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In this paper, a phononic crystal with acoustic black hole (ABH) characteristics is designed based on the compression effect of ABHs on acoustic wavelengths. The simulation results show that the lower limit of the first bandgap of the phononic crystal with ABH is reduced by 127.8 Hz, the upper limit is increased by 694.4 Hz, and the bandgap width is increased by 822.2 Hz compared with that of the phononic crystal without ABH. The mechanism of bandgap expansion is discussed based on the mechanism of bandgap formation and the acoustic modulation effect of the ABH. The influence of the geometric and material parameters of the ABH on the bandgap is analyzed. The ABHs offer a new way of optimizing phononic crystals, and this work can be used as a reference for their design. [ABSTRACT FROM AUTHOR]

With the rapid development of cities, metro transportation has also developed rapidly to solve the congestion problems caused by urban development. However, with the continuous development of metro transportation, the vibration problems caused by it have become increasingly obvious. Based on the phonon crystal theory, this paper investigates the vibration characteristics of the metro track structure. It analyzes the influence of the track structure parameters on the band gap characteristics to regulate the metro vibration band gap range. To study the band gap characteristics of metro monolithic bed track structure, establish the double-layer Euler beam model and use the plane wave expansion method (PWE) to calculate its energy band structure; use the finite element method (FEM) to calculate to get its band structure, frequency response function, and time domain analysis. The calculation of PWE shows that there is a band gap in the range of 0–300 Hz for the metro monolithic track bed, which is 0–194.5 Hz; the calculation of FEM shows that the range of band gap is 0–193.7 Hz. Fastening spacing, stiffness, and sub-slab support stiffness will have an impact on the band gap, so appropriate fastening and spacing need to be selected for effective vibration damping of the track structure. The results show that the band gap characteristics of the metro monolithic track bed can be calculated effectively and accurately by using the phononic crystal theory. [ABSTRACT FROM AUTHOR]

This study presents a tunable phononic crystal (PnC) composed of liquid–solid components, demonstrating adjustable waveguiding and directional transmission capabilities through the rotation of embedded scatterers. A two-dimensional model featuring grooved steel rods in water is analyzed using finite element simulations to evaluate band structures and transmission spectra. To achieve the widest full band gap, a genetic algorithm is integrated to optimize the structural parameters. By examining a supercell with a central defect, wave localization is achieved, facilitating tunable waveguide formation. Analysis of equifrequency contours reveals that, at a scatterer rotation angle of 0∘, the structure enables directional transmission, with wave propagation preferentially aligned with specific crystal axes. This work pioneers a new strategy for designing tunable acoustic metamaterials with applications in advanced waveguiding and directed acoustic manipulation technologies. [ABSTRACT FROM AUTHOR]

In this paper, the multi-objective optimization problem (MOOP) of selecting suitable materials from four materials for phononic crystals layouts is investigated based on an optimization method combined nondominated sorting-based genetic algorithm II (NSGA-II) and finite element method (FEM). Driven by different optimization objectives, the changes in the optimized structure compared to the seed structure are the change of the bandgap mechanism from a local resonance mechanism to a Bragg scattering mechanism, the change of the included materials from four to three, and the significant change in the location and extent of the pores and other materials, respectively. The obtained nondominated Pareto solution of MOOP can balance the bandgap and the structural mass, which provides the decision-maker trade-off to select the appropriate optimized solution. Compared with the single-objective optimization problem (SOOP), the MOOP not only obtains a nondominated solution close to the result of SOOP, but also obtains other nondominated solutions of MOOP, which proves the effectiveness of the optimization algorithm in this paper. The design method in this paper can be easily extended to select suitable materials from a wider variety of materials for bandgap optimization design of PnCs, which has very promising applications. [ABSTRACT FROM AUTHOR]

We investigate the energy band structure and transport properties of electrons in superlattice structure based on semi-Dirac material with one-dimensional periodic potentials of square barriers. The influence of different parameters on transmission probability in superlattice structure is studied. It is found that two new Dirac points are formed in the superlattice structure by adjusting the gap parameter. The position of the new Dirac points can be regulated by changing the size of the potential barrier, the ratio of well width to barrier width, and the gap parameter. Some forbidden bands appear in the transmission probability, the location and width of the forbidden bands can be regulated by changing the system parameters. [ABSTRACT FROM AUTHOR]

