The research explores nonlinear phononic behavior in periodic meta-materials, with the intent of enabling the development of low-power wave-based devices with novel functionality, enhanced performance, and adaptive tunability. Phononic meta-materials with periodic microstructures exhibit extraordinary wave properties such as band-gaps, response directionality, left-handedness, and negative acoustic refraction, all of which can be employed for the design of acoustic devices operating over a broad range of frequencies and length scales. As devices miniaturize, nonlinear behavior becomes the norm and not the exception, as witnessed in part by the complex potentials used to describe small-scale interactions. This research investigates the effects of nonlinearities on dispersion characteristics, band-gaps, and directionality and specifically explores nonlinearities as means to achieve novel functionalities that enrich the design space of periodic media. Stiffening and softening effects, normal versus shear modes of response, amplitude-dependent dispersion, and the presence of super- and sub-harmonics may in fact positively affect the wave guiding characteristics of a given medium and may be exploited to achieve tunability of the wave properties. Analytical and computational techniques will be formulated to investigate the nature of nonlinearities in nonlinear phononic systems, and to predict their wave mechanics effects.

The developed tools will enable the design of tunable pass-band filters with controllable bandwidth and of acoustic meta-materials capable of directing and focusing the acoustic energy towards specific directions. The application of these concepts to filters, waveguides, logic ports, and ultrasonic transducer arrays which perform a variety of acoustics-based signal processing functions is very attractive particularly at frequencies where electronics suffer from severe power limitations. The project is expected to significantly advance knowledge and understanding in the general area of nonlinear meta-material wave mechanics, which will be important for the development of high-frequency, tunable devices for use in communication systems (mobile phones, GPS units, etc.), noise isolation, energy-directing materials, tunable ultrasound for medical devices, tunable acoustic microphones and receivers, and acoustic beamformers.

Project Report

Manmade metamaterials are designed to possess physical properties not available in these natural products. Indeed, manufactured multi-component, or multi-phase material assemblies such as multicomponent composites, cellular structures and periodic porous or foam-like systems have physical properties that natural materials cannot possess. In particular, acoustic meta-materials are specially designed to exhibit advantageous wave properties such as band gaps, response directionality, left handedness and negative acoustic refraction. The adapted functionality of these meta-materials means they can perform a variety of acoustic-based signal processing functions, at frequencies where electronics may suffer from power limitations . Unsurprisingly, there has been significant interest in the behaviour and application of acoustic and other meta-materials in a variety of engineering fields. Up till now, research has focused on the production and refinement of meta-materials to deliver up-to-date designs and produce a range of synthetic materials with a variety of functionalities. The challenge now is to fine tune, or adaptively modify, the unique properties in meta-materials to provide them with adaptivity and tunability, so that their operation can be adapted to changing operational environments It is hypothesized that by creating a new class of material systems and knowing how to adapt their properties would promote the application of meta-materials to a broad range of industries as a result of their novel behaviours. Professors Massimo Ruzzene and Michael Leamy’s, the principal investigators for this project, through the support from the National Science Foundation (NSF), are among the first to investigate the functionality of meta-materials with engineered nonlinearities. In order to investigate the wave propagation characteristics of nonlinear acoustic metamaterials, they developed and used cutting edge analytical and computational techniques. Acoustic meta-materials generally consist of periodically repeating unit cells, which provide them with wave dispersive properties and corresponding propagation and attenuation zones (or band gaps), which correspond to ranges of frequencies that permit or prohibit wave propagation. By observing how the band gaps shift with nonlinear interaction, the research team hoped to better understand the complex unit cell design and band gap engineering. Multiple scale perturbation analysis was applied to discrete multiple degree of freedom systems in order to generate analytical results describing, to first order, nonlinear interactions useful in unit cell design and band gap engineering. The research group found that nonlinearities lead to equivalent properties in the materials, which strongly depend on the amplitude of the waves that travel through the system, and on the interaction of any coexisting waves. They also identified that the attenuation zone increases with wave intensity due to a hardening nonlinearity present within the system. And that this resulted in higher frequency propagation being permitted for higher amplitude waves. Furthermore, it was noted that additional nonlinear interactions such as wave-wave processes potentially lead to additional tunability and that this functionality could be used to produce devices capable of saturation or switching through the application of external stimuli. These results demonstrated ample opportunities for tuning of the meta-material mechanical properties. The advantageous wave dispersion properties the team had witnessed, and the understanding that they had gained into the behaviour and adaptability of these meta-materials, could have applications in communication systems such as mobile phones and GPS units. As well as having other uses in tunable filters, tunable waveguides, directed-energy devices, ultra high-frequency resonators, tunable negative refraction, super-lenses, and acoustic cloaking devices. These novel research findings will help to promote further work in the development of tools required to design and produce the next generation of ‘meta-devices’. Future research plans include an investigation into the applications for metamaterials in the telecommunication market and for energy generation and harvesting. Outside of the direct business applications is the enhancement this new knowledge brings to academia. Teaching in academic courses on wave propagation will benefit from the findings of Ruzzene and Leamy. On-going programmes at the Georgia Institute of Technology aim to broaden under represented student participation in this subject area. In addition, educational laboratory activities and classroom modules, developed through the GIFT program at the institute, are exposing high school and middle school under represented students to basic results of the research and to underlying wave mechanics principles.

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Georgia Tech Research Corporation
United States
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