一种分析旋转梁振动的梁柱有限元

针对旋转柔性梁的弯曲振动问题,提出了一种高精度的有限元——梁柱元。根据旋转梁弯曲时与梁柱相同的受力特点,推导了梁柱元弯曲变形的形状函数,采用传递矩阵方法导出了单元的刚度矩阵及相应的一致质量阵。证明了梁柱元刚度矩阵中各元素的泰勒展开式前两项正好是采用常规弯曲梁元形状函数得到的弹性刚度矩阵和几何刚度矩阵对应的元素的和,因而采用梁柱元分析旋转梁元弯曲振动问题具有很好的精度。对铰支和固支旋转梁振动分析的数值算例也证明了这个结论。

Beam-Column Element for Vibration Analysis of Rotating Beam

In this paper, a new type of beam-column element is proposed for the finite element analysis of vibration of rotating beam. According to the mechanical property of rotating beam, the static deflection of beam-column is adopted as the shape function of beam-column element and the effect of centrifugal force of the element is taken into account in the shape function. The stiffness matrix of beam-column element is derived using transfer matrix approach. It is also verified that the first two terms of the Taylor expansion of the beam-column stiffness matrix are just the elastic stiffness matrix and geometrical stiffness of conventional beam finite element with centrifugal force effect, respectively. Hence it is expected that the present element can give results with higher accuracy. Numerical examples are also presented to show the accuracy of vibration analysis using this type of element.