A new arrayed phononic crystal (PnCs) with defects is proposed. The supercell method is used to calculate the band structures. Energy localization can be found around the defects and energy harvesting (EH) can be realized by the attachment of piezoelectric patches around the designed defects. The EH can be concentrated on the frequency of 64–64.1 kHz with output voltage of 8.22 V. By the change of the piezoelectric patch from circular to oval shape, the frequency of EH can be changed. By the optimization of geometric shapes of piezoelectric patches and the optimal design of unit cell, the EH output voltage can be increased to 4.21 times higher than the original state and the EH frequency band is effectively broadened. The amplification factor can be increased to 327.13. [ABSTRACT FROM AUTHOR]

The capacity of Phononic crystals (PCs) to form bandgaps (BGs) that limit the transmission of elastic/acoustic waves is a key property that is particularly beneficial for vibration/sound isolation and signal processing. In this work, a parametric analysis of Poisson's ratio of rubber, and the density, geometry and size of scatterer on the BGs of porous, solid/solid, fluid/solid and solid/fluid PCs is presented. Based on the simulation results, it is found that the width of the first absolute bandgaps (FABGs) of porous PCs is not necessarily proportional to the porosity due to the pore shape; when Poisson's ratio of compressible and incompressible rubber is increased, the FABG width of porous PC decreases dramatically. In addition, the FABGs of solid/solid PCs are strongly dependent on whether the rubber is a matrix or scatterer; the fluctuation of the FABGs is also highly related to the density of the solid. Fluid–structure PCs have smaller FABGs than porous and solid/solid PCs, and these FABGs usually occur within higher-order energy bands. Rubber compressibility significantly affects the FABGs of porous and solid/solid PCs, but almost not fluid-structural PCs. The results presented in this work offer guidance to tune the BG and design acoustic devices in various practical applications such as noise and vibration insulators. [ABSTRACT FROM AUTHOR]

As an efficient, environmentally friendly, and economical urban public transportation tool, the subway has significant advantages compared to other urban public transportation tools and plays an irreplaceable role in the urban rail transit system. While the subway brings many conveniences to people, its operation has also brought a series of problems to urban development and residents’ lives, especially the vibration and noise problems generated by the subway have become unavoidable and urgent problems to be solved. The traditional wave barriers have a certain effect on attenuating and suppressing the vibration generated by the subway, but it has shortcomings in terms of the width and quantity of elastic wave bandgap (BG), so its application in low-frequency vibration reduction and isolation of subway systems is greatly limited. In order to broaden the elastic BG width and quantity of the wave barrier, this paper designs a novel phononic-like crystal subway wave barrier (PLCSWB) for subway vibration isolation based on locally resonant theory. Firstly, the dispersion curves of the novel PLCSWB are calculated using the improved plane wave expansion method and finite element method (FEM), and compared with the dispersion curves of traditional phononic crystal (PC) wave barriers. Secondly, the frequency response function of the novel PLCSWB is calculated using FEM to evaluate its attenuation effect on vibration, and the energy distribution characteristics at its BG boundary are analyzed. Then, the main factors affecting the BG of the novel PLCSWB are analyzed, and a spring–mass system equivalent model of the novel PLCSWB is established to theoretically estimate its BG range. Finally, the vibration data of the tunnel wall monitored on site are used to analyze and verify the vibration isolation effect of the novel PLCSWB. The results show that the novel PLCSWB opens five low-frequency BGs in the 200Hz frequency band, which increased the total width of the opened BGs by 49% compared to traditional PC wave barriers. In the frequency range of the BG, the attenuation value of the novel PLCSWB to vibration is mostly above 30dB, and the energy distribution inside the structure is mainly concentrated in the primitive cell that controls the BG, indicating good attenuation and control effects on vibration. The main factors affecting the BG of the novel PLCSWB are the density of the scatterer material, the elastic modulus, and the thickness of the wrapping layer material. Moreover, during subway operation, the novel PLCSWB has a good attenuation effect on the vibration transmitted from the tunnel wall to the soil. Among them, the maximum vibration acceleration amplitude of the novel PLCSWB with nine rows is reduced by 47%, and the vibration isolation performance is remarkable. The relevant research results of this paper provide a novel approach and method for the study of subway vibration reduction and isolation, and can also provide specific references for the design and development of wave barriers. [ABSTRACT FROM AUTHOR]

