Some Interesting Traveling Waves in a Transversely Isotropic Incompressible Hyperelastic Semi-infinite Rod  

作　　者：Ran Wang Xuegang Yuan Hongwu Zhang Jie Xu Jing Zhang 

机构地区：[1]State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116024,China [2]College of Science,Dalian Minzu University,Dalian 116600,China [3]College of Mathematics and Information,North Minzu University,Yinchuan 750021,China

出　　处：《Acta Mechanica Solida Sinica》2018年第6期698-716,共19页固体力学学报（英文版）

基　　金：National Natural Science Foundation of China (Nos.11672069, 11702059,11232003,11672062);the Ph.D.Programs Foundation of Ministry of Education of China (No.20130041110050);the Research Start-up Project Plan for Liaoning Doctors (No.20141119);the Fundamental Research Funds for the Cen- tral Universities (No.DC201502050407,DC201502050203,DC201502050403,20000101);the Natural Science Foundation of Liaoning Province (No.20170540199);and the 111Project (B08014).

摘　　要：In this paper,the bounded traveling wave solutions are examined for a system of partial differential equations with certain boundary conditions.Interestingly,this system can be used to describe the axially symmetric motion of a semi-infinite incompressible hyperelastic cylindrical rod.With the aid of traveling wave transformations,the partial differential equations can be reduced to a traveling wave equation.The implicit analytical expressions determining the traveling waves are derived.Significantly,the influences of material parameters on the qualitative properties are discussed in detail by using the phase portraits of the traveling wave system. Smooth solutions such as the periodic traveling wave solutions and the solitary wave solutions with the peak form are shown.In particular,some interesting singular traveling wave solutions including the solitary cusp wave solutions and the periodic cusp wave solutions with the peak form are obtained.Numerical examples for all these waves are given.

关 键 词：SEMI-INFINITE cylindrical ROD Planar dynamical system Bound traveling WAVE Solitary CUSP WAVE 

分 类 号：O3[理学—力学]