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

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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.