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位移法浅水波方程的解及其特性
投稿时间:2015-12-23  修订日期:2016-01-12  点此下载全文
引用本文:姚征,钟万勰.位移法浅水波方程的解及其特性[J].计算机辅助工程,2016,25(2):1-4.
作者单位E-mail
姚征 大连海事大学 交通运输装备与海洋工程学院 yaozheng@dlmu.edu.cn 
钟万勰 大连理工大学 工业装备结构分析国家重点实验室 wxzhong@dlut.edu.cn 
基金项目:国家自然科学基金(11202040);中央高校基本科研业务专项资金(3132015100)
中文摘要:不同于传统流体力学,在Lagrange坐标下推导浅水波方程.若将水平位移作为基本变量,则推导出的浅水波数学模型可描述为固体力学的非线性大位移问题.运用不可压缩条件,通过变分原理推导出位移法浅水波方程,给出椭圆函数形式的行波解,并分析孤波解产生的条件.该基础研究建立了在分析结构力学中分析浅水波问题的理论基础,有利于进一步开展水动力学的研究.
中文关键词:浅水波  Lagrange坐标  孤立波  椭圆函数  微分代数方程  保辛  分析结构力学
 
Solutions and characteristics of shallow water equation based on displacement method
Abstract:The shallow water wave equation is obtained in Lagrange coordinates, which is different from the traditional hydrodynamics. The horizontal displacement is defined as the basic variable, and the deduced mathematical model of shallow water wave just likes the nonlinear large displacement problem in solid mechanics. Under the incompressible condition, the variational principle for shallow water dynamic equation is given on the basis of the displacement method, and the corresponding elliptic traveling wave solutions are presented the conditions of obtaining solitary wave solutions are also discussed. As a basic research work, the present study establishes the theoretical foundation of analyzing the shallow water waves in analytical structural mechanics and is valuable for the further research in hydrodynamics.
keywords:shallow water wave  Lagrange coordinate  solitary wave  elliptic function  differential algebraic equation  symplectic constraint  analytical structural mechanics
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