中文摘要：

分析了当外激励频率等于吸振器的固有频率且是曲轴的固有频率的2倍的条件下，系统发生1：2内共振时的吸振器的分岔特性。首先由复规范形法得到了平均方程，结果表明曲轴的零点不是系统的唯一解，系统还可能有其他的解。再由奇异性理论分析了当曲轴的振幅为零时吸振器系统的分岔特性。得到了吸振器系统的转迁集和转迁集上相应的分岔图。对吸振器系统分岔行为研究，有助于内燃机曲轴的吸振器参数的优化设计。

英文摘要：

Study deeply the dynamical character of crankshaft-vibration absorber of the internal combustion engineering is important. The system is studied when the one-to-two internal resonance occurred under the condition of the frequency of the excitation equal to the frequency of the absorber and coincidently is the double time of the crankshaft of the internal combustion engineering. First the normal form of the system is obtained by the complex normal form method and the average equation is derived from the normal form of the system. The result shows that the zero solution of the crankshaft system is not the unique, the other solution maybe exist also. Then the bifurcation n character of the absorber is studied when the crankshaft is at zero position by the singularity theory. At the zero position of the crankshaft system, the transition sets and the perturbed persistent bifurcation diagrams of the absorber system are obtained. The study is possible to optimize the parameters of the vibration absorber of the crankshaft of the internal combustion engineering.