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Propagation of nonlinear elastic waves and non-local dynamic behaviour of composite materials

非线性弹性波的传播与复合材料的非局部动态行为

基本信息

批准号：
184036807
负责人：
Professor Dr.-Ing. Dieter Weichert
金额：
--
依托单位：
Lehrstuhl und Institut für Allgemeine Mechanik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2010
资助国家：
德国
起止时间：
2009-12-31 至 2013-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/184036807?language=en
关键词：
Propagation nonlinear elastic waves non

项目摘要

This renewal proposal aims to continue ongoing studies of nonlinear dynamic properties of periodic composite materials. We intend to consider new problems that have emerged during evaluation of the previous DFG grant and are crucially important for the analysis and verification of the obtained results. To the time being, we studied propagation of stationary nonlinear waves. However, a number of significant nonlinear effects are related to non-stationary dynamic behaviour of composite solids. The key objectives of the project are as follows:1. Study of evolution of 1D and 2D nonlinear waves from different initial excitations. Investigation whether and how fast stable stationary modes can be developed. Comparison of numerical and analytical results.2. Study of resonance interactions between 2D nonlinear plane waves propagating in different directions. Resulting from such interactions, filtering or amplification of 2D solitary waves.3. Study of nonlinear waves propagating in viscoelastic composites. Derivation of macroscopic nonlinear wave equations with dispersive and dissipative terms. Investigation of the interplay between the effects of nonlinearity and dissipation.Additionally to the new tasks listed above, we plan to complete the solution of several problems from the previous project, namely, clarification of the links between discrete and continuous models of nonlinear composite materials; verification of the derived macroscopic dynamical equations and estimation of their area of applicability. As to the methodology, asymptotic approaches based on regular and singular perturbation techniques and the asymptotic homogenization method will be used. Non-stationary dynamic problems will be studied by the pseudo-spectral numerical procedure. Integration in the time domain will be performed by finite-difference approaches. For the spatial discretization, the Fourier series expansions will be applied. We intend to improve essentially the convergence of the series and to reduce the Gibbs-Wilbraham phenomenon with the help of the method of Fourier-Padé approximants.

该更新建议旨在继续进行周期性复合材料的非线性动力学性能的研究。我们打算考虑在以前的DFG赠款评估过程中出现的新问题，这些问题对于分析和验证所获得的结果至关重要。到目前为止，我们研究了定常非线性波的传播。然而，一些重要的非线性效应与复合固体的非平稳动态行为有关。该项目的主要目标如下：1. 不同初始激励下一维和二维非线性波的演化研究。调查是否以及如何快速稳定的稳态模式可以开发。数值计算和分析结果的比较。2. 二维非线性平面波在不同方向传播时的共振相互作用研究。由于这种相互作用，2D孤立波的滤波或放大。粘弹性复合材料中非线性波传播的研究。含色散和耗散项的宏观非线性波动方程的推导。研究非线性和耗散效应之间的相互作用。除了上面列出的新任务外，我们计划完成以前项目中的几个问题的解决方案，即澄清非线性复合材料的离散和连续模型之间的联系;验证导出的宏观动力学方程并估计其适用范围。至于方法，渐近方法的基础上定期和奇异摄动技术和渐近均匀化方法将被使用。非平稳动力学问题将采用拟谱数值方法进行研究。时域积分将采用有限差分法。对于空间离散化，将应用傅立叶级数展开。我们打算从本质上改善级数的收敛性，并减少吉布斯-威尔布拉姆现象的帮助下，傅立叶-Padé逼近的方法。

项目成果

期刊论文数量（6）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Spatial localization of linear elastic waves in composite materials with defects

DOI：
10.1002/zamm.201200273
发表时间：
2014-12
期刊：
ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
影响因子：
0
作者：
I. Andrianov;Vladyslav V. Danishevs'kyy;J. Awrejcewicz
通讯作者：
I. Andrianov;Vladyslav V. Danishevs'kyy;J. Awrejcewicz

Asymptotic analysis of perforated plates and membranes. Part 1: Static problems for small holes

穿孔板和膜的渐近分析第 1 部分：小孔的静态问题