The bifurcation dynamics of shallow arch which possesses initial deflection under periodic excitation for the case of 1:2 internal resonance is studied in this paper. The whole parametric plane is divided into several...The bifurcation dynamics of shallow arch which possesses initial deflection under periodic excitation for the case of 1:2 internal resonance is studied in this paper. The whole parametric plane is divided into several different regions according to lire types of motions; then the distribution of steady state motions of shallow arch on the plane of physical parameters is obtained. Combining with numerical method, the dynamics of the system in different regions, especially in the Hopf bifurcation region, is studied in detail. The rule of the mode interaction and the route to chaos of the system is also analysed at the end.展开更多
文摘The bifurcation dynamics of shallow arch which possesses initial deflection under periodic excitation for the case of 1:2 internal resonance is studied in this paper. The whole parametric plane is divided into several different regions according to lire types of motions; then the distribution of steady state motions of shallow arch on the plane of physical parameters is obtained. Combining with numerical method, the dynamics of the system in different regions, especially in the Hopf bifurcation region, is studied in detail. The rule of the mode interaction and the route to chaos of the system is also analysed at the end.
