周期激励浅拱分岔研究

研究了一阶和二阶模态在１：２内共振条件下浅拱的复杂动力学行为，指出当周期激励浅拱具有初始静变形时，系统的一阶模态和二阶模态会产生内共振，系统两共振模态之间会产生相互作用，系统的能量会在其低阶和高阶模态之间相互传递，对称破缺后的Ｈｏｐｆ分岔解会通过一系列的倍化周期分岔导致混沌，在混沌域中还会发现稳定的周期解窗口．

BIFURCATION STUDY OF SHALLOW ARCH UNDER PERIODIC FORCE 1)

The complicated dynamics of shallow arch with periodic excitation for the case of 1:2 internal resonance is studied in this paper.It is pointed out that when the arch has an initial deflection,the first order and the second order modes can be in resonance and react to each other;therefore the energy can be transimitted between the low and high modes.The Hopf bifurcation solution after symmetric breaking can lead to chaos by a sequence of period-doubling bifurcations. The steady state periodic solutions can also be found in the paremetric region of chaos.