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非圆截面杆中非线性扭转波方程的解析求解
引用本文:杨丽英,刘官厅.非圆截面杆中非线性扭转波方程的解析求解[J].固体力学学报,2010,31(4):392-396.
作者姓名:杨丽英  刘官厅
作者单位:1. 内蒙古农业大学2. 内蒙古师范大学
基金项目:国家自然科学基金项目,内蒙古自然科学基金项目 
摘    要:研究了非圆截面杆中非线性扭转波动方程的精确求解问题.利用直接积分与微分变换相结合的方法,得到了该方程的隐式通解.通过对积分常数和方程系数的不同情形的讨论,给出了该方程三角函数、双曲函数、椭圆函数、指数函数以及它们的组合形式的解,分别对应于非线性扭转波的孤立波、周期波以及冲击波等多种传播形式.

关 键 词:非圆截面杆中非线性扭转波方程的解析求解  
收稿时间:2010-01-20

THE ANALYTIC SOLVING FOR NONLINEAR TORSIONAL WAVE EQUATION IN NON-CIRCULAR CROSS-SECTIONAL ROD
Liying Yang,Guanting Liu.THE ANALYTIC SOLVING FOR NONLINEAR TORSIONAL WAVE EQUATION IN NON-CIRCULAR CROSS-SECTIONAL ROD[J].Acta Mechnica Solida Sinica,2010,31(4):392-396.
Authors:Liying Yang  Guanting Liu
Abstract:The exact solving problem of nonlinear torsional wave equation in non-circular cross-sectional rod is investigated. Using the method of direct integral together with differential transformation, an implicit general solution of the nonlinear torsional wave equation are obtained. Through analyzing arbitrary integral constants and coefficients of the known equation, various solutions of this equation are given, including trigonometric function solution, hyperbolic function solution, exponential function solution, elliptic function solution and their composite function. These solutions correspond to solitary waves, shock waves and periodical waves and so on.
Keywords:
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