Metastable modular metastructures for on-demand reconfiguration of band structures and nonreciprocal wave propagation

Embodying Multifunctional Mechano-Intelligence in and Through Phononic Metastructures Harnessing Physical Reservoir Computing

Recent advances in autonomous systems have prompted a strong demand for the next generation of adaptive structures and materials to possess built-in intelligence in their mechanical domain, the so-called mechano-intelligence (MI). Previous MI attempts mainly focused on specific case studies and lacked a systematic foundation in effectively and efficiently constructing and integrating different intelligent functions. Here, a new approach is uncovered to create multifunctional MI in adaptive structures using physical reservoir computing (PRC). That is, to concurrently embody computing power and the key elements of intelligence, namely perception, decision-making, and commanding, directly in the mechanical domain, advancing from conventional reliance on add-on computers and massive electronics. As an exemplar platform, a mechanically intelligent phononic metastructure is developed by harnessing its high-degree-of-freedom nonlinear dynamics as PRC power. Through analyses and experiments, multiple intelligent structural functions are demonstrated ranging from self-tuning wave controls to wave-based logic gates. This research provides the much-needed basis for creating future smart structures and materials that greatly surpass the state of the art-such as lower power consumption, more direct interactions, and better survivability in harsh environments or under cyberattacks. Moreover, it enables the addition of new functions and autonomy to systems without overburdening the onboard computers.

Architected material with independently tunable mass, damping, and stiffness via multi-stability and kinematic amplification

We report on a class of architected material lattices that exploit multi-stability and kinematic amplification to independently adjust the local effective mass, damping, and stiffness properties, thereby realizing congruent alterations to the acoustic dispersion response post-fabrication. The fundamental structural tuning element permits a broad range in the effective property space; moreover, its particular design carries the benefit of tuning without altering the original size/shape of the emerging structure. The relation between the tuning element geometry and the achieved variability in effective properties is explored. Bloch's theorem facilitates the dynamic analysis of representative one- and two-dimensional (1D/2D) systems, revealing, e.g., bandgap formation, migration, and closure and positive/negative metadamping in accordance with the tuning element configuration. To demonstrate a utility, we improvise a waveguide by appropriately patterning the tuning element configuration within a 2D system. We believe that the proposed strategy offers a new way to expand the range of performance and functionality of architected materials for elastodynamics.

Acoustic topological beam nonreciprocity via the rotational Doppler effect

Reciprocity is a fundamental principle of wave physics related to time-reversal symmetry. Nonreciprocal wave behaviors have been pursued for decades because of their great scientific significance and tremendous potential applications. However, nonreciprocity devices have been based on manipulation of non-topological charge (TC) in most studies to date. Here, we introduce the rotational Doppler effect (RDE) into the acoustic system to achieve nonreciprocal control of the TC beam. We use the metasurface to generate a vortex beam with a defined TC. By rotating the metasurface with specific angular velocity, the wave vector of the transmitted wave obtains positive and negative transition flexibly due to the RDE. As a result, isolated and propagating states of the vortex beam can be realized by controlling the rotation direction, representing nonreciprocal propagation. Our work also provides an alternative method for the application of TC beams and the realization of nonreciprocity.

Programming nonreciprocity and reversibility in multistable mechanical metamaterials

Nonreciprocity can be passively achieved by harnessing material nonlinearities. In particular, networks of nonlinear bistable elements with asymmetric energy landscapes have recently been shown to support unidirectional transition waves. However, in these systems energy can be transferred only when the elements switch from the higher to the lower energy well, allowing for a one-time signal transmission. Here, we show that in a mechanical metamaterial comprising a 1D array of bistable arches nonreciprocity and reversibility can be independently programmed and are not mutually exclusive. By connecting shallow arches with symmetric energy wells and decreasing energy barriers, we design a reversible mechanical diode that can sustain multiple signal transmissions. Further, by alternating arches with symmetric and asymmetric energy landscapes we realize a nonreciprocal chain that enables propagation of different transition waves in opposite directions.

This work presents a mechanical metamaterial with 1D array of bistable arches where nonreciprocity and reversibility can be independently programmed. The effects of asymmetry both at the structural and element level on propagation of transition waves are examined.

Non-Reciprocal Supratransmission in Mechanical Lattices with Non-Local Feedback Control Interactions

We numerically investigate the supratransmission phenomenon in an active nonlinear system modeled by the 1D/2D discrete sine-Gordon equation with non-local feedback. While, at a given frequency, the typical passive system exhibits a single amplitude threshold marking the onset of the phenomenon, we show that the inclusion of non-local feedback manifests additional thresholds that depend upon the specific boundary from which supratransmission is stimulated, realizing asymmetric (i.e., non-reciprocal) dynamics. The results illustrate a new means of controlling nonlinear wave propagation and energy transport for, e.g., signal amplification and mechanical logic.

Tunable mechanical diode of nonlinear elastic metamaterials induced by imperfect interface

In this investigation, the non-reciprocal transmission in a nonlinear elastic metamaterial with imperfect interfaces is studied. Based on the Bloch theorem and stiffness matrix method, the band gaps and transmission coefficients with imperfect interfaces are obtained for the fundamental and double frequency cases. The interfacial influences on the transmission behaviour are discussed for both the nonlinear phononic crystal and elastic metamaterial. Numerical results for the imperfect interface structure are compared with those for the perfect one. Furthermore, experiments are performed to support the theoretical analysis. The present research is expected to be helpful to design tunable devices with the non-reciprocal transmission and diode behaviour of the elastic metamaterial.

