GEOMETRICAL NONLINEAR WAVES IN FINITE DEFORMATION ELASTIC RODS

• Published in: Applied mathematics and mechanics Vol. 26; no. 5; pp. 667 - 674
• Main Author: 郭建刚 周丽军 张善元
• Format: Journal Article
• Language: English
• Published: Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, P.R.China%Department of Mechanical Engineering, Tianjin University of Technology and Education, Tianjin 300222, P.R. China 01.05.2005
• Subjects: 几何非线性波; 多尺度法; 惯性转换; 有限形变; 粘滞效应; finite deformation; multi-scale method; viscous effect; nonlinear wave; transverse inertia effect
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/BF02466342

By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave.If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.