection becomes better than that of the variable crosssection beam. When the elastic modulus reaches a certain value, the motion of constant crosssection beam becomes stable.