“C.R.Johnston直接法”求解弹性地基支撑充液管中的非线性波  

A direct approach for simulation of nonlinear wave in a fluid-filled elastic tube supported by elastic foundation

作　　者：周义清[1,2] 张伟[1] 张善元[3] 

机构地区：[1]北京工业大学机电学院,北京100124 [2]北京城市学院城市建设学部,北京100083 [3]太原理工大学应用力学与生物医学工程研究所,太原030024

出　　处：《应用力学学报》2016年第3期414-420,545,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11402005;11202190);北京市博士后科研经费资助项目(Q6001015201401)

摘　　要：输油管道液体流动、血管中血液流动等都可抽象为充液弹性管流体流动模型,对其固液耦合非线性波动问题进行深入研究具有重要的理论价值和潜在的应用前景。本文以充有理想流体、受弹性地基力作用的无限长充液管为研究对象,考虑管壁材质为橡胶类或软组织材料,利用"C.R.Johnston直接法"研究了充液管中的非线性波动问题,得到了系统的孤立波解,并与约化摄动法所得孤波图形进行了比较分析。图形对比表明,"C.R.Johnston直接法"求解所得图形孤波波幅较高,传播速度较快。相关文献曾指出:如果在支配方程中保留高次项,那么所得结果就会更精确,对应孤波解波幅较高,传播速度也较快。由此说明"C.R.Johnston直接法"是一种求解过程简单,求解结果精度较摄动法更高的方法。在给定参数的情况下,只需初始条件满足w(0)≤2.466200,对于任意的波速c,都可以得到对应的精确孤立波解。The fluid flow in oil pipeline and the blood flow in blood vessels can be simplified as the fluid flow model in fluid-filled elastic tube. Studies on the propagation of nonlinear pressure wave in fluid-filled elastic tube have important theoretical value and potential application. In this paper, the propagation of nonlinear pressure wave in an elastic tube filled with incompressible inviscid fluid is studied. The reaction of foundation is calculated via Winkler model. The material of tube is considered as rubber or parenchyma. The solution of tube fluid-filled is given by using direct approach presented by C.R.Johnston. The results comparison between direct approach and reductive perturbation technique is carried out. The solitary wave obtained by C.R.Johnston direct approach become larger, taller and moves faster. Literature[4] observed that with successive(higher order) approximations, the predicted solitary wave became larger, taller and moved faster. It shows that the direct approach is not limited to long-wave approximation with high precision. The exact solitary wave solutions can be obtained for given parameters and any wave velocity with initial condition w(0)≤2.466200.

关 键 词：C.R.Johnston直接法 弹性地基力 充液管 孤立波 

分 类 号：O347.4[理学—固体力学]