Mathematical Sciences: Analysis and Numerical Modeling of Wave Phenomena in Composite Materials

时间相关问题的一个困难来源是， 复合材料是存在一个额外的长度尺度， 观察的频率或时间。 这个目标 项目是为了获得一个令人信服的描述的反应， 复合材料的时间依赖性负载，并达到有效的 介质理论，宏观地描述了 反应 在这个持续研究的阶段， 重点将放在那些情况下， 含边界复合材料中的应力场和位移场 预计会很强。 有趣的是， 边界层型现象，及其对 复合材料的宏观行为。 使用的工具将是 渐近分析的组合，分析方法， 偏微分方程和数值实验。 最终的目标是达到准确和有效地 可计算模型的波传播，和振动， 复合结构 复合材料现在是普通的建筑材料， 特别是在高科技应用中， 了解它们的机械性能。 本研究的目的 项目是建立在知识基础上的机械 复合材料的性能，特别强调其 动态行为

One source of difficulty for time dependent problems for composites is the presence of an additional length scale in the form of frequency or time of observation. The goal of this project is to obtain a cogent description of the response of composites to time-dependent loadings and to arrive at effective medium theories which give a macroscopic description of the response. In this phase of this continuing research, the emphasis will be on those cases where the interaction of the stress and displacement field in the composite with the boundary is expected to be strong. Of interest is the description of boundary layer-type phenomena, and their influence on the macroscopic behavior of the composite. The tools used will be a combination of asymptotic analysis, analytical methods for partial differential equations, and numerical experimentation. The eventual goal is to arrive at accurate and efficiently computable models of wave propagation in, and vibration of, composite structures. Composite materials are now commonplace building materials, especially in high-tech applications, therefore it is important to know their mechanical properties. The goal of this research project is to build on the knowledge-base on the mechanical properties of composites, with particular emphasis on their dynamic behavior.