For fixed damping and fixed excited frequency the motion of the beam under small amplitude of force is periodic, but becomes chaotic through period doubling bifurcation with increase of the force.
Conditions for the existence of solutions to periodic and isolated waves of limited amplitude are directly obtained based on qualitative geometric theory for ordinary differential equations.
利用微分方程解的几何定性理论，直接得到该方程存在有限振幅的周期波与孤立波解的存在条件。
3
Some stabilized different periodic orbits were obtained in the mode of single limited amplitude, and simulation results are in accord with the experiment.