摘要
本文运用FEM将受周期轴向动载荷的铁木辛柯交叉梁系的动力稳定性控制方程化为Mathieu-Hill型方程,然后用谐调平衡方法得到临界频率方程。针对临界频率方程所代表的3类不同问题分别用子空间迭代法和改进的Lanczos方法进行求解,求出了具有一根交叉构件、不同主向梁数目的正交铁木辛柯梁系的动力不稳定区。计算结果显示了主向梁数目和载荷参数对动力不稳定区的影响。
In this paper the control equation of the dynamic stability of the Timoshenko cross beams which undergo the periodic axial dynamic load is transformed into Mathieu—Hill type equation by using the finite element method. Then the critical frequency equation is obtained with the harmonic balance method. To solve three kinds of different problems represented by the critical frequency equation, the Subspace Iteration Method and the modified Lanczos Method are used respectively, and the dynamic instability region of the orthogonal Timoshenko beams consisting of one cross-component and different number of main beams is obtained. The calculation results show the effect of the number of main beams and the load parameters on the dynamic instability region.
关键词
交叉梁系
动力稳定性
不稳定区
Timoshenko cross beams
dynamic stability
instability region