Programmable stopbands and supratransmission effects in a stacked Miura-origami metastructure

Origami-based mechanical metamaterials and metastructure have been demonstrated to exhibit unique properties originating from their intricate geometries of folding. This research aims to extend the current investigation level from quasistatics to dynamics. In detail, this research focuses on the wave dynamics of a metastructure composed of stacked Miura-origami (SMO) units. The SMO unit could possess two stable configurations, endowing the metastructure with rich possibilities in the layout of its periodic repeating cell. Through linear dispersion analyses and numerical studies, we show that the long-desired stopband tunability and programmability of the metastructure along the three principal directions can be acquired by strategically programming the layout of the periodic cell. Based upon that, we further discover that energy supratransmission through the metastructure is possible within the stopband by increasing the driving amplitude. Through numerical means, the amplitude threshold of supratransmission is obtained. We demonstrate that the fundamental mechanism that triggers the supratransmission phenomenon is the transition of the responses from the low-energy intrawell oscillations to the high-energy interwell oscillations. Numerical studies also indicate that the supratransmission threshold can be effectively tailored by adjusting the periodic cell layout. The results of this research provide a wealth of fundamental insights into the origami wave dynamics and offer useful guidelines for developing origami metastructures with tunable and programmable dynamic characteristics.

Acoustic response for nonlinear, coupled multiscale model containing subwavelength designed microstructure instabilities

Nonperiodic arrangements of inclusions with incremental linear negative stiffness embedded within a host material offer the ability to achieve unique and useful material properties on the macroscale. In an effort to study such types of inclusions, the present paper develops a time-domain model to capture the nonlinear dynamic response of a heterogeneous medium containing a dilute concentration of subwavelength nonlinear inclusions embedded in a lossy, nearly incompressible medium. Each length scale is modeled via a modified Rayleigh-Plesset equation, which differs from the standard form used in bubble dynamics by accounting for inertial and viscoelastic effects of the oscillating spherical element and includes constitutive equations formulated with incremental deformations. The two length scales are coupled through the constitutive relations and viscoelastic loss for the effective medium, both dependent on the inclusion and matrix properties. The model is then applied to an example nonlinear inclusion with incremental negative linear stiffness stemming from microscale elastic instabilities embedded in a lossy, nearly incompressible host medium. The macroscopic damping performance is shown to be tunable via an externally applied hydrostatic pressure with the example system displaying over two orders of magnitude change in energy dissipation due to changes in prestrain. The numerical results for radial oscillations versus time, frequency spectra, and energy dissipation obtained from the coupled dynamic model captures the expected response for quasistatic and dynamic regimes for an example buckling inclusion for both constrained and unconstrained negative stiffness inclusions.

Gradient-Index Granular Crystals: From Boomerang Motion to Asymmetric Transmission of Waves

We present a gradient-index crystal that offers extreme tunability in terms of manipulating the propagation of elastic waves. For small-amplitude excitations, we achieve control over wave transmission depth into the crystal. We numerically and experimentally demonstrate a boomeranglike motion of a wave packet injected into the crystal. For large-amplitude excitations on the same crystal, we invoke nonlinear effects. We numerically and experimentally demonstrate asymmetric wave transmission from two opposite ends of the crystal. Such tunable systems can thus inspire a novel class of designed materials to control linear and nonlinear elastic wave propagation in multiscales.

Solitary waves in a nonintegrable chain with double-well potentials

We study solitary waves in a one-dimensional lattice of identical masses that are connected in series by nonlinear springs. The potential of each spring is nonconvex, where two disjoint convex regions, phase I and phase II, are separated by a concave, spinodal region. Consequently, the force-strain relation of the spring is nonmonotonous, which gives rise to a bistable behavior. Based on analytical treatment, with some approximations, combined with extensive numerical simulations, we are able to reveal important insights. For example, we find that the solitary-wave solution is indifferent to the energy barrier that separates the two energy wells associated with phase I and phase II, and that the shape of the wave can be described by means of merely two scalar properties of the potential of the springs, namely, the ratio of stiffness in phase II and phase I, and the ratio between the Maxwell's force and corresponding transition strain. The latter ratio provides a useful measure for the significance of the spinodal region. Linear stability of the solitary-wave solution is studied analytically using the Vakhitov-Kolokolov criterion applied to the approximate solutions obtained in the first part. These results are validated by numerical simulations. We find that the solitary-wave solution is stable provided that its velocity is higher than some critical value. It is shown that, practically, the solitary waves are stable for almost the entire range of possible wave velocities. This is also manifested in the interaction between two solitary waves or between a solitary wave and a wall (rigid boundary). Such interaction results in a minor change of height and shape of the solitary wave along with the formation of a trail of small undulations that follow the wave, as expected in a nonintegrable system. Even after a significant number of interactions the changes in the wave height and shape are minor, suggesting that the bistable chain may be a useful platform for delivering information over long distances, even concurrently with additional information (other solitary waves) passing through the chain.

Acoustic radiation pressure for nonreciprocal transmission and switch effects

Systems capable of breaking wave transmission reciprocity have recently led to tremendous developments in wave physics. We report herein on a concept that enables one-way transmission of ultrasounds, an acoustic diode, by relying on the radiation pressure effect. This effect makes it possible to reconfigure a multilayer system by significantly deforming a water-air interface. Such a reconfiguration is then used to achieve an efficient acoustic transmission in a specified direction of propagation but not in the opposite, hence resulting in a highly nonreciprocal transmission. The corresponding concept is experimentally demonstrated using an aluminum-water-air-aluminum multilayer system, providing the means to overcome key limitations of current nonreciprocal acoustic devices. We also demonstrate that this diode functionality can even be extended to the design and operations of an acoustic switch, thus paving the way for new wave control possibilities, such as those based on acoustic transistors, phonon computing and amplitude-dependent filters.