We introduce the concept of effective phononic crystals, which combine periodicity with varying isotropic material properties to force periodic coefficients in the elastic equations of motion in a non-Cartesian basis. Periodic coefficients allow for band structure calculation using Bloch theorem. Using the band structure, we demonstrate band gaps and topologically protected interface modes can be obtained in cylindrically propagating waves. Through effective phononic crystals, we show how behaviors of Cartesian phononic crystals can be realized in regions close to sources, where near field effects are non-negligible.
Three-dimensional (3D) elastic phononic topological insulator, featuring two-dimensional (2D) surface states, which support the high-efficient and robust elastic wave propagation without backscattering in all spatial dimensions, remains a challenge due to the nature of multiple polarized elastic modes and their complex hybridization in 3D. Here, a 3D elastic phononic topological insulator is designed and observed experimentally by emulating the quantum valley Hall effects. The spatial inversion of adjacent atoms gives rise to a valley topological phase to an insulating regime with complete 3D …
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…
Topological defects (including disclinations and dislocations) which commonly exist in various materials have shown an amazing ability to produce excellent mechanical and physical properties of matters. In this paper, disclinations and dislocations are firstly introduced into the valley-polarized elastic phononic plate. Deformation of the lattice yields the interface expressing as the topologically protected wave guiding, due to the valley-polarized phase transition of phononic crystals (PnCs) across the interface. Then, disclinations are introduced into the Wannier-type elastic phononic plate…
Precise control of elastic waves in modes and coherences is of great use in reinforcing nowadays elastic energy harvesting/storage, nondestructive testing, wave-mater interaction, high sensitivity sensing and information processing, etc. All these implementations are expected to have elastic transmission with lower transmission losses and higher degree of freedom in transmission path. Inspired by topological states of quantum matters, especially quantum spin Hall effects (QSHEs) providing passive solutions of unique disorder-immune surface states protected by underlying nontrivial topological …
We investigate the effect of small spatiotemporal modulations in subwavelength-dimensioned phononic crystals with large band gaps, on the frequency spectrum for elastic waves polarized in the plane of periodicity. When the radius of cylinders periodically placed inside a matrix of highly-contrasting elastic properties is time-varying, we find that due to the appearance of frequency harmonics throughout the spectrum, the notion of a band gap is destroyed in general, although with the appropriate tuning of parameters, in particular the modulation frequency, it is possible that some band-gap regi…
Topologically protected gapless edge states are phases of quantum matter which behave as massless Dirac fermions, immunizing against disorders and continuous perturbations. Recently, a new class of topological insulators (TIs) with topological corner states have been theoretically predicted in electric systems, and experimentally realized in two-dimensional (2D) mechanical and electromagnetic systems, electrical circuits, optical and sonic crystals, and elastic phononic plates. Here, we demonstrate a pseudospin-valley-coupled phononic TI, which simultaneously exhibits gapped edge states and to…
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…
Acoustic waves in a linear time-invariant medium are generally reciprocal; however, reciprocity can break down in a time-variant system. In this Letter, we report on an experimental demonstration of nonreciprocity in a dynamic one-dimensional phononic crystal, where the local elastic properties are dependent on time. The system consists of an array of repelling magnets, and the on-site elastic potentials of the constitutive elements are modulated by an array of electromagnets. The modulation in time breaks time-reversal symmetry and opens a directional band gap in the dispersion relation. As s…
We demonstrate that HOTIs with the quantization of the quadrupole moments can be realized in the two-dimensional elastic phononic crystals (PnCs). Both one-dimensional (1D) topological edge states and zero-dimensional (0D) topological corner states are visualized and can be transformed each other by tuning the crystalline symmetry in a hierarchical structure. The systematic band structure calculations indicate that elastic wave energy in the hierarchical structure can be localized with remarkable robustness, which is very promising for new generations of integrated solid-state phononic circuit…
Defects play a crucial role in the physical properties of crystals, whether for classical or quantum systems. For example, in photonic/phononic crystals, defects can serve as precise guidance and localization of classical electromagnetic or mechanical waves. Rainbow concentrating, a recently proposed exotic wave localization [Phys. Rev. Lett. 126, 113902 (2021)] exploits defects to enable the collection and frequency routing of weak signals in real space. In this paper, using a solid-state phononic crystal (PnC) plate, we experimentally verify this phenomenon by deliberately infusing a homogen…
The rising need for hybrid physical platforms has triggered a renewed interest for the development of agile radio-frequency phononic circuits with complex functionalities. The combination of travelling waves with resonant mechanical elements appears as an appealing means of harnessing elastic vibration. In this work, we demonstrate that this combination can be further enriched by the occurrence of elastic non-linearities induced travelling surface acoustic waves (SAW) interacting with a pair of otherwise linear micron-scale mechanical resonators. Reducing the resonator gap distance and increas…
