弹性支撑浅拱的非线性动力行为分析

RESEARCH ON THE NONLINEAR DYNAMIC BEHAVIORS OF ELASTIC SUPPORT SHALLOW ARCH

本文研究了两端转角均为转动弹簧支撑的铰支浅拱在外激励作用下的非线性动力学行为.基于弹性支撑浅拱的基本动力控制方程,采用多尺度法对内共振进行了摄动分析,并得到了极坐标形式的平均方程.弹性约束的刚度通过特征方程影响结构的自振频率和模态,且与平均方程的相关系数一一对应,文中还以最低两阶模态之间1:1内共振为对象进行了数值分析.结果显示系统存在模态交叉与转向两种内共振形式,另一方面结构参数处于某一范围之内时外激励激发的模态作用可导致出现准周期运动和混沌运动.

The nonlinear dynamic behaviors of an elastic support hinged-hinged uniform shallow arch with two torsional springs located at two ends respectively under external excitation are investigated. Based on the control equation of elastic support shallow arch the muhiple scale method was used for the perturbation analysis of internal resonances, and the averaging equation with its polar form was determined. The influence of the stiffness for elastic boundary, which has a one-to-one relationship to the corresponding coefficient in the averaging equation, can be reflected in the natural frequencies and mode shapes of arch structure via the characteristic equation. Then the 1 ： 1 internal resonance between the lowest two modes was selected as studying object for numerical calculation. The analytical results show that there exist internal resonance forms for both cross and veer in the torsional elastic support shallow arch, further the two-mode interaction induced by external excitation may lead to quasi-periodic oscillation and chaotic motion when the systematical parameters are controlled in a certain range.