In this paper, a novel design concept for active self-adaptive metamaterial (ASAMM) plates is proposed based on an active self-adaptive (ASA) control strategy guided by the particle swarm optimization (PSO) technique. The ASAMM plates consist of an elastic base plate and two periodic arrays of piezoelectric patches. The periodic piezoelectric patches place on the bottom plate surface act as sensors, while the other ones attached on the top plate surfaces act as actuators. A simplified plate model is established by the Hamilton principle. By assuming a uniform or constant plate thickness, the plane wave expansion (PWE) method is adopted to calculate the band structures. The finite element method (FEM) using 2D plate and 3D solid elements is also used to calculate the band structures and the transmission spectra or frequency responses. The conventional displacement, velocity and acceleration feedback control methods are introduced and analyzed. Then, a novel ASA control strategy based on combining the displacement and acceleration feedback control methods and guided by the PSO technique is developed. Numerical results will be presented and discussed to show that the proposed ASAMM plates can automatically and intelligently evolve different feedback control schemes to adapt to different stimulations on demand. Compared to the conventional metamaterial (MM) plates, the proposed ASAMM plates exhibit improved and enhanced band-gap characteristics and suppression performance for flexural waves at frequencies outside the band-gaps
This paper investigates the pseudo-spin based edge states for flexural waves in a honeycomb perforated phononic plate, which behaves an elastic analogue of the quantum spin Hall effect. We utilize finite element method to analyse the dispersion for flexural waves based on Mindlin's plate theory. Topological transition takes place around a double Dirac cone at $Γ$ point by adjusting the sizes of perforated holes. We develop an effective Hamiltonian to describe the bands around the two doubly degenerated states and analyse the topological invariants. This further leads us to observe the topologi…
A novel design of an elastic metamaterial with anisotropic mass density is proposed to manipulate flexural waves at a subwavelength scale. The three-dimensional metamaterial is inspired by kirigami, which can be easily manufactured by cutting and folding a thin metallic plate. By attaching the resonant kirigami structures periodically on the top of a host plate, a metamaterial plate can be constructed without any perforation that degrades the strength of the pristine plate. An analytical model is developed to understand the working mechanism of the proposed elastic metamaterial and the dispers…
In this paper, we numerically and experimentally demonstrate negative refraction of flexural waves in phononic crystal(PC) plates which is employed for designing flat elastic lenses. We propose a thickness contrast-based plate design to achieve refractive index equal to -1 at the interface of the PC and host plate. The thickness contrast between the PC and host plate enables matching their wave numbers in the all angle negative refraction (AANR) frequency regime. The PC-lens design is then numerically and experimentally verified to achieve the image of an omnidirectional subwavelength excitati…
We provide an analytical formulation to model the propagation of elastic waves in a homogeneous half-space supporting an array of thin plates. The technique provides the displacement field obtained from the interaction between an incident wave generated by a harmonic source and the scattered fields induced by the flexural motion of the plates. The scattered field generated by each plate is calculated using an ad-hoc set of Green's functions. The interaction between the incident field and the scattered fields is modeled through a multiple scattering formulation. Owing to the introduction of the…
Bianisotropy is common in electromagnetics whenever a cross-coupling between electric and magnetic responses exists. However, the analogous concept for elastic waves in solids, termed as Willis coupling, is more challenging to observe. It requires coupling between stress and velocity or momentum and strain fields, which is difficult to induce in non-negligible levels, even when using metamaterial structures. Here, we report the experimental realization of a Willis metamaterial for flexural waves. Based on a cantilever bending resonance, we demonstrate asymmetric reflection amplitudes and phase…
In elasticity, the design of a cloaking for an inclusion or a void to leave a vibrational field unperturbed by its presence, so to achieve its invisibility, is a thoroughly analyzed, but still unchallenged, mechanical problem. The 'cloaking transformation' concept, originally developed in electromagnetism and optics, is not directly applicable to elastic waves, displaying a complex vectorial nature. Consequently, all examples of elastic cloaking presented so far involve complex design and thick coating skins. These cloakings often work only for problems of unidirectional propagation, within na…
In this paper, we present numerical and experimental evidence of directional wave behavior, i.e. beaming and diffraction, along high-order rotational symmetries of quasicrystalline elastic metamaterial plates. These structures are obtained by growing pillars on an elastic plate following a particular rotational symmetry arrangement, such as 8-fold and 10-fold rotational symmetries, as enforced by a design procedure in reciprocal space. We estimate the dispersion properties of the waves propagating in the plates through Fourier transformation of transient wave-fields. The procedure identifies, …
