中北大学学报（自然科学版）2017，Vol.38Issue(1)：15-18,4.DOI:10.3969/j.issn.1673-3193.2017.01.003
有限挠度Bernoulli-Euler梁中的非线性波与混沌行为
Nonlinear Wave and Chaos Property in Finite-Deflection Bernoulli-Euler Beam
摘要
Abstract
Based on the finite-deflection beam theory,the nonlinear partial differential equations for flex-ural waves in a Bernoulli-Euler beam are derived.Using the traveling wave method and integration skills,the nonlinear partial differential equations can be converted into an ordinary differential equation. The qualitative analysis indicates that the corresponding dynamic system has a heteroclinic orbit under a certain condition.The exact periodic solution of nonlinear wave equation is obtained by means of Jacobi elliptic function expansion.The shock wave solution is given when the modulus of Jacobi elliptic func-tion m→1 in the degenerate case.It is easily thought that the introduction of damping and external load can result in break of heteroclinic orbit and appearance of transverse heteroclinic point.The threshold condition of the existence of transverse heteroclinic point is given by help of Melnikov function.It shows that the system has chaos property under Smale horseshoe meaning.关键词
Bernoulli-Euler梁/有限变形/非线性波/混沌/Melnikov函数Key words
Bernoulli-Euler beam/finite-deflection/nonlinear wave/chaos property/Melnikov function分类
数理科学引用本文复制引用
周义清,张伟,张善元..有限挠度Bernoulli-Euler梁中的非线性波与混沌行为[J].中北大学学报（自然科学版）,2017,38(1):15-18,4.基金项目
国家自然科学基金资助项目(11402005,11202190) （11402005,11202190）
北京市博士后科研经费资助项目(Q6001015201401) （Q6001015201401）