Eshelby tensors in elasticity are obtained for two-dimensional (2D) decagonal quasicrystal containing an ellipsoidal inclusion. Based on the intrinsic strain formula and Mori–Tanaka theory, the effective elastic properties of 2D decagonal composites are obtained. The effects of inclusion volume fraction and inclusion aspect ratio on elastic properties of composites with 2D decagonal quasicrystal are discussed. [ABSTRACT FROM AUTHOR]

The mixed spin Ising nanowire with random and dilute crystal fields has been explored based on the finite cluster approximation. Much concern has been addressed in treating the effects of the randomness with two distribution types of the crystal field on the phase diagrams. It has been demonstrated that for a low random crystal field D marked by the fluctuation d, all transition lines are of second order and are not particularly sensitive to the fluctuation; whereas, for high values of D, the transition temperature depends on the fluctuation and may display tricritical points. Under the effect of the dilute crystal field, according to the surface shell coupling strength, the tricritical behavior occurs exclusively for higher values of the concentration p where a large majority of spins are influenced by the crystal field. All these behaviors have been confirmed by examination of magnetizations. [ABSTRACT FROM AUTHOR]

For a class of embedded elastic metamaterial plate, a general vibration analysis process is given based on the idea of equivalent analysis, which combines the equivalent medium theory and the classical thin plate vibration theory. The embedded elastic metamaterial plate is treated as an equivalent homogeneous plate with abnormal effective medium parameters by using the equivalent medium theory, and then the natural vibration characteristics and steady-state vibration characteristics are investigated. The results show that the semi-analytic form of the vibration analysis process is effective, which can obtain the vibration characteristics of such heterogeneous and complex structures quickly and accurately within the medium and low frequency regions. The results also reveal the plate's anomalous behaviors that are quite different from the traditional homogeneous plates. For the natural vibration, there exists no natural frequency in the band gap and they can be formed only in the pass band. These modes tend to gather gradually when approaching the initial frequency of the band gap, and the closer to the lower band edge of the band gap, the smaller the distance between natural frequencies and the greater the modal density. Additionally, the modes of the corresponding orders before and after the band gap are identical on the macro level but completely different on the unit-cell level. For the steady-state vibration, there is no resonance peak in the band gap, the resonance peaks are distributed denser and denser when approaching the initial frequency of the band gap, and the distribution of the displacement field at corresponding order of resonance peaks before and after the band gap is also similar on the macro level. This work not only facilitates the design and analysis of elastic metamaterial plate structures, but also deepens the understanding of their extraordinary vibration characteristics and expands the design space of mode characteristics. [ABSTRACT FROM AUTHOR]

In this paper, we design a phononic crystal plate with periodic lattices based on acoustic black holes (ABHs). The basic structure is composed of a triangular lattice with ABHs in the x − y plane whose symmetry ensures that the Dirac cone exists at the corners of the Brillouin zone. The space inversion symmetry can be broken by alternating the parameter values of ABHs. Due to the symmetry of parameters, two topologically distinct phases can be obtained by analogy with the quantum valley Hall effect. We connect them together to create topological edge states. More specifically, the interface between these two phases supports the topologically protected elastic guided mode in the horizontal plane which features quasi-unidirectional propagation. Then, simulations and experiments are carried out to verify this phenomenon. [ABSTRACT FROM AUTHOR]

