复杂固体并式微结构模型及孤立波的存在性

那仁满都拉

doi:10.21656/1000-0887.380074

复杂固体并式微结构模型及孤立波的存在性

doi: 10.21656/1000-0887.380074

那仁满都拉

内蒙古民族大学物理与电子信息学院, 内蒙古通辽 028000

基金项目: 国家自然科学基金（11462019）

详细信息

作者简介:
那仁满都拉（1963—），男，教授，博士，硕士生导师(E-mail: nrmdltl@126.com).

中图分类号: O331|O347
计量
- 文章访问数: 640
- HTML全文浏览量: 54
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- 被引次数: 0
出版历程
- 收稿日期: 2017-03-31
- 修回日期: 2017-05-21
- 刊出日期: 2018-01-15

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

NARANMANDULA

College of Physics and Electronic Information, Inner Mongolia University for the Nationalities, Tongliao, Inner Mongolia 028000, P.R.China

Funds: The National Natural Science Foundation of China(11462019)

摘要

摘要: 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.
- 并式微结构模型 /
- 非对称孤立波 /
- 存在条件
Abstract: 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.
- concurrent microstructured model /
- asymmetric solitary wave /
- existence condition

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参考文献(16)

[1]	ENGELBRECHT J, BEREZOVSKI A. Internal structures and internal variables in solids[J]. Journal of Mechanics of Materials and Structures,2012,7(10): 983-996.
[2]	BEREZOVSKI A, ENGELBRECHT J, PEETS T. Multiscale modeling of microstructured solids[J]. Mechanics Research Communications,2010,37(6): 531-534.
[3]	BEREZOVSKI A, ENGELBRECHT J, SALUPERE A, et al. Dispersive waves in microstructured solids[J]. International Journal of Solids and Structures,2013,50(11/12): 1981-1990.
[4]	PASTRONE F, ENGELBRECHT J. Nonlinear waves and solitons in complex solids[J]. Mathematics and Mechanics of Solids,2016,21(1): 52-59.
[5]	CASASSO A, PASTRONE F. Wave propagation in solids with vectorial microstructures[J]. Wave Motion,2010,47(6): 358-369.
[6]	ENGELBRECHT J, BEREZOVSKI A. Reflections on mathematical models of deformation waves in elastic microstructured solids[J]. Mathematics and Mechanics of Complex Systems,2015,3: 43-82.
[7]	张丽俊, 陈立群. 一类高阶非线性波方程的子方程与精确行波解[J]. 应用数学和力学, 2015,36(5): 548-554.(ZHANG Lijun, CHEN Liqun. Sub-equations and exavt traveling wave solutions to a class of high-order nonlinear wave equations[J]. Applied Mathematics and Mechanics,2015,36(5): 548-554.(in Chinese))
[8]	王恒, 王汉权, 陈龙伟, 等. 耦合Higgs方程和Maccari系统的行波解分支[J]. 应用数学和力学, 2016,37(4): 434-440.(WANG Heng, WANG Hanquan, CHEN Longwei, et al. Bifurcations of exact travelling wave solutions to coupled Higgs equations and Maccari systems[J].Applied Mathematics and Mechanics,2016,37(4): 434-440.(in Chinese))
[9]	LI Jibin.Singular Traveling Wave Equations: Bifurcations and Exact Solutions [M]. Beijing: Science Press, 2013.
[10]	LI Jibin. Bifurcations of traveling wave solutions in a microstructured solid model[J]. International Journal of Bifurcation and Chaos,2013,23(1): 1350009-1-1350009-18.
[11]	LI Jibin, DAI Huihui. On the Study of Singular Traveling Wave Equations: Dynamical System Approach [M]. Beijing: Science Press, 2007.
[12]	谢怡, 王砚. 高度非线性孤立波与弹性大板的耦合作用研究[J]. 固体力学学报, 2017,38（1）: 65-73.(XIE Yi, WANG Yan. The coupling mechanism between highly nonlinear solitary waves with large plate[J]. Chinese Journal of Solid Mechanics,2017,38（1）: 65-73.(in Chinese))
[13]	YANG J, RESTUCCIA F, DARAIO C. Highly nonlinear granular crystal sensor and actuator for delamination detection in composite structures[J]. Structure Health Monitoring,2013,2: 1424-1433.
[14]	JANNO J, ENGELBRECHT J. Solitary waves in nonlinear microstructured materials[J]. Journal of Physics A: Mathematical and General,2005,38: 5159-5172.
[15]	SALUPERE A, TAMM K. On the influence of material properties on the wave propagation in Mindlin-type microstructured solids[J]. Wave Motion,2013,50(7): 1127-1139.
[16]	那仁满都拉. 微结构固体中的孤立波及其存在条件[J]. 物理学报, 2014,63(19): 194301-1-194301-8.(NARANMANDULA. Solitary waves and their existence conditions in microstructured solids[J]. Acta Physica Sinica,2014,63(19): 194301-1-194301-8.(in Chinese))