The global bifurcation and chaos for the coupling between longitudinal and transverse vibration of a thin elastic plate in large overall motion

This paper presents the global bifurcation and chaotic behavior for the coupling of longitudinal and transverse vibration of a thin elastic plate in large overall motion. First the parametric equations of the homoclinic orbits of such a system is obtained. Then, by using the Melnikov method and digital computer simulation. the behavior of bifurcation and chaos of this vibration system is investigated in the cases of different resonances. The obvious difference between the transverse vibration and the coupling of transverse and longitudinal vibration is also shown.The project supported by the National Natural Science Foundation of China.