Elastic wave metamaterials, such as phononic crystals (PnCs) always composed of several materials in terms of periodical structures, possess unique acoustic characteristic which can exhibit outstanding performance in forbidding wave propagation with some specific frequencies. In this paper, due to the thermal sensitivity of the thermally induced shape memory polymers (SMP) and period thermal fields, a tunable planar acoustic metamaterial which is constituent homogeneous is proposed and designed to realize the function of waveguides. A thin plate model composed of homogenous thermally induced SMP and adhered with a series of metallic films at the top boundary which plays the role of local heating sources is established. The homogenous plate can be transferred into acoustic metamaterial once the non-uniform period thermal fields are imported. Based on the Fourier law of heat conduction and finite element method (FEM), a two-dimensional numerical model via COMSOL Multiphysics is carried out to perform the in-plane mode band structures and transmission spectra. The results show that the bandgap will be effectively opened and change obviously as the injected heat flux increases. Furthermore, band structures of 7 × 1 supercell with thermal defect are performed to reveal the design guideline of waveguides which is supposed to be the basis of line-type and L-type waveguides. The tunable characteristics of waveguides based on thermal fields with thermal defects are also discussed. These results may pave a new avenue for the design of tunable acoustic metamaterial composed of thermal sensitive material which own a prospect to be applied in area of acoustic waveguides. [ABSTRACT FROM AUTHOR]

In this paper, the effective electroelastic properties of one-dimensional (1D) hexagonal piezoelectric quasicrystal containing randomly oriented inclusions are considered. The explicit expressions are obtained for the Eshelby tensors for 1D hexagonal piezoelectric quasicrystals containing rod-shaped and penny-shaped inclusions. The closed forms of the electroelastic constants are acquired for four special cases of random orientations of inclusions. Numerical results are given for the 1D hexagonal piezoelectric quasicrystal containing randomly oriented ellipsoidal inclusions. The results indicate that the effective electroelastic properties of 1D hexagonal piezoelectric quasicrystal composites are strongly affected by both the aspect ratio and the orientation of inclusions. [ABSTRACT FROM AUTHOR]

As a kind of new intelligent materials, liquid crystal elastomer (LCE) has attracted widespread interest. In this paper, we introduce LCE into chiral phononic crystal (CPC), and investigate the properties of band structures based on the iterative calculation method. The effects of dextral bending angle, chiral geometric parameters b and h , and the director rotation angle on bandgaps are mainly discussed. This work is a meaningful try for application of LCE in acoustic field and propose a new strategy in designing of PC with tunable bandgaps. [ABSTRACT FROM AUTHOR]

Structural stiffness of phononic crystals (PnCs) can affect their bandgap properties. It thus needs to consider stiffness in the design of the unit cell of a PnC. In this paper, a local resonant (LR) rod composed of tri-wing rhombus ligament (TRL) resonators arranged periodically within a common hollow rod is proposed to create a low-frequency flexural vibration bandgap. The dispersion relations, mode of resonances and vibration transfer function are studied using a finite element method. Low-frequency forbidden bands can be effectively shifted by changing the resonator geometries. In addition, both numerical simulations and sample test are conducted to verify the low-frequency bandgap. The results show that the hollow rod with TRL resonators can create a low-frequency flexural vibration bandgap as well as have high support structure stiffness. [ABSTRACT FROM AUTHOR]

We study the angle-dependent reflection spectra of two-dimensional photonic crystal (PC) slabs, which we use for developing mid-infrared surface-emitting lasers. The PC design produces a perfect resonance between material gain frequencies and the Γ -point band edge in the first Brillouin zone. Hence, we expect laser emission to occur in a direction normal to the slab surface. We fabricate PC slabs, which consist of a square lattice of nanopillars with different lateral cross-sections, i.e., circles, triangles, and pentagons, and discuss their impact on the mode characteristics. We consider that our angle-resolved spectroscopic technique will be useful for characterizing mid-infrared PC slabs to be used in vertical surface-emitting quantum cascade lasers. [ABSTRACT FROM AUTHOR]

The vibration induced by low-frequency elastic wave reduces the working accuracy of precision instruments. The locally resonant phononic crystal provides a feasible measure for low-frequency vibration isolation because of its bandgap characteristics. In this paper, a locally resonant phononic crystal structure with a broad bandgap is proposed, which consists of a periodic phononic crystal plate with double-sided steel stubs coated by rubber layers. Through finite element analysis, it can be found that the proposed structure can produce a bandgap with 355 Hz bandwidth within the range of 0–500 Hz and isolate vibration in the range of bandgap. By analyzing the local resonance modes of the proposed structure, we further propose the equivalent mass–spring model to predict its bandgap range. The predicted bandgap results from equivalent models of the proposed structure agree well with the results from the finite element analysis. These equivalent models provide an effective and simple method for bandgap optimization of the proposed phononic crystal structure. [ABSTRACT FROM AUTHOR]