Photonics Initiative, Advanced Science Research Center, City University of New York（纽约市立大学高级科学研究中心光子学倡议）；Gulliver, CNRS, ESPCI Paris, Université PSL（巴黎高等物理化工国立学院CNRS Gulliver实验室）；Laboratory of Wave Engineering, EPFL（洛桑联邦理工学院波工程实验室）；Faculty of Mechanical Engineering, Technion–Israel Institute of Technology（以色列理工学院机械工程学院）；University of Chicago, James Franck Institute（芝加哥大学詹姆斯·弗兰克研究所）；University of Chicago, Kadanoff Center for Theoretical Physics（芝加哥大学卡达诺夫理论物理中心）；Walker Department of Mechanical Engineering, The University of Texas at Austin（德克萨斯大学奥斯汀分校沃克机械工程系）；Physics Program, Graduate Center, City University of New York（纽约市立大学研究生院物理学项目）
Phononic metamaterials enabled the realization of many acoustic components analogous to their electronic counterparts, such as transistors, logic gates and calculators. A key component among these is the demultiplexer, a device that receives multiple signals and sorts them based on their frequencies into separate channels. Previous experimental realizations of acoustic and elastic multiplexers have employed plates with pillars or holes to demultiplex frequencies. However, existing realizations are confined to two-dimensions, which can limit potential acoustic or elastic circuit design. Here we…
Topological phononics offers numerous opportunities in manipulating elastic waves that can propagate in solids without being backscattered. Due to the lack of nanoscale imaging tools that aid the system design, however, acoustic topological metamaterials have been mostly demonstrated in macroscale systems operating at low (kilohertz to megahertz) frequencies. Here, we report the realization of gigahertz topological valley Hall effect in nanoelectromechanical AlN membranes. Propagation of elastic wave through phononic crystals is directly visualized by microwave microscopy with unprecedented se…
In this work we propose a topological valley phononic crystal plate and we extensively investigate the refraction of valley modes into the surrounding homogeneous medium. This phononic crystal includes two sublattices of resonators (A and B) modeled by mass-spring systems. We show that two edge states confined at the AB/BA and BA/AB type domain walls exhibit different symmetries in physical space and energy peaks in the Fourier space. As a result, distinct refraction behaviors, especially through an armchair cut edge, are observed. On the other hand, the decay depth of these localized topologi…
Soft electroactive materials can undergo large deformation subjected to either mechanical or electrical stimulus, and hence they can be excellent candidates for designing extremely flexible and adaptive structures and devices. This paper proposes a simple one-dimensional soft phononic crystal cylinder made of dielectric elastomer to show how large deformation and electric field can be used jointly to tune the longitudinal waves propagating in the PC. A series of soft electrodes are placed periodically along the dielectric elastomer cylinder, and hence the material can be regarded as uniform in…
Topological insulators, which allow edge or interface waves but forbid bulk waves, have revolutionized our scientific cognition of acoustic/elastic systems. Due to their nontrivial topological characteristics, edge (interface)waves are topologically protected against defects and disorders. This superior and unique characteristic could lead to a wealth of new opportunities in applications of quantum and acoustic/elastic information processing. However, current acoustic/elastic topological insulators are still at an infancy stage where the theory and prediction only work in laboratories and ther…
Accomplishing a wide elastic wave bandgap with single phase constituent is of primary interest in developing phononic metamaterials. In the present article, exploiting spatial periodicity, a single phase lattice is configured towards achieving a large frequency bandgap in sonic range. Numerical simulations reveal the presence of a comprehensive bandgap of 18 kHz in the 2 to 22 kHz range with systematically localizing the same constituent material in the lattice. Bloch wave modes unravel the involvement of dipole, monopole, and quadrupole resonances for wide and connected bandgaps. The existenc…
Phononic crystals and metamaterials take advantage of pre-designed geometrical structures to sculpt elastic waves, controlling their dispersion using different mechanisms. These mechanisms revolve mostly around Bragg scattering (BS), local resonances (LR) and inertial amplification (IA), which employ ad-hoc, often problem-specific geometries. Here, we use parametrized, spiraling unit cells as building blocks for designing various types of phononic materials. We focus on planar spirals that are easy to fabricate, yet give rise to the desirable complex dynamics. By simple modifications of the sp…
Serpentine interconnects are highly stretchable and frequently used in flexible electronic systems. In this work, we show that the undulating geometry of the serpentine interconnects will generate phononic band gaps to manipulate elastic wave propagation. The interesting effect of `bands-sticking-together' is observed. We further illustrate that the band structures of the serpentine interconnects can be tuned by applying pre-stretch deformation. The discovery offers a way to design stretchable and tunable phononic crystals by using metallic interconnects instead of the conventional design with…
We present the realization of the topological valley-protected zero-order antisymmetric (A0) or symmetric (S0) and zero-order shear-horizontal (SH0) Lamb waves at different domain walls based on topologically distinct asymmetric double-sided pillared phononic crystals. The elastic periodic structures have either the triangular or the honeycomb symmetry and give rise to a double-negative branch in the dispersion curves. By artificially folding the doubly negative branch, a degenerate Dirac cone is achieved. Different polarization-dependent propagation along the same primary direction along the …
