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

该学院早期职业发展（CAREER）奖的研究目标是建立精确和近似的分析连续体配方，用于处理（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自由色散波动特性的影响，并在复频率和波矢量的完整空间中进行。然后，这些工具将被应用到分析的减少维，低重量/高刚度的晶格结构，以及板状和散装声子晶体和超材料配置。在一个平行的轨道上，一系列的实验范围从简单的振动测试，激光超声探测的复杂性将进行，以提供参考数据的验证开发的理论公式。 这项研究将提供一个广义的理论处理周期性材料中的波动，结合非线性和耗散的影响，并将提供一个彻底的和验证的理解的基本物理机制。这项研究将促进力学的范围，传统上福尔斯在凝聚态物理学领域内的一个领域，通过提供所需的配方和分析工具，以研究声子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。免费教育部分提出了一种被称为“学生纵向一体化，以培养语音学奖学金"的理念。在该计划中，本科生将帮助开发与振动，波传播和声子相关的教育工具，从而使研究生阶段的教育活动成为可能，反之亦然。此外，研究活动将投入到模块的开发中，模块反过来将帮助高级学生更好地了解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.