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Schematics of the generalized Snell's law of refraction (a) and reflection (b). dx is the distance between two beams at the plane of incidence. Φ is the phase shift of the blue beam and Φ + dΦ is the phase shift of the red beam.
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Metamaterials are composed of arrays of subwavelength-sized artificial structures; these architectures give rise to novel characteristics that can be exploited to manipulate electromagnetic waves and acoustic waves. They have been also used to manipulate elastic waves, but such waves have a coupling property, so metamaterials for elastic waves uses...
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Abstract The last 20 years have witnessed growing impacts of the topological concept on the branches of physics, including materials, electronics, photonics, and acoustics. Topology describes objects with some global invariant property under continuous deformation, which in mathematics could date back to the 17th century and mature in the 20th cent...
The paper proposed a model of a locally resonant (LR) piezoelectric/elastic phononic crystal (PC) nanobeam with periodically attached “spring-mass” resonator and additional spring between upper and lower nanobeams, as well as horizontal spring between mass and foundation. Euler beam theory and nonlocal piezoelectricity theory are coupled and introd...
![Figure 7. Principle of stealth cloak [33,39].](publication/341979319/figure/fig4/AS:902156169256960@1592102200039/Principle-of-stealth-cloak-33-39_Q320.jpg)
As a new type of acoustic functional material, phononic crystal has great research value and application environment. It is a periodic structure of two or more elastic materials, which are derived from photonic crystals. The main research work on phononic crystals focuses on the two band gap formation mechanisms of Bragg scattering and local resona...
Citations
... Phononic crystals are structured materials designed to manipulate and control the propagation of mechanical vibrations or sound waves, enabling the modulation of their characteristics such as frequency, velocity, and transmission. These crystals are engineered to exhibit specific and unique properties that can alter the behavior of waves passing through them [1,2]. The properties of phononic crystals have potential applications such as filters [3][4][5], sensors [6,7], and waveguides [8][9][10]. ...
In mechanical engineering, focusing on elastic waves is pivotal for applications, such as energy harvesting, shock mitigation, and wave manipulation. While phononic crystals have historically been a key method for managing wave propagation, this study explores a novel technique. This method introduces Gradient Refractive-Index (GRIN) lenses by altering the plate thickness and creating localized high-refractive-index zones. Unlike traditional methods, this localized GRIN approach aims to overcome the fabrication and structural limitations, particularly in thin structures. The patch-shaped lenses, with their smoothly transitioning profiles, offer the potential for improved performance in thinner structures. Through numerical analysis, we established design principles and examined the elastic wave propagation and focusing characteristics across various thickness variation profiles. This study conducts a thorough analytical and experimental evaluation of these lenses to confirm their effectiveness, structural robustness, and suitability for optimizing wave concentration in various mechanical engineering applications. The research represents an alternative, innovative, and promising pathway in the field of wave focusing, transcending the traditional constraints of thin plate structures.
... 6,7 As a kind of artificial inhomogeneous material, acoustic metamaterials are synthetic materials formed by a periodic variation in the mechanical properties of materials (i.e., elasticity modulus and mass density), and it can suppress and manipulate acoustic waves transmission. [8][9][10][11] Acoustic metamaterials have unique mechanical properties, such as negative equivalent mass density, negative equivalent bulk modulus, and negative shear modulus, which are achieved through topology design of micro-structure and materials distribution design. [12][13][14] Acoustic scattering is caused by acoustic reflection of the interface, obstacles, or targets in the acoustic transmission process; reducing acoustic scattering is of great significance to improve the acoustic stealth ability. ...
The acoustic wave transmission manipulation ability is the most important performance for the acoustic metamaterials. To manipulate the acoustic transmission, the combination acoustic metamaterials structures are involved, and the two-directional acoustic penetration cloaking scheme are constructed. The combination acoustic metamaterials include chiral metamaterials and self-collimation metamaterials, the acoustic wave transmission path are manipulated to bypass from the acoustic scattering target in the penetration cloaking, and the target scattering stealth problem are effectively solved. In the end, the acoustic transmission manipulation performances are verified by numerical analysis with a finite-width acoustic metamaterial structure plates. The results provide technical support for design and application for acoustic transmission manipulation with acoustic metamaterials.
