Melnikov analysis of the perturbed thin bar
受扰细杆的Melnikov分析

The dynamical response of one-dimensional metal bar considering Peierls-Nabarro force and viscous effect of solid has been researched. Movement of displacement wave in the bar follows SG type equation. According to "Collective coordinate approach", solution of the SG type equation is assumed as breather-type solution of undisturbed system. Separation between the center of mass of the kink and the anti-kink that make up the breather is researched under perturbation. The partial differential equation is reduced to the ordinary differential equation through describing the Hamiltonian of the system with collective coordinate. The hetero-clinic orbit of unperturbed system is analyzed through potential function and this is used in Melnikov method. Necessary condition for appearance of the cross-sectional heteroclinic point is given to forecast happening of chaotic.