Piezoelectric elastic metamaterials offer the ability to overcome the fixed, narrow bandwidth characteristics of passive elastic metamaterials. Interesting ultrasonic band gaps exist in piezoelectric plate metamaterials with periodic electrodes connected to shunted circuits. These band gaps result from an avoided crossing between electrical and mechanical bands, and can arise at lower frequencies than Bloch wave band gaps. Current analytical modeling techniques for these systems are numerically cumbersome, and assume an infinitely periodic plate. We present an approximate two-dimensional analy…
We report the realization of simultaneously negative effective mass density and shear modulus in a single-phase asymmetric double-sided pillared metamaterial. The negative effective mass density is achieved by the combination of bending and compressional resonances of one pillar whereas the rotational resonance of the other pillar leads to the negative effective shear modulus. The coupling between these two pillars is investigated to describe the formation of the doubly negative property. Then, a pillared system featuring chirality is designed in order to make efficient the excitation of the r…
We present here how a coherent perfect absorber-laser (CPAL) enabled by parity-time ($\mathcal{PT}$)-symmetry breaking may be exploited to build monochromatic amplifying devices for flexural waves. The fourth order partial differential equation governing the propagation of flexural waves leads to four by four transfer matrices, and this results in physical properties of the $\mathcal{PT}$-symmetry specific to elastic plate systems. We thus demonstrate the possibility of using CPAL for such systems and we argue the possibility of using this concept to detect extremely small-scale vibration pert…
A zero-frequency seismic metamaterial (ZFSM) consisting of a three-component seismic metamaterial plate and a half space is proposed to attenuate ultra-low frequency seismic surface waves. The design concept and models are verified firstly by lab-scale experiments on the seismic metamaterial consisting of a two-component seismic metamaterial plate and a half space. Then we calculate the band structures of the one-dimensional and two-dimensional ZFSMs, and evaluate their attenuation ability to Rayleigh waves. A wide band gap and a zero-frequency band gap (ZFBG) can be found as the band structur…
As 2D materials with subwavelength structures, elastic metasurfaces show remarkable abilities to manipulate elastic waves at will through artificial boundary conditions. However, the application prospects of current metasurfaces may be restricted by their phase-only modulating boundaries. Herein, we present the next generation of elastic metasurfaces by additionally incorporating amplitude-shift modulation. A general theory for target wave fields steered by metasurfaces is proposed by modifying the Huygens-Fresnel principle. As examples, two amplitude-shift metasurfaces concerning flexural wav…
In this paper, we employ the novel design of the metamaterial half-wave plate by using the multiple layers of the metamaterials with some specific rotation angles. The rotation angles are given by composite pulse control which is the well-known quantum control technique. A big advantage of this method can analytically calculate the rotation angles and can be easily extended to the multiple layers. The more layers of the metamaterials can present more bandwidth of half-wave plate. In this paper, we present 1, 3, 5, 7 configurations of layers of a metamaterial half-wave plate and we demonstrate …
Subwavelength imaging of elastic/acoustic waves using phononic crystals (PCs) is limited to a narrow frequency range via the two existing mechanisms that utilize either the intense Bragg scattering in the first phonon band or negative effective properties (left-handed material) in the second (or higher) phonon band. In the first phonon band, the imaging phenomenon can only exist at frequencies closer to the first Bragg band gap where the equal frequency contours (EFCs) are convex. Whereas, for the left-handed materials, the subwavelength imaging is restricted to a narrow frequency region where…
In this paper, we describe the manifestation of localized states through coherent and incoherent analyses of a diffuse elastic wavefield inside a two-dimensional metamaterial made of a collection of vertical long beams glued to a thin plate. We demonstrate that localized states arise due to multi-wave interactions at the beam-plate attachment when the beams acts as coupled resonators for both compressional and flexural resonances on the metasurface. Due to the low-quality factor compressional resonance of the beams, inside the main bandgap the modal density of the systel drops to near a high-q…
Nonlinear acoustic metamaterial (NAM) initiates new fields for controlling elastic waves. In this work, the flexural wave propagation in the half-infinite NAM beam consisting of periodic Duffing resonators is reported by considering the third harmonic generation (THG). Different analytical methods are proposed to describe the wave propagation in the equivalent homogenous medium. Then their effectiveness and accuracy are demonstrated in comparison with the finite element methods. We unveil analytically and numerically extensive physical properties of the strongly nonlinear AM, including the non…
A numerical study on the elastic response of single- and multi-layer systems formed by alternating pentamode lattices and stiffening plates is presented. Finite element simulations are conducted to analyze the dependence of the effective elastic moduli of such structures upon suitable aspect ratios, which characterize the geometry of the generic pentamode layer at the micro- and macro-scale, and the lamination scheme of the layered structure. The given numerical results highlight that the examined structures exhibit bending-dominated response, and are able to achieve low values of the effectiv…
