一维非线性周期结构中弹性波传播的辛数学方法

侯秀慧; 邓子辰; 周加喜

doi:10.3879/j.issn.1000-0887.2010.11.004

一维非线性周期结构中弹性波传播的辛数学方法

doi: 10.3879/j.issn.1000-0887.2010.11.004

1.
西北工业大学力学与土木建筑学院,西安 710072;2.大连理工大学工业装备结构分析国家重点实验室,辽宁大连 116024;3.湖南大学机械与运载工程学院,长沙 410082

基金项目: 国家自然科学基金资助项目(10972182;10772147;10632030);国家基础研究计划973项目(2006CB601202);111引智计划项目(B07050);中国博士后科学基金资助项目(200904500170);大连理工大学工业装备结构分析国家重点实验室开放基金重点项目(GZ0802);西北工业大学博士创新基金(CX200908);西北工业大学基础研究基金(JC200938)的资助

详细信息

作者简介:
侯秀慧(1983- ),女,山东武城人,博士生(E-mail:houxiuhui@yahoo.com.cn);邓子辰,教授,博士生导师(联系人.E-mail:dweifan@nwpu.edu.cn).

中图分类号: O347.4
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出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-10-01
- 刊出日期: 2010-11-15

Symplectic Analysis for Wave Propagation in One-Dimensional Nonlinear Periodic Structures

1.
Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, P. R. China;

摘要

摘要: 利用辛数学方法分析了质量-弹簧非线性周期结构链中弹性波的传播问题．首先利用能量方法得到频域动力方程，随后通过小量变换将非线性动力方程线性化，得到辛矩阵，进而通过求解辛矩阵的本征值问题来研究波的传播性能．质量-弹簧模型中的弹簧刚度非线性对结构链的传播特性影响很大，研究发现非线性明显改变了周期结构的传播性能，而且不同于线性结构，非线性结构的传播特性与入射波强度有关．数值算例表明随着非线性强度及入射波强度的增大，传播通带宽度逐渐减小，禁带宽度逐渐增大．当入射波强度增大到一定值时，弹性波无法在结构中进行传播．与一般递归方法的比较分析，验证了辛数学方法在非线性周期结构波传播问题中的有效性与优越性．
- 辛数学方法 /
- 非线性周期结构 /
- 弹性波传播
Abstract: The wave propagation problem in nonlinear periodic mass-spring structure chain was analyzed using the symplectic mathematical method. Firstly the energy method was applied to construct the dynamical equation and then the nonlinear dynamical equation was linearized using the small parameter perturbation method. The eigen-solutions of the symplectic matrix were applied to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain,arising from the nonlinear spring stiffness effect,has profound effects on the overall transmission of the chain. The wave propagation characteristics are not only altered due to the nonlinearity but also related with the incident wave intensity, which is a genuine nonlinear effect that is not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to a closing of the transmitting gaps. Comparison with the normal recursive approach demonstrates the effectiveness and superiority of the symplectic method in wave propagation problem for nonlinear periodic structures.
- symplectic mathematical method /
- nonlinear periodic structure /
- elastic wave propagation

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参考文献(26)

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一维非线性周期结构中弹性波传播的辛数学方法

doi: 10.3879/j.issn.1000-0887.2010.11.004

作者简介:
侯秀慧(1983- ),女,山东武城人,博士生(E-mail:houxiuhui@yahoo.com.cn);邓子辰,教授,博士生导师(联系人.E-mail:dweifan@nwpu.edu.cn).

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Symplectic Analysis for Wave Propagation in One-Dimensional Nonlinear Periodic Structures

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一维非线性周期结构中弹性波传播的辛数学方法

doi: 10.3879/j.issn.1000-0887.2010.11.004

作者简介: 侯秀慧(1983- ),女,山东武城人,博士生(E-mail:houxiuhui@yahoo.com.cn);邓子辰,教授,博士生导师(联系人.E-mail:dweifan@nwpu.edu.cn).

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出版历程

Symplectic Analysis for Wave Propagation in One-Dimensional Nonlinear Periodic Structures

计量

出版历程

目录

作者简介:
侯秀慧(1983- ),女,山东武城人,博士生(E-mail:houxiuhui@yahoo.com.cn);邓子辰,教授,博士生导师(联系人.E-mail:dweifan@nwpu.edu.cn).