... Controlling waves using metamaterials has becoming a hot topic due to their extraordinary properties that are not found in naturally occurring materials. Recently, the concept of metamaterials has been successfully exploited in diverse fields, including electromagnetics [1], acoustics [2,3] and elastodynamics [4]. Metasurfaces, as the subwavelength planar counterparts of metamaterials, manipulate wavefronts of propagating waves through phase profile designing. ...
... In particular, periodic materials with heavy, stiff inclusions with a soft coating embedded in a stiff matrix have been demonstrated to have broad spectral gaps at low frequency, see, for example [1,2]. The intervals of frequency inside which waves are attenuated can have different applications in vibration isolation and impact absorption [3][4][5][6][7][8]. ...
Elastic wave propagation in solids can be controlled and manipulated by properly designed metamaterials. In particular, polarization conversion can be obtained by using anisotropic materials. In this paper, we propose a three-component locally resonant material with non-symmetrically coated inclusions, and we study the effect of the anisotropic equivalent mass on band gap formation and the polarization conversion of elastic waves. The equivalent frequency-dependent mass tensor is obtained through the two-scale homogenization approach. The study of the eigenvalues of the mass tensor enables to predict band gaps and polarization bands, as well as identifying a priori the effect of different geometric and material parameters, thus opening the way to metamaterial optimization.
... Willis couplings do not appear in the constitutive relations of the constituents, hence the resultant Willis materials are a type of metamaterial, the behavior of which is fundamentally different from the behavior of their building blocks [21][22][23][24][25][26][27][28][29]. The surge of interest in metamaterials has resulted in renewed interest in eponymous Willis materials, with numerous theoretical studies and experimental realizations [30][31][32][33][34][35][36][37], including their application to elastic and acoustic wave control for, e.g., cloaking and sound manipulation [38][39][40][41][42][43][44][45][46]. One of the fundamental * meshmuel@technion.ac.il theoretical works on this topic by Sieck et al. [33] addressed the physical origins of the Willis coupling, and showed that the homogenized description must include this coupling in order to be physically meaningful. ...
... We then combine Eqs. (37)- (39) to end up with the following expressions relating the stress and momentum of the charged mass-spring system to the externally applied strain, velocity, and electric fields: ...
Willis dynamic homogenization theory revealed that the effective linear momentum of elastic composites is coupled to their effective strain. Recent generalization of Willis dynamic homogenization theory to the case of piezoelectric composites further revealed that their effective linear momentum is also coupled to the effective electric field. Here, we introduce the simplest possible model—a one-dimensional discrete model—that exhibits this so-called electromomentum coupling in subwavelength composites. We utilize our model to elucidate the physical origins of this phenomenon, illustrate its mechanism, and identify local resonances which lead to elevated Willis and electromomentum coupling in narrow frequency bands. The results provide intuitive guidelines for the design of this coupling in piezoelectric metamaterials.
... In recent years, elastic metamaterials have generated considerable interest as artificial period materials owing to their supernormal physical properties [1][2][3][4][5] and strong designability [6,7]. One of their most useful properties is their bandgap [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], a frequency range in which the propagation of elastic waves is prevented. ...
... One of their most useful properties is their bandgap [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], a frequency range in which the propagation of elastic waves is prevented. This ability to arrest wave propagation leads to potential applications in waveguides or vibration and noise reduction [6,7,24,25]. Most studies on elastic metamaterials were focused on microstructural cell designs [10][11][12][13][14][15][16][17][18], bandgap formation mechanisms [19][20][21][22][23], and property-influencing factors [8,9]. ...
... Controlling waves using artificial metamaterials has attracted attention in various fields, including electromagnetics [1], acoustics [2], and elastodynamics [3,4], because of the unprecedented capabilities of these materials. Metasurfaces, as a kind of ultrathin planar metamaterials, steer waves mainly through phase modulation governed by the generalized Snell's law (GSL) [5]. ...