This study examines the mechanical behavior of a novel class of mechanical metamaterials alternating pentamode lattices and stiffening plates. The unit cell of such lattices consists of a sub-lattice of the face cubic-centered unit cell typically analyzed in the current literature on pentamode materials. The studied systems exhibit only three soft deformation modes in the infinitesimal stretch-dominated regime, as opposed to the five zero-energy modes of unconfined pentamode lattices. We develop analytical formulae for the vertical and bending stiffness properties and study the dependence of s…
The ability to control and manipulate elastic waves is important for applications such as structural health monitoring, signal processing, and vibration isolations. In this paper, we investigated the feasibility of using the Rays Inserting Method, an approach originally proposed for optical elements, to design structural components for flexural wave manipulation. The RIM entails a simple process that allows to design thickness variations in a thin plate with a desirable refractive index distribution for an intended wave path. Based on this method, a focusing and collimating lens and a waveguid…
The advent of acoustic metamaterials opened up a new frontier in the control of sound transmission. A key limitation, however, is that an acoustic metamaterial based on a single local resonator in the unit cell produces a restricted narrow-band attenuation peak; and when multiple local resonators are used the emerging attenuation peaks -- while numerous -- are each still narrow and separated by pass bands. Here, we present a new acoustic metamaterial concept that yields a sound transmission loss through two antiresonances -- in a single band gap -- that are fully coupled and hence provide a br…
Motivated by the importance of lattice structures in multiple fields, we investigate the propagation of flexural waves in a thin woven plate augmented with two classes of metastructures for wave mitigation and guiding, namely metabarriers and metalenses. The cellular architecture of this plate invokes the well-known octet topology, while the metadevices rely on novel customized octets either comprising spherical masses added to the midpoint of their struts or variable node thickness. We numerically determine the dispersion curves of a doubly-periodic array of octets, which produce a broad band…
Wave Focusing in Metamaterials: Tactile Displays Beyond the Diffraction Limit
Media Arts and Technology Program（媒体艺术与技术项目）；Department of Mechanical Engineering（机械工程系）；Department of Electrical and Computer Engineering（电气与计算机工程系）；University of California, Santa Barbara（加州大学圣芭芭拉分校）
We present a methodology to perform inverse analysis on reconfigurable topological insulators for flexural waves in plate-like structures. First the unit cell topology of a phononic plate is designed, which offers two-fold degeneracy in the band structure by topology optimization. In the second step, piezoelectric patches bonded over the substrate plate are connected to an external circuit and used appropriately to break space inversion symmetry. The space inversion symmetry breaking opens a topological band gap by mimicking quantum valley Hall effect. Numerical simulations demonstrate that th…
The unusual viscoelastic properties of silica aerogel plates are efficiently used to design subwavelength perfect sound absorbers. We theoretically, numerically and experimentally report a perfect absorbing metamaterial panel made of periodically arranged resonant building blocks consisting of a slit loaded by a clamped aerogel plate backed by a closed cavity. The impedance matching condition is analyzed using the Argand diagram of the reflection coefficient, i.e., the trajectory of the reflection coefficient as a function of frequency in the complex plane. The lack or excess of losses in the …
Chua's mem-components are ideal for creating adaptive metasurfaces for manipulating EM waves given that they hold their state without external biases. In this paper, we propose a generic adaptive reactive element that is in fact a memcapacitor/meminductor. This element makes use of a polymer that demonstrates reversible trans-cis photochemical isomerization, thus making it possible to change the distance between two conductive plates by up to 25%. Furthermore, a design methodology for utilizing these devices is presented.
We present the concept of a feedback-based topological acoustic metamaterial as a tool for realizing autonomous and active guiding of sound beams along arbitrary curved paths in free two-dimensional space. The metamaterial building blocks are acoustic transducers, embedded in a slab waveguide. The transducers generate a desired dispersion profile in closed-loop by processing real-time pressure field measurements through preprogrammed controllers. In particular, the metamaterial can be programmed to exhibit analogies of quantum topological wave phenomena, which enables unconventional and except…
Dynamically switchable half-/quarter-wave plates have recently been the focus in the terahertz regime. Conventional design philosophy leads to multilayer metamaterials or narrowband metasurfaces. Here we propose a novel design philosophy and a VO2-metal hybrid metasurface for achieving broadband dynamically switchable half-/quarter-wave plate (HWP/QWP) based on the transition from the overdamped to the underdamped resonance. Results show that, by varying the VO2 conductivity by three orders of magnitude, the proposed metasurface's function can be switched between an HWP with polarization conve…
It is well known in metamaterials that local resonance and hybridization phenomena dramatically influence the shape of dispersion curves; the metasurface created by a cluster of resonators, subwavelength rods, atop an elastic surface being an exemplar with these features. On this metasurface, band-gaps, slow or fast waves, negative refraction and dynamic anisotropy can all be observed by exploring frequencies and wavenumbers from the Floquet-Bloch problem and by using the Brillouin zone. These extreme characteristics, when appropriately engineered, can be used to design and control the propaga…
