Symmetric Solitary Waves and Their Existence Conditions in Cubic Nonlinear Microstructured Solids
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摘要: 考虑固体材料的宏观尺度立方非线性效应、微尺度立方非线性效应以及微尺度频散效应并根据修正的Mindlin理论,建立了一维微结构固体中纵波传播的一种新模型.用动力系统的定性分析方法,证明了适当条件下立方非线性微结构固体中可存在对称钟型孤立波和反钟型孤立波,并给出了两种孤立波的存在条件.用数值方法分析了微尺度立方非线性效应对钟型与反钟型孤立波的影响,结果显示随着微尺度非线性效应的增强(或负增强),两种孤立波的宽度变窄(或变宽)而幅度保持不变.Abstract: In view of the macroscale cubic nonlinear effect, the microscale cubic nonlinear effect and the microscale dispersion effect of solid materials, a new model for the longitudinal wave propagation in 1D microstructured solids was established based on the modified Mindlin theory. The qualitative analysis method was applied to the dynamical system, the existence of symmetric bell and anti-bell type solitary waves in the cubic nonlinear microstructured solid was proved under appropriate conditions, and the existence conditions of the 2 solitary waves were given. The microscale cubic nonlinear effect on the bell and anti-bell type solitary waves was analyzed with the numerical method. The results indicate that the widths of the 2 solitary waves decreases (or increases) with the rise (or fall) of the microscale nonlinear effect while the amplitudes of the 2 solitary waves remain unchanged.
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Key words:
- Mindlin theory /
- microstructured solid /
- solitary wave /
- existence condition
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