复杂固体并式微结构模型及孤立波的存在性

A Concurrent Microstructured Model for Complex Solids and Existence of Solitary Waves

把复杂固体看作具有两种不同性质的微结构,进而考虑两种微尺度非线性效应,建立了描述复杂固体运动的并式微结构非线性模型.利用动力系统的定性分析理论和分岔理论,证明了在一定条件下并式微结构固体中可以存在一类非对称孤立波并给出了其存在条件.分析表明两种微尺度非线性效应同时影响孤立波的对称特性,微尺度非线性效应越强,孤立波的非对称特性越明显.最后用数值方法进一步验证了定性分析结果.

A concurrent microstructured nonlinear model involving 2 kinds of microscale nonlinear effects was established to describe the motion of complex solids with 2 microstructures of different properties. The existence of asymmetric solitary waves was proved according to the qualitative analysis theory and the bifurcation theory for dynamic systems under certain conditions in concurrent microstructured solids,and the existence conditions for the asymmetric solitary waves were given. The results indicate that the symmetry properties of solitary waves were influenced by the 2 kinds of microscale nonlinear effects simultaneously.The asymmetric properties of solitary waves are more obvious when the microscale nonlinear effects become stronger. Finally,the results of qualitative analysis were validated further through numerical simulation.