有限变形弹性杆中的几何非线性波  

Geometrical Nonlinear Waves in Finite Deformation Elastic Rods

作　　者：郭建刚[1] 周丽军[2] 张善元[1] 

机构地区：[1]太原理工大学应用力学研究所,太原030024 [2]天津工程师范学院机械系,天津300222

出　　处：《应用数学和力学》2005年第5期614-620,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10472076);山西省自然科学基金资助项目(20031011;20011003)

摘　　要：　利用有限变形理论的Lagrange描述,借助非保守系统的Hamilton型变分原理,导出了描述弹性杆中几何非线性波的波动方程·　为了使非线性波动方程有稳定的行波解,计及了粘性效应引入的耗散和横向惯性效应导致的几何弥散·　运用多重尺度法将非线性波动方程简化为KdV_Berg ers方程,这个方程在相平面上对应着异宿鞍-焦轨道,其解为振荡孤波解·　如果略去粘性效应或横向惯性,方程将分别退化为KdV方程或Bergers方程,由此得到孤波解或冲击波解。By usinge 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.

关 键 词：非线性波 有限变形 粘性效应 横向惯性效应 多尺度法 

分 类 号：O347.4[理学—固体力学]