CAREER: Nonlinear, Dissipative Mechanics of Phononic Materials: An Integrated Research and Education Plan

该学院早期职业发展奖的研究目标是建立精确和近似的分析连续公式，以处理(1)粘性和非粘性阻尼以及(2)几何和材料非线性对声子材料的自由频散波动特性的影响，并在复杂频率和波矢的完整空间中这样做。然后，这些工具将被用于分析降维、低重量/高刚度的晶格结构以及板状和块状声子晶体和超材料配置。在平行轨道上，将进行一系列复杂的实验，从简单的振动测试到激光超声探测，以便为验证所开发的理论公式提供参考数据。这项研究将提供一个包含非线性和耗散效应的周期材料中波动的广义理论处理，并将提供对潜在的物理机制的彻底和验证的理解。这项研究将通过提供必要的公式和分析工具来研究声子学在许多技术领域的应用，例如声学/振动控制、爆炸保护、射频传感、声学成像、数字信号处理、能量转换等，从而促进力学对传统上属于凝聚态物理领域的影响。免费教育部分提出了一种被描述为“学生垂直整合，以培养语音方面的学术能力(语音方面的愿景)”的理念。在这个项目中，本科生将帮助开发与振动、波传播和声学相关的教育工具，使研究生水平的教育活动成为可能，反之亦然。此外，研究活动将用于模块的开发，而模块反过来将帮助高级学生更好地欣赏他们正在研究的物理现象，特别是关于非线性和耗散的影响。

The research objective of this Faculty Early Career Development (CAREER) award is to establish exact and approximate analytical continuum formulations for the treatment of the effects of (1) viscous and nonviscous damping and (2) geometric and material nonlinearities on the free dispersive wave motion characteristics of phononic materials, and to do so in the complete space of complex frequencies and wavevectors. These tools will then be applied to the analysis of reduced-dimension, low-weight/high-stiffness lattice structures as well as plate-like and bulk phononic crystal and metamaterial configurations. On a parallel track, a series of experiments ranging in complexity from simple vibration testing to laser ultrasonic probing will be conducted in order to provide reference data for validation of the developed theoretical formulations. This research will deliver a generalized theoretical treatment of wave motion in periodic materials incorporating the effects of nonlinearity and dissipation, and will provide a thorough and verified understanding of the underlying physical mechanisms. The research will promote the reach of mechanics to an area that traditionally falls within the realm of condensed matter physics by providing needed formulations and analytical tools to investigate the application of phononics in many areas of technology, for example, acoustic/vibration control, blast protection, radio frequency sensing, acoustic imaging, digital signal processing, energy conversion, among others. The complimentary education component proposes a philosophy described as "Vertical Integration of Students In Order to Nurture Scholarship in Phononics (VISIONS in Phononics)". In this program, students at the undergraduate level will help develop education tools related to vibrations, wave propagation and phononics that will enable educational activities at the graduate level, and vice versa. Furthermore, the research activities will feed into the development of the modules, and the modules in turn will help advanced students gain better appreciation of the physical phenomena they are researching especially concerning the effects of nonlinearities and dissipation.