变刚度薄壁杆件的动力稳定性

采用有限单元法，研究无阻尼条件下受轴向周期性动力荷载作用的变刚度薄壁杆件动力稳定问题，承受轴向周期性变化外荷载的薄壁杆件，其非线性几何刚度矩阵随着轴向外荷载的变化而改变。因此，所研究的问题在本质上为变刚薄壁杆件的动力稳定性问题。用有限单元离散变刚度薄壁杆件，通过公式变换，将无阻尼条件下变刚度薄壁杆件的振动方程转化为Mathieu方程，应用Matlab程序设计语言编制程序，确定在轴向周期性动力荷载作用下，变刚度薄壁杆件可能发生的相应于弯曲振动，扭转与翘曲耦合振动的动力不稳定区域，并给出相应的结论。

Dynamic Stability of Thin-Walled Member with Variable Rigidity

The dynamic stability of thin walled member with variable rigidity is studied under the condition of no damp and the action of axially and periodically dynamic load. It is studied by adopting finite element method. The thin walled member subjects to axially periodically changed external load,its nonlinearly geometric rigidity matrix changes with the change of axially external load. Thus the problem studied here is essentially the dynamic stability of thin walled member with variable rigidity. The thin walled member with variable rigidity is dispersed by finite element method; and its vibration equation under undamped condition is transformed into Mathieu equation by formala transformation. By applying Matlab programming language, a program is developed for determining regions of dynamic instability which may occur in thin walled member with variable rigidity under the action of axially periodically dynamic load relevant to flexural vibrations, torsion, and warping and coupling vibration. The corresponding conclusions are given finally.