Pai Wang

Topological Phononic Crystals with One-Way Elastic Edge Waves

We report a new type of phononic crystals with topologically nontrivial band gaps 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 (anomalous) Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern numbers of 1 and 2, indicating that these structures support single and multimode edge elastic waves immune to backscattering. 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.

Multistable Architected Materials for Trapping Elastic Strain Energy

3D printing and numerical analysis are combined to design a new class of architected materials that contain bistable beam elements and exhibit controlled trapping of elastic energy. The proposed energy-absorbing structures are reusable. Moreover, the mechanism of energy absorption stems solely from the structural geometry of the printed beam elements, and is therefore both material- and loading-rate independent.

Harnessing Deformation to Switch On and Off the Propagation of Sound

A new class of architected materials is designed to control the propagation of sound. The proposed system comprises an array of elastomeric helices in background air and is characterized by frequency ranges of strong wave attenuation (bandgaps) in the undeformed configuration. Upon axially stretching the helices, such bandgaps are suppressed, enabling the design of a new class of acoustic switch.

Three-dimensional adaptive soft phononic crystals

We report a new class of three-dimensional (3D) adaptive phononic crystals whose dynamic response is controlled by mechanical deformation. Using finite element analysis, we demonstrate that the bandgaps of the proposed 3D structure can be fully tuned by the externally applied deformation. In fact, our numerical results indicate that the system acts as a reversible phononic switch: a moderate level of applied strain (i.e., −0.16) is sufficient to completely suppress the bandgap, and upon the release of applied strain, the deformed structure recovers its original shape, which can operate with a sizable bandgap under dynamic loading. In addition, we investigate how material damping significantly affects the propagation of elastic waves in the proposed 3D soft phononic crystal. We believe that our results pave the way for the design of a new class of soft, adaptive, and re-configurable 3D phononic crystals, whose bandgaps can be easily tuned and switched on/off by controlling the applied deformation.

Architected Materials with Ultra-Low Porosity for Vibration Control.

Periodic structures with extremely low porosities capable of forming large band gaps-frequency ranges with strong wave attenuation-are designed by patterning an elastic sheet with an array of alternating crack-like pores separated by small ligaments. The results indicate that the presence and size of the band gaps are controlled by the smallest geometric -feature in the system (which can be easily controlled by tuning the aspect ratio of the pores), providing an important guideline for the design of systems with the -desired response.

Wave propagation in fractal-inspired self-similar beam lattices

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 resonantband 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 gapproperties (i.e., possessing band gaps that arises from both Bragg scattering and localized resonance).

Wave propagation in cross-linked random fiber networks

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 fiber-segment 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.

Harnessing Geometric Frustration to Form Band Gaps in Acoustic Channel Lattices

We demonstrate both numerically and experimentally that geometric frustration in two-dimensional periodic acoustic networks consisting of arrays of narrow air channels can be harnessed to form band gaps (ranges of frequency in which the waves cannot propagate in any direction through the system). While resonant standing wave modes and interferences are ubiquitous in all the analyzed network geometries, we show that they give rise to band gaps only in the geometrically frustrated ones (i.e., those comprising of triangles and pentagons). Our results not only reveal a new mechanism based on geometric frustration to suppress the propagation of pressure waves in specific frequency ranges but also open avenues for the design of a new generation of smart systems that control and manipulate sound and vibrations.

Motion microscopy for visualizing and quantifying small motions

Significance Humans have difficulty seeing small motions with amplitudes below a threshold. Although there are optical techniques to visualize small static physical features (e.g., microscopes), visualization of small dynamic motions is extremely difficult. Here, we introduce a visualization tool, the motion microscope, that makes it possible to see and understand important biological and physical modes of motion. The motion microscope amplifies motions in a captured video sequence by rerendering small motions to make them large enough to see and quantifies those motions for analysis. Amplification of these tiny motions involves careful noise analysis to avoid the amplification of spurious signals. In the representative examples presented in this study, the visualizations reveal important motions that are invisible to the naked eye. 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.

Harnessing geometric and material nonlinearities to design tunable phononic crystals

We investigate numerically and experimentally the effects of geometric and material nonlinearities introduced by deformation on the linear dynamic response of two-dimensional phononic crystals. Our results not only show that deformation can be effectively used to tune the band gaps and the directionality of the propagating waves, but also reveal how geometric and material nonlinearities contribute to the tunable response of phononic crystals. Our 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.