非线性弹性杆中孤波的演变

Evolution of Solitary Waves in a Non-Linear Elastic Rod

1.基本方程非线性弹性杆内的纵向应变波的广义Korteweg-de Vries-Burgers方程为(1·1)为了明确起见,本文研究n=2的硬非线性材料(软非线性材料μ<0仿此处理)情形,此时μ>0.作变换x→(6μ)^(1/2)x,t→6(6μ)^(1/2)t,u→-u,(1·1)变为(1·2)其中ε=(6/μ)^(1/2)δ,方程(1·1)与(1·2)右端项为粘弹性阻尼的贡献,右端第三项来自横向惯性所引起的应力.当忽略耗散时,ε=0,(1·2)就是通常的KdV方程,此时杆内有纵向传播的稳定孤波.本文研究当耗散较小(ε<<1),但不可忽略时,它对应变孤波运动的影响,此时(1·2)看作是含微扰的KdV方程.

In this paper, by using the method of perturbation theory, the research on the influence of viscoelastic damping on strain solitary waves in a nonlinear elastic rod is made, the evolutionary rules of solitary waves are given, while some results are discussed.