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

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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.