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Characterization and Simulation of Dispersive Elastodynamic Media in Time Domain

时域色散弹性动力介质的表征和仿真

基本信息

批准号：
2039472
负责人：
Reza Abedi
金额：
$ 38.36万
依托单位：
University of Tennessee Space Institute
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-01-15 至 2025-12-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2039472&HistoricalAwards=false
关键词：
Characterization Simulation Dispersive Elastodynamic Media

项目摘要

Many materials are dispersive, i.e., their properties are frequency-dependent. The interaction of waves with material microstructure can result in a complex dispersive response. This effect is exploited in the design of metamaterials to effectuate novel properties that are otherwise not observed in conventional materials. This award supports fundamental research on the characterization and analysis of elastodynamic dispersive materials as a function of their mechanical layout and level of disorder at the microscale. Understanding the response of dispersive materials is important for a broad range of applications towards national prosperity and welfare and the national defense. For example, elastodynamic metamaterials find applications in seismic wave mitigation, vibration control, and blast wave mitigation. Moreover, disorder is inherent in the microstructure of many natural and man-made dispersive materials. For metamaterials, disorder is unavoidable due to manufacturing imperfections, but this inevitability can be used to improve wave mitigation properties and facilitate novel designs for non-destructive evaluation and energy harvesting applications. This award will also support student internship and faculty research opportunities through collaboration with a predominantly undergraduate institution, graduate research and course development, and publicly shared software modules.The first objective of this project is the formulation of advanced homogenization methods that derive dynamic properties of dispersive materials followed by numerical methods that incorporate such properties for transient analysis. Homogenized properties are generally valid only from quasi-static to long wavelength regimes. Higher order scattering coefficients and spatial dispersion terms will be used to extend this and derive effective dynamic properties that are meaningful up to medium to short wavelength regimes. The resulting effective properties can be quite complex, for example, by having a tensorial mass density and resulting in Willis constitutive equations. Modeling dispersive relations in time domain poses additional challenges. An automated method will be formulated to derive complex auxiliary differential equations for analysis in the time domain. The second objective is understanding the effect of disorder on various response measures of dispersive materials. Specifically, disorder can enhance wave mitigation properties of a metamaterial design by expanding the frequency range of the stopband(s), making the absorption more omnidirectional, and red-shifting the stopband which is often a welcomed effect. Statistical analysis will be used to analyze the sensitivity and stability of stopband and other dynamic properties versus disorder.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

许多材料都是色散的，即它们的特性与频率相关。波与材料微观结构的相互作用会导致复杂的色散响应。这种效应在超材料的设计中被利用，以实现传统材料中观察不到的新颖特性。该奖项支持弹性动力色散材料的表征和分析的基础研究，作为其机械布局和微观尺度无序水平的函数。了解色散材料的响应对于国家繁荣、福利和国防的广泛应用非常重要。例如，弹动力超材料可应用于减轻地震波、振动控制和冲击波减轻。此外，许多天然和人造色散材料的微观结构固有无序性。对于超材料来说，由于制造缺陷，无序是不可避免的，但这种不可避免的情况可用于改善波浪缓解特性，并促进无损评估和能量收集应用的新颖设计。该奖项还将通过与本科院校合作、研究生研究和课程开发以及公开共享的软件模块来支持学生实习和教师研究机会。该项目的第一个目标是制定先进的均质化方法，导出分散材料的动态特性，然后采用结合这些特性进行瞬态分析的数值方法。均匀化特性通常仅在准静态到长波长范围内有效。高阶散射系数和空间色散项将用于扩展这一点并导出对中短波长范围有意义的有效动态特性。由此产生的有效属性可能非常复杂，例如，通过具有张量质量密度并产生威利斯本构方程。在时域中建模色散关系提出了额外的挑战。将制定一种自动化方法来导出复杂的辅助微分方程以在时域中进行分析。第二个目标是了解无序对色散材料各种响应措施的影响。具体来说，无序可以通过扩大阻带的频率范围、使吸收更加全向以及使阻带红移（这通常是受欢迎的效果）来增强超材料设计的波抑制特性。统计分析将用于分析阻带和其他动态特性与无序的敏感性和稳定性。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。