全部

力学与实践 ›› 2009, Vol. 31 ›› Issue (6): 25-29.doi: 10.6052/1000-0879-2009-183

• 应用研究 • 上一篇    下一篇

弹性地基内充液压力管道中的非线性波

张涛1 张善元   

  1. 太原理工大学应用力学与生物医学工程研究所,太原,030024 太原理工大学土木工程系
  • 收稿日期:2009-04-23 修回日期:2009-08-19 出版日期:2009-12-10 发布日期:2009-12-08

NONLINEAR WAVE IN A FLUID-FILLED THIN ELASTIC TUBE BURIED INSIDE ELASTIC FOUNDATION

  • Received:2009-04-23 Revised:2009-08-19 Online:2009-12-10 Published:2009-12-08

摘要: 研究了埋置于弹性地基内充液压力管道中非线性波的传播. 假设管壁是线弹 性的,地基反力采用Winkler线性地基模型,管中流体为不可压缩理想流体. 假定系统初始 处于内压为$P_0$的静力平衡状态,动态的位移场及内压和流速的变化是叠加在静 力平衡状态上的扰动. 基于质量守恒和动量定理,建立了管壁和流体耦合作用的非 线性运动方程组; 进而用约化摄动法, 在长波近似情况下得到了KdV方程,表征 着系统有孤立波解.

关键词: 弹性地基,充液圆管,约化摄动法,孤立波

Abstract: Propagation of nonlinear waves in a fluid-filled thin elastic foundation is studied in this paper. The material of the tube is assumed to be linear elastic, the reaction of foundation is calculated based on Winkler model, and the fluid is incompressible and inviscid. Initially, the tube subjected to a uniform inner pressure $P_0 $ is in a state of static equilibrium. The dynamic displacement field and the variations of inner pressure and fluid velocity are considered as a disturbance superimposed on this static deformation. The nonlinear equations of motion are obtained by considering the mass conservation and the balance of linear momentum. With the reductive perturbation method, the KdV equation is derived in the longwave approximation. It is shown that the system can have a solitary wave solution.

Key words: elastic foundation, fluid-filled circular tube, reductive perturbation method, solitary wave