基于突变理论的扁拱结构非线性动力稳定分析

Nonlinear Dynamic Stability Analysis of Shallow Arches Based on Catastrophe Theory

通过突变理论分析扁拱结构在简谐荷载(模拟风荷载)作用下的非线性响应。在假定条件下由扁拱的偏微分运动方程得到非线性振动方程,采用增量谐波法进一步等效为尖点突变模型的标准形式;通过一系列计算数据定量分析了扁拱非线性响应的复杂特征,包括稳定区域和突跳的特点以及各参数的影响。结果表明:扁拱结构的非线性动力响应存在突变现象,跨度、矢高、荷载、阻尼比对扁拱的稳定区域均有影响,合理地选择参数可减小非线性的影响而使结构稳定。

The nonlinear dynamic stability of shallow arches is analyzed by the catastrophe theory under the action of simple harmonic load （Analog wind load）. The nonlinear vibration equation is obtained from the partial differential motion equation under some assumptions, and is equivalent to the standard form of cusp catastrophic model by using incremental harmonic balance method. The complex feature of nonlinear response is analyzed quantitatively, included the characteristics of stable region and snap-through and the effects of parameters. The results show that the nonlinear dynamic response of shallow arches has the phenomenon of catastrophe. Stable region is effected by span, rise, load and damping ratio respectively, an appropriate option of parameters can decrease the influences of nonlinear and stabilize the structure.