有限变形弹性杆中的非线性波及周期解  

NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD

作　　者：刘志芳[1] 张善元[1] 

机构地区：[1]太原理工大学应用力学研究所,太原030024

出　　处：《固体力学学报》2006年第1期1-5,共5页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(10472076)资助

摘　　要：利用Ham ilton变分原理,导出了计及有限变形和横向Possion效应的弹性杆中非线性纵向波动方程.利用Jacob i椭圆正弦函数展开和第三类Jacob i椭圆函数展开法,对该方程和截断的非线性方程进行求解,得到了非线性波动方程的两类准确周期解及相应的孤波解和冲击波解,讨论了这些解存在的必要条件.A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of Hamihon principle. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expan- sion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition for the existence of exact periodic solutions, shock solution and solitary solution is discussed.

关 键 词：非线性波 有限变形 Possion效应 JACOBI椭圆函数 

分 类 号：O347[理学—固体力学]