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.
The exact solution 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 is obtained.By 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,periodical waves and so on.
出处
《固体力学学报》
CAS
CSCD
北大核心
2010年第4期392-396,共5页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金项目(10761005)
内蒙古自然科学基金项目(2009MS0102
2009BS0104)资助
关键词
非线性扭转波方程
椭圆函数
孤立波
周期波
nonlinear torsional wave equation
elliptic function
solitary wave
periodical wave
