CAREER: Transformation Elastodynamics and its Application to Wave Control in Solids

该学院早期职业发展（Career）项目支持实现固体中波浪控制机制所需的基础研究。世界上的信息和能量以波的形式从一点传播到另一点。例子包括电磁波，如光波和无线电波，空气和水中的声波，以及固体中的弹性波。因此，控制这些波的流动的能力间接导致了控制这些波所代表的信息和能量的能力。强有力的材料设计机制最近已经发展到控制电磁波和声波的流动。然而，控制固体中的波被证明是更加困难的，解决相关的挑战是该项目的主要重点。这项研究将对美国的经济、安全和能源利益产生有益的影响。它将导致振动传感器、换能器和成像设备设计的改进，并应用于航空航天、汽车、民用基础设施等各个行业。这将产生新的民用结构抗震技术和敏感工业设备的减振技术。通过本文提出的各种推广工作，这项研究将有助于扩大公众对海浪及其控制这一高度跨学科课题的参与。变换方法已经成为控制电磁波和声波的有效工具。然而，在弹性动力学（固体中的波）方面还没有取得类似的成功。本研究旨在通过研究耦合本构形式（威利斯形式）来填补知识空白，在此基础上建立转换弹性动力学的原理和应用。此外，本研究旨在通过应用因果原理和散射理论，为任何变换器件的性能提供基本的限制和界限。PI将对弹性动力均匀化、转换弹性动力设备的性能界限进行理论研究，并将通过应用欧几里得和非欧几里得转换类来评估性能增益。基于水平集的并行计算算法也将用于基于变换的设备的逆向设计。转换弹性动力装置的三维打印模型，在单元格和器件水平上，将通过超声波测量进行实验验证。

This Faculty Early Career Development (CAREER) project supports fundamental research needed to realize mechanisms of control of waves in solids. Information and energy in the world travel from one point to another in the form of waves. Examples include electromagnetic waves such as light and radio waves, sound waves in air and water, and elastic waves in solids. The ability to control the flow of these waves, therefore, indirectly leads to the ability to control the information and energy which these waves represent. Strong material design mechanisms have recently been developed to control the flow of electromagnetic and acoustic waves. However, controlling waves in solids has proven to be more difficult, and resolving associated challenges is the main focus of this project. This research will have beneficial impact on several U.S. economic, security, and energy interests. It will lead to improvements in the design of vibration sensors, transducers, and imaging devices with applications to various industries such as aerospace, automobile, civil infrastructure. It will lead to novel earthquake mitigation techniques for civil structures and vibration mitigation techniques for sensitive industry equipment. Through the various outreach efforts proposed here, this research will help in broadening the participation of the general public in the highly multi-disciplinary subject of waves and their control.Transformation methods have emerged as effective tools for the control of electromagnetic and acoustic waves. However, analogous successes have not been achieved for elastodynamics (waves in solids). This research aims to fill the knowledge gap by investigating a coupled constitutive form (Willis form) as the basis upon which the principles and applications of transformation elastodynamics can be built. Furthermore, this research aims to provide fundamental limits and bounds on the performance of any transformation device through the application of causality principle and scattering theory. The PI will conduct theoretical studies into elastodynamic homogenization, performance bounds of transformation-elastodynamic devices and will assess performance gains through the application of classes of Euclidean and non-Euclidean transformations. Level-set based parallel computational algorithms will be also developed for inverse design of transformation-based devices. Three-dimensional printed models of transformation-elastodynamic devices, at both the unit cell and the device levels, will be fabricated and tested through ultrasonic wave measurements for experimental verification.