Wave splitting, one of the most valuable applications in wavefront modulation, is of great significance in both practical engineering and academia. However, to date, the available techniques to split waves are scarce aside from using conventional metasurfaces governed by the generalized Snell's law. To this end, based on the newly proposed high-order diffraction theory, we design a type of simply structured elastic metagrating for the splitting of flexural waves in plate-like structures. Theoretical models are established to characterize wave propagation behavior in metagratings and functional units. Theoretical analysis confirms the validity of our designs, which is also supported by numerical simulations and experiments. The present study provides a general method for the designing of wave splitters.
... Propagation of the elastic waves in periodic structures has recieved much attention in recent decades. Possibility to completly disable the elastic wave propagation in a certain frequency range (Wang, Li, Kishimoto, Wang, & Huang, 2010;Zou, Chen, Liang, & Cheng, 2007), control the wave propagation direction (Zhu & Semperlotti, 2016;Tanaka, Yano, & Tamura, 2007), and focus them (Philippe, 2015;Park, Lee, & & Rho, 2020), allows to use the periodic structures as mechanical filters, waveguides, acoustic lenses etc. which is perspective in many areas, including non-destructive testing. ...
Periodic structure is wildly used in metamaterial design in different fields. It has great potential in NDE and SHM fields due to different features, like focusing, bandgap, direction manipulation, and mode selection. First fundamental torsional mode T(0,1) can be focused by adding periodic structure based on phononic crystals and gradient index refraction. In the present study influence of the periodic structure with different element shape on torsional wave is discussed. Eigenfrequency analysis was performed for different configurations of the periodic structure by using the finite element method and floquet boundary condition. Dispersion curves for the torsional wave were obtained as an analysis result. Propagating wave creates a local resonance which leads to the bandgaps between modes and the first torsional mode T(0,1) becomes dispersive. The influence of the configuration on the dispersion curves is shown. Additionally mentioned that negative group velocity can be achieved.
... On the other hand, there is a great need for beam splitters to generate multiple beams from a single source, which has potential applications in beam multiplexing [31], multi-beam structural health monitoring [32], and ultrasonic medical imaging [33]. Phononic crystal structures and metamaterials have been explored for splitting an incident beam into two or more output beams. ...
In this article, we report a lens design based on a concentric circular structure with continuous changing of thickness defined in a thin plate structure for focusing a plane wave into three spots (triple focusing) and for splitting elastic waves emanating from a point source into three collimated beams of different directions (three-beam splitting). Inspired by the principle of optical graded index triple focusing lens, the governing equations of the gradient refractive index profiles necessary for achieving such structural lens were obtained. The refractive index profiles were realized by using a lens design with two concentric circular areas of different thickness variation profiles defined in a thin plate. Analytical, numerical, and experimental studies were conducted to investigate the functionalities of the variable thickness structural lens. The results showed that the lens developed in this study were able to perform triple focusing and three-beam splitting with broadband property. Furthermore, the locations of focal points and directions of collimated beams can be engineered by changing the lens thickness profiles according to the governing equations. In addition, the proposed lens is miniature and simple design, which overcome the limitations of previous triple focusing and beam splitters.
... However, external energy input was needed to realize tuning of the structure frequency. On the other hand, there is a great need for beam splitters to generate multiple beams from a single source, which has potential applications in beam multiplexing [31], multi-beam structural health monitoring [32], and ultrasonic medical imaging [33]. Phononic crystal structures and metamaterials have been explored for splitting an incident beam into two or more output beams. ...
In this article, we report a lens design based on a concentric circular structure with continuous changing of thickness defined in a thin plate structure for focusing a plane wave into three spots (triple focusing) and for splitting elastic waves emanating from a point source into three collimated beams of different directions (three-beam splitting). Inspired by the principle of optical graded index triple focusing lens, the governing equations of the gradient refractive index profiles necessary for achieving such structural lens were obtained. The refractive index profiles were realized by using a lens design with two concentric circular areas of different thickness variation profiles defined in a thin plate. Analytical, numerical, and experimental studies were conducted to investigate the functionalities of the variable thickness structural lens. The results showed that the lens developed in this study were able to perform triple focusing and three-beam splitting with broadband property. Furthermore, the locations of focal points and directions of collimated beams can be engineered by changing the lens thickness profiles according to the governing equations. In addition, the proposed lens is miniature and simple design, which overcome the limitations of previous triple focusing and beam splitters.
