考虑阻尼的变刚度薄壁杆件动力稳定

采用有限单元法，研究有阻尼条件下，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，即本质为变刚度薄壁杆件的动力稳定性问题。用有限单元法离散变刚度薄壁杆件，通过公式变换，将有阻尼条件下变刚度薄壁杆件的振动方程，转化为Mathieu方程。同时应用Matlab程序，设计语言编制程序求解。通过算例求得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。指出由于薄壁杆件的动力不稳定区域具有连续的激发区域，阻尼的增加并不能绝对地抑制振幅无限增长。对薄壁杆件的共振，以及动力不稳定的参数激发振动进行分析比较，指出它们表现形式虽然有相似之处，却是完全不同的两种振动形式。提出防止薄壁杆件动力不稳定的发生，比防止薄壁杆件的共振更复杂。在许多情况下，通用的减振和隔振方法，对于参数激发振动的动力不稳定是无效的。

Dynamic Stability of Thin-Walled Member with Variable Stiffness in Consideration of Damping

Regarding to a thin walled member with variable stiffness, the dynamic stability is studied by finite element method under the condition of bearing an axial periodic load and having damping. The nonlinear geometric stiffness matrix of this thin walled member bearing axial and periodically changing external load changes with the change of axial external load, so the problem to be studied is essentially dynamic stability of thin walled member with variable stiffness. Finite element method is used for the discretion of thin walled member with variable stiffness. By formula transformation, the vibration equation of thin walled member with variable stiffness in the presence of damping will change into Mathieu equation, Matlab programming language is applied to work out program for solving. By examples of computation, the site of dynamic instability is solved to be occured possibly in the thin walled member with variable stiffness corresponding to its fluxural vibration, torsion warping, and coupled vibration. The author believes in that the increase of damping can not completely inhibit the infinite growth of amplitude due to the presence of continuous excitation site in the region of dynamic instability in this thin walled member. By analysing and comparing parametric excitation vibrations of resonance and dynamic instability, the author believes in that they are two quite different forms of vibrations despite similar in form of expression. To prevent the occurrence of dynamic instability in this thin walled member is still more complex than to prevent resonance in it. The general methods to attenuate and to isolate vibration are ineffective in many occasions.