Acoustic Field Transport in Periodic and Disordered Metamaterials: a Fractional-order Continuum Approach.

声学超材料是一种工程化的材料结构系统（或介质），具有天然材料难以实现的特性。原型超材料由一个或多个几何形状的结构元件组成，有时以长度尺度的层次为特征。超材料经常被设计的一个目的是实现一种能够以自然界中找不到的非常独特的方式传递声音的介质。当声音在固体介质中传播时，它会产生噪音和振动，从长远来看，这些噪音和振动会导致结构退化和潜在的灾难性故障。超材料的复杂性和多尺度性质带来了许多计算挑战，到目前为止，这些挑战限制了它们在现实世界中的应用。该奖项支持基础研究，以开发数学和计算方法，使超材料的设计和模拟成为可能。设计能够控制声音传播的材料的能力可以对实现更安静，更安全，更耐用的运输系统和航空航天，机械，土木和生物医学工程领域的基础设施的能力产生重大影响，从而促进科学的进步;推进国家健康，繁荣和福利;该项目的教育部分涉及开发新的工具和练习，以帮助学生可视化工程概念并将其融入学术课程。微积分发展一个计算连续介质力学框架的超材料中的声场输运分析。分数阶算子包含了从记忆效应到非局部性，从多尺度特征到混合输运机制等各种非传统性质，使它们特别适合于模拟非均匀介质中弹性波的动力学。该研究将开发从基本原理合成分数阶波传播模型的方法，并将其应用于周期性和随机超材料的设计和性能预测。这项研究将在物理和数学水平上发展关键能力。在物理层面上，它将允许捕获和预测异常声场传输机制，否则将无法检测到。在数学层面上，它将开发方法来找到精确或近似的分析解决方案，这将改变逆向材料设计问题的方法。该项目有三个主要重点领域：1）发展必要的理论背景，从第一原理导出非均匀介质的分数连续模型，2）将框架应用于周期性和无序超材料的分析，特别强调理解异常传播机制，和3）对代表性声学超材料的理论和计算框架进行实验验证。该奖项反映了NSF的法定使命，通过使用基金会的知识价值和更广泛的影响审查标准进行评估，

Acoustic metamaterials are engineered material-structures systems (or media) that exhibit properties not readily achievable in natural materials. A prototypical metamaterial consists of an assembly of structural elements in one or more geometric shapes, sometimes characterized by a hierarchy of length scales. One purpose for which metamaterials are frequently designed for is to achieve a medium that is capable of transferring sound in remarkably unique ways that are not found naturally. When sound propagates in a solid medium it gives rise to noise and vibrations that, in the long term, are responsible for structural deterioration and potentially catastrophic failure. The complexity and multiscale nature of metamaterials poses many computational challenges that have so far limited their use in real-world applications. This award supports fundamental research to develop mathematical and computational methods that will enable the design and simulation of metamaterials. The ability to design materials capable of controlling the propagation of sound can have major implications on the ability to achieve quieter, safer, and more durable transportation systems and infrastructures in the fields of aerospace, mechanical, civil, and biomedical engineering, thereby promoting the progress of science; advancing national health, prosperity, and welfare; and securing the national defense The educational part of this project involves developing new tools and exercises to help students visualizing engineering concepts and integrating them in the academic curriculum.This research takes full advantage of the potential and unique features of fractional calculus to develop a computational continuum mechanics framework for the analysis of acoustic field transport in metamaterials. Fractional order operators encompass a variety of non-traditional properties ranging from memory effects to non-locality, from multi-scale features to hybrid transport mechanisms that make them uniquely suited to simulate the dynamics of elastic waves in inhomogeneous media. The research will develop methodologies to synthesize fractional-order wave propagation models from fundamental principles and it will apply them to the design and performance prediction of periodic and random metamaterials. This research will develop key capabilities at both physical and mathematical level. At physical level, it will allow capturing and predicting anomalous acoustic field transport mechanisms that otherwise would be undetected. At mathematical level, it will develop methodologies to find exact or approximate analytical solutions that would transform the way inverse material-design problems are approached. The project has three main thrust areas: 1) development of the necessary theoretical background to derive fractional continuum models of inhomogeneous media from first principles, 2) application of the framework to the analysis of periodic and disordered metamaterials with particular emphasis on understanding anomalous propagation regimes, and 3) experimental validation of the theoretical and computational framework on representative acoustic metamaterials.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.