摘要
给出了包含宏观应变和微形变的全部二次项以及宏观应变三次项的一种新的自由能函数.利用新自由能函数并根据Mindlin微结构理论,建立了描述微结构固体中纵波传播的一种新模型.利用近来发展的奇行波系统的动力系统理论,分析了系统的所有相图分支,并给出了周期波解、孤立波解、准孤立尖波解、孤立尖波解以及紧孤立波解.孤立尖波解和紧孤立波解的得到,有效地证明了在一定条件下,微结构固体中可以形成和存在孤立尖波和紧孤立波等非光滑孤立波.此结果进一步推广了微结构固体中只存在光滑孤立波的已有结论.
A new free energy function was given with all quadratic terms of macro strain and micro deformation, as well as cubic terms of macro strain. A new model for description of the longitudinal wave propagation in microstructured solids was established by means of the new free energy function and Mindlin’s microstructure theory. Based on the dynamical system theory for singular traveling wave systems developed recently, all bifurcations of phase portraits of the traveling wave systems were analyzed, and the periodic wave solutions, the solitary wave solutions, the quasi peakon solutions, the peakon solutions and the compacton solutions were given. The obtained peakon and compacton solutions effectively prove that non-smooth solitary waves such as the peakon and the compacton can form and exist in microstructured solids under certain conditions. The results further exceed the conclusion that only smooth solitary waves can exist in microstructured solids.
作者
那仁满都拉
韩元春
张芳
NARANMANDULA;HAN Yuanchun;ZHANG Fang(College of Physics and Electronic Information, Inner MongoliaUniversity for Nationalities, Tongliao, Inner Mongolia 028000, P.R.China;College of Mathematics, Inner Mongolia University for Nationalities,Tongliao, Inner Mongolia 028000, P.R.China)
出处
《应用数学和力学》
CSCD
北大核心
2019年第4期433-442,共10页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11462019)~~
关键词
模型
微结构固体
非光滑孤立波
演变
model
microstructured solid
non-smooth solitary wave
evolution
