In this paper, an enhanced solid finite element formulation for rotor dynamics analysis is presented. The element kinematics is first defined with a Total Lagrangian formulation in order to account for possible centrifugal stiffening effect and its associated pre-stress deformation. The novelty of the three-dimensional element proposed in this study is then to correctly consider the effect of inertia due to small rotational deformation occurring around the pre-stressed equilibrium position. The rotational motion is characterized by interpolation of the translational degrees of freedom of the element. The accuracy and convergence of the proposed finite element are tested on several numerical examples consisting of a rotating rigid disk and a rotating Timoshenko beam with different slenderness ratios. All results agree well with analytical solutions excerpted from literature and demonstrate the usefulness and applicability of the proposed finite element formulation.

在本文中，提出了一种用于转子动力学分析的增强型实体有限元公式。单元运动学首先用总拉格朗日公式定义，以考虑可能的离心硬化效应及其相关的预应力变形。本研究中提出的三维单元的新颖之处在于正确考虑了由于在预应力平衡位置周围发生的小旋转变形而产生的惯性效应。旋转运动的特征在于元素平移自由度的插值。在由旋转刚性盘和具有不同长细比的旋转铁木辛柯梁组成的几个数值例子上测试了所提出的有限元的准确性和收敛性。