非线性弹性杆中MKdV应变孤波的演变

EVOLUTION OF MKdV STRAIN SOLITARY WAVES IN A NON-LINEAR ELASTIC ROD

本文利用微扰论方法,从连续谱方面详细研究了非线性弹性杆中的粘弹性阻尼对杆内纵向MKdV应变孤波传播的影响.结论指出:耗散的存在不仅使孤波的能量发生耗散,高度随时间变矮,速度减慢,而且在初时刻,孤波的后面会随时间逐渐生长出一个振荡形式的尾迹.

By using perturbation theory,authors have studied the influenceof the viscoelastic damping on the propagation of MKdV strain solitarywaves in a nonlinear elastic rod in continious spectrum. The results showthat the viscoelastic damping lead to main effects on a strain solitarywave as follows:besides deforming its shape,decelerating its velocity,dissipating its energy, in initial time, the solitary wave will have a'tail' which is a small amplitude vibrating wave packet with growinglength.