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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 response of flat arch structure under simple harmonic load (simulated wind load) is analyzed by catastrophe theory. The nonlinear vibration equation is obtained from the partial differential equations of motion of the flat arch under the assumption, and the incremental harmonic method is further used as the standard form of the cusp catastrophe model. A series of calculation data are used to quantitatively analyze the nonlinear response of the flat arch nonlinear response Complex features, including the characteristics of stable regions and sudden jumps, as well as the impact of various parameters. The results show that there is a sudden change in the nonlinear dynamic response of the flat arch structure. The span, sag height, load and damping ratio all have influence on the stability of the flat arch. Reasonable choice of parameters can reduce the nonlinear effect and stabilize the structure.