流动压力作用下板状叠层结构的分岔与混沌

BUFURCATION AND CHAOS IN A PARALLEL PLATE-TYPE STRUCTURE UNDER FLOWING PRESSURE

研究了轴向流作用下板状叠层结构在非线性弹性支承下的分岔与混沌行为.假设叠层结构中各板在同一时刻有相同的变形,同时考虑三次非线性弹性支承对板状梁的影响,系统的非线性偏微分方程经过转化可表示为一阶的状态方程.数值迭代计算表明,板状叠层结构具有丰富的非线性动力学现象.通过对几个关键系统参数的研究,发现板状梁结构的振动存在复杂的分岔现象和混沌响应,系统是经由经典的倍周期分岔通向混沌的.

The bifurcation and chaotic behavior of a parallel plate-type structure with nonlinear elastic support in axial flow were investigated. By assuming that all the plates have the same deflections at any instant, and considering the effect of cubic elastic spring on the plate-type beam, the partial differential equation of the system was transformed to the first-order-state equation. Based on this, numerical simulations show that the parallel plate-type structure has rich nonlinear dynamics. The complex bifurcations and chaotic motions were detected by analyzing several key system parameters, and the route to chaos was shown to be via classical perioddoubling bifurcations.