超音速板颤振问题中的局部分岔现象及某些全局行为

 本文研究了两边简支的二维板在其一个侧面处于超音速流中时的局部稳定性和分岔问题。主要考察了在具有两个零特征值的重退化平衡点附近该系统所发生的不稳定现象和分岔现象。利用动力系统理论中的定性简化方法,发现在某参数平面上,此系统可发生3种不同类型的余维数二分岔现象。对各种分岔现象进行了数值模拟,并用数值分析方法研究了局部分岔解的某些全局行为。

LOCAL BIFURCATIONS AND SOME GLOBAL BEHAVIOR IN A SUPERSONIC PANEL FLUTTER PROBLEM

The stability and bifurcations of a two-dimensional simply supported plate exposed to a supersonic flow are studied. Attention is paid to local behavior of the system near a degenerate equilibrium in which the system has a linear part with double zero eigenvalues. The center manifold and normal form theory are applied to reduce the equation of motion of the system to a simple low-dimensional one near the degenerate system. The main result obtained is that three kinds of codimension and two bifurcations are found on certain parameter plane in that system. Numerical simulations are performed by using the original four-dimensional equation to confirm the analytical results. Some global behavior of the system is also investigated numerically.