高速旋转柔性矩形薄板的动力学建模和近似算法

研究了做高速旋转柔性矩形薄板的耦合动力学建模理论和模态截断法的应用.从连续介质力学中关于柔性薄板的变形理论出发,找出了由于在结构动力学中对无大范围运动柔性薄板的动力学性质影响很小而被忽略的变形量.基于Jourdain速度变分原理,先推导出做高速旋转薄板的动力学连续变分方程,再用有限元法对柔性薄板进行离散.因为用有限元离散时,柔性薄板的广义坐标规模较大,故仿真计算需要时间较长,所以模态截断法被用来缩减广义坐标数量,提高计算效率.此外通过对有限元法和模态截断法的计算结果进行比较,揭示了当矩形薄板作高速旋转时,模态截断法截取低阶模态时会引起误差,选取更高的模态可以用来提高计算精度,通过数值对比得到了模态截断的规律.

Dynamic modeling and modal truncation approach for a high-speed rotating thin elastic rectangular plate

In this paper,dynamic modeling and application of the modal truncation approach(MTA) to a high-speed rotating thin elastic plate are studied.Based on continuum medium mechanics,the foreshortening displacement is kept in the deformation.The equations of a high-speed rotating plate are obtained using Jourdain's velocity variation principle and the finite element method(FEM) and MTA are used for discretization.Since the number of generalized coordinates is large when using the finite element method,MTA is usually used for improving computational efficiency and only lower-order modes are chosen.Furthermore,the comparison of the results obtained by the FEM and MTA shows that in the case of a high-speed rotation,using lower-order modes for modal truncation can cause error, addition of more modes may improve the result.At last,through the numerical comparison,the law for the MTA are revealed.