非线性弹性杆中的孤波解及其数值分析  

Solitary Wave Solution and Its Numerical Analysis in a Nonlinear Elastic Bar

作　　者：韩强[1] 郑向锋[1] 

机构地区：[1]华南理工大学交通学院,广东广州510640

出　　处：《华南理工大学学报（自然科学版）》2004年第4期92-96,共5页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目 (10 2 72 0 4 6 );广东省自然科学基金资助项目 (0 2 0 85 8)

摘　　要：推导了非线性弹性杆中波动方程的一般形式 ,采用修正的完全近似法 ,得到了孤波的渐近解 ,并对其进行了数值分析 ,发现了钟状和振荡型两种孤波 .理论和数值分析表明 ,孤波是由材料非线性和杆的横向效应相互作用引起的 ,其传播速度与波幅有关 ,波幅越大 ,波传播速度越大 ;波宽与波速的平方根成反比 ,波速越大 ,波宽越窄 ;The general form of the nonlinear wave equation in a nonlinear elastic bar was derived. An asympto-tic solution of the solitary wave was obtained by means of the modified complete-approximate method and was numerically analyzed, from which two kinds of solitary waves—the bell-type solitary wave and the oscillatory-type solitary wave—were found. Theoretical and numerical analyses indicate that the solitary wave is caused by the action of the material nonlinearity and the lateral effect of the bar, and that the propagation velocity of the solitary wave is related to its amplitude, i.e. the larger the amplitude is, the larger the propagation velocity is; and that the wave width is of inverse ratio with the square root of wave propagation velocity and is related to the parameter indicating the dispersion effect of the wave—the larger the propagation velocity is, the shorter the wave width is.

关 键 词：非线性弹性杆 孤波 KdV—mKdV方程 数值分析 

分 类 号：O322[理学—一般力学与力学基础]