This research investigates dynamic response of tunable periodic structures and homogenization methods in magnetoelastic composites (MECs). The research on tunable periodic structures is focused on the design, modeling and understanding of wave propagation phenomena and the dynamic response of smart phononic crystals. High amplitude wrinkle formation is employed to study a one-dimensional phononic crystal slab consists of a thin film bonded to a thick compliant substrate. Buckling induced surface instability generates a wrinkly structure triggered by a compressive strain. It is demonstrated tha…
Owing to their periodic and intricate configurations, metamaterials engineered for acoustic and elastic wave control inevitably suffer from manufacturing anomalies and deviate from theoretical dispersion predictions. This work exploits the Polynomial Chaos theory to quantify the magnitude and extent of these deviations and assess their impact on the desired behavior. It is shown that uncertainties stemming from surface roughness, tolerances, and other inconsistencies in a metamaterial's unit cell parameters alter the targetted band gap width, location and the confidence level with which it is …
We report about the effect of an applied external mechanical load on a periodic structure exhibiting band gaps induced by inertial amplification mechanism. If compared to the cases of Bragg scattering and ordinary local resonant metamaterials, we observe here a more remarkable curve shift, modulated through large but fully reversible compression(stretch) of the unit cell, eventually triggering significant (up to two times) enlargement(reduction) of the width of a specific band gap. An important up(down)-shift of some dispersion branches over specific wavenumber values is also observed, showing…
Topological phononic crystals have attracted intensive attention due to their peculiar topologically protected interface or edge states. Their operating frequency, however, is generally fixed once designed and fabricated. Here, we propose to overcome this limitation by utilizing soft topological phononic crystals. In particular, we design a simple one-dimensional periodic system of soft cylindrical waveguides to realize mechanically tunable topological interface states for longitudinal waves. To this end, we employ the nonlinear elasticity theory and its linearized incremental version to fully…
Elastic and acoustic metamaterials can sculpt dispersion of waves through resonances. In turn, resonances can give rise to negative effective properties, usually localized around the resonance frequencies, which support band gaps at subwavelength frequencies (i.e., below the Bragg-scattering limit). However, the band gaps width correlates strongly with the resonators' mass and volume, which limits their functionality in applications. Trampoline phenomena have been numerically and experimentally shown to broaden the operational frequency ranges of two-dimensional, pillar-based metamaterials thr…
The quest for novel designs for lightweight phononic crystals and elastic metamaterials with wide lowfrequency band gaps has proven to be a significant challenge in recent years. In this context, lattice-type materials represent a promising solution, providing both lightweight properties and significant possibilities of tailoring mechanical and dynamic properties. Additionally, lattice structures also enable the generation of hierarchical architectures, in which basic constitutive elements with different characteristic length scales can be combined. In this work, we propose 1D- and 2D-periodic…
Phononic crystals and acoustic metamaterials are architected lattices designed to control the propagation of acoustic or elastic waves. In these materials, the dispersion properties and the energy transfer are controlled by selecting the lattices' geometry and their constitutive material properties. Most designs, however, only affect one mode of energy propagation, transmitted either as acoustic, airborne sound or as elastic, structural vibrations. Here, we present a design methodology to attenuate both acoustic and elastic waves simultaneously in all polarizations. We experimentally realize t…
Large area Waveguide Energy Harvesting Based on Fully Polarized Elastic Topological Metamaterials
Zhejiang-Italy Joint Lab for Smart Materials and Advanced Structures, School of Mechanics and Engineering Science, Ningbo University（宁波大学力学与工程科学学院智能材料与先进结构中意联合实验室）
Critical couplings in topological-insulator waveguide-resonator systems observed in elastic waves
National Laboratory of Solid State Microstructures & Department of Materials Science and Engineering, Nanjing University（南京大学固态微结构实验室与材料科学与工程系）；Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University（南京大学江苏省人工功能材料重点实验室）
A deep dive into Tollmien-Schlichting wave control via passive wall deformations: The battle between local and downstream stabilization, lessons learned, and implications for phononic subsurfaces
University at Buffalo (SUNY)（布法罗纽约州立大学）；Purdue University（普渡大学）
In this study, a reduced micromorphic model for multiscale materials is developed. In the context of this model, multiscale materials are modeled with deformable microstructures. The deformation energy is formed depending on microstrain and macroscopic strain residual fields. The constitutive equations according to the reduced micromorphic model only depend on eight material coefficients for linear elastic materials. These material coefficients are related to the material micro/macro-stifnesses and the material microstructural features. The wave dispersions in multiscale materials are then der…
