Person:

Wang, Pai

We investigate the effects of geometric and material nonlinearities introduced by deformation on the linear dynamic response of two-dimensional phononic crystals. Our analysis not only shows that deformation can be effectively used to tune the band gaps and the directionality of the propagating waves, but also reveals how geometric and material nonlinearities contribute to the tunable response of phononic crystals. Our numerical study provides a better understanding of the tunable response of phononic crystals and opens avenues for the design of systems with optimized properties and enhanced tunability.

We numerically investigate the propagation of small-amplitude elastic waves in random fiber networks. Our analysis reveals that the dynamic response of the system is not only controlled by its overall elasticity, but also by the local microstructure. In fact, we find that the longest fibersegment plays a key role in dynamics when the network is excited with waves of short wavelength. In this case, the Bloch modes are highly non-affine as the longest segments oscillate close to their resonances. Based on this observation, we predict the low frequency dispersion curves of random fiber networks.

We combine numerical analysis and experiments to investigate the effect of hierarchy on the propagation of elastic waves in triangular beam lattices. While the response of the triangular lattice is characterized by a locally resonant band gap, both Bragg-type and locally resonant gaps are found for the hierarchical lattice. Therefore, our results demonstrate that structural hierarchy can be exploited to introduce an additional type of band gaps, providing a robust strategy for the design of lattice-based metamaterials with hybrid band gap properties (i.e., possessing band gaps that arises from both Bragg scattering and localized resonance).

We report a new type of phononic crystals with topologically non-trivial bandgaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern number of 1 and 2, indicating that these structures support single and multi-mode edge elastic waves immune to back-scattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication and acoustic imaging.

Phononic crystals and acoustic metamaterials are heterogeneous materials that enable manipulation of elastic waves. An important characteristic of these heterogeneous systems is their ability to tailor the propagation of elastic waves due to the existence of band gaps -- frequency ranges of strong wave attenuation. In this Thesis, I report discoveries of three new types of band gaps: i) Band gaps induced by geometric frustration in periodic acoustic channel networks; ii) Band gap induced by high connectivity in periodic beam lattices; and iii) Topological band gaps in gyroscopic phononic crystals that protects one-way edge waves. The investigations presented here shed new light on the rich dynamic properties of phononic crystals and acoustic metamaterials, opening avenues for new strategies to control mechanical waves in elastic systems.

Although the human visual system is remarkable at perceiving and interpreting motions, it has limited sensitivity, and we cannot see motions that are smaller than some threshold. Although difficult to visualize, tiny motions below this threshold are important and can reveal physical mechanisms, or be precursors to large motions in the case of mechanical failure. Here, we present a “motion microscope,” a computational tool that quantifies tiny motions in videos and then visualizes them by producing a new video in which the motions are made large enough to see. Three scientific visualizations are shown, spanning macroscopic to nanoscopic length scales. They are the resonant vibrations of a bridge demonstrating simultaneous spatial and temporal modal analysis, micrometer vibrations of a metamaterial demonstrating wave propagation through an elastic matrix with embedded resonating units, and nanometer motions of an extracellular tissue found in the inner ear demonstrating a mechanism of frequency separation in hearing. In these instances, the motion microscope uncovers hidden dynamics over a variety of length scales, leading to the discovery of previously unknown phenomena.