Influence of the initial breather on the perturbed thin bar

摘要

Considering Peierls-Nabarro force and viscous effect of solid, the dynamic response of onedimensionalfinite thin bar is researched under Neumann boundary condition and harmonically driving. TheSine-Gordon type equation has been derived to describe nonlinear wave propagating in this bar. When theinitial condition is given as a single-hump Sine-Gordon breather, variation of spatial structures and long-timeasymptotic behaviors of the bar with the phase of initial breather is studied numerically. Chaotic effect wouldtake place with certain driving amplitude and initial phase.We found that the phase of initial breather is also animportant factor in affecting the motion of this system.