In this paper, a ring-slotted spiral local resonant phononic crystal structure is investigated. The energy band characteristics and transmission losses of the structure are calculated using the finite element method. The numerical results show that the structure can generate bandgap in the range of 23.54–102.87 Hz. Combined with the modal coupling theory, the vibrational modes of the ring-slotted spiral local resonant phononic crystal are analyzed to reveal the bandgap formation mechanism of the structure. The effects of the various dimensional parameters and material hardness on the bandgap of the structure are analyzed by varying them. The results show that by varying the filling radius of silicone rubber in the ring-slotted spiral local resonant phononic crystal, the structure can be made to have an onset frequency of 19.42 Hz and generate a bandgap in the range of 19.42–78.16 Hz. A new idea is provided for the application of phononic crystal in low-frequency environment for vibration and noise reduction. [ABSTRACT FROM AUTHOR]

We study the thermodynamical properties of two-dimensional mixed spin Ising system consisting of spin- 1 ∕ 2 and spin-1 with four-spin interactions in crystal field interactions on a square lattice within the framework of the finite cluster approximation based on single-site cluster theory. In this paper, the phase diagrams show qualitatively and quantitatively interesting features. In fact, the system exhibits a variety of interesting features resulting from the introduction of the four-spin interactions and the crystal field interactions. Finally, using the same method, we study the behavior of the total magnetization of the Ising model with four-spin interactions in the crystal field to show the existence of compensation points and point intervals for certain values of D. [ABSTRACT FROM AUTHOR]

An elastic topological insulator with pseudo-spin characteristics is designed based on honeycomb lattice phononic crystals with positive hexagonal carriers, which can realize path defect immunity and backscattering suppression transmission characteristics. By introducing a positive hexagon carrier with a certain size at the narrow diameter junction of the two-dimensional honeycomb structure to achieve symmetry breaking, a four-fold accidental degeneracy point can be obtained by adjusting the cell parameters. The main variable of the primitive cell is the hexagonal carrier side length S. It is found that the four-fold Dirac point can be opened and a band gap can be formed by contracting the positive hexagonal carrier. Inversion of the energy band occurred in the separated two-fold degenerate state, for which the transformation of mediocre state and nonmediocre state had been realized so that the structure with acoustic pseudo-spin and topological edge state could be obtained. Based on the principle of body-edge state correspondence, the topologically protected edge acoustic transmission is simulated by the construction of the edge states combined with the connection of different structural systems. Further, different elastic phonon crystal structures are constructed, and the characteristics of path defect immunity and back-scattering suppression of elastic wave propagation by topological edge states are verified. The designed elastic topological insulators have great application prospects in the regulation of elastic waves. [ABSTRACT FROM AUTHOR]

As an artificial periodic material, phononic crystals (PnCs) are suitable for energy harvesting from vibration and noise environments of equipments. A two-dimensional (2D) PnC with a point defect is presented to design a piezoelectric energy-harvesting (PEH) device. Using finite element (FE) simulations, bandwidth and electric power of the initial supercell using the PnC are obtained but do not attain the optimal performance. Therefore, five geometric parameters are considered to perform the numerical experiment using a five-factor and seven-level experimental design. The two relationships between the five geometric parameters and PnCs bandwidth, the five geometric parameters, and output power are finally obtained. The two functional relationships are regarded as a unified objective function to further optimize five geometric parameters. The optimized PnC-based PEH device will achieve better output power within broadband. It is expected to be used to design PEH devices to achieve better output power in wider bandwidth. [ABSTRACT FROM AUTHOR]

In the present work, the piezoelectric properties of TlIn 0. 9 Ga 0. 1 Se2 single crystals are investigated. Single crystals were grown by the Bridgman–Stockbarger method. The results show that when periodic mechanical vibrations are excited in these crystals, the electrical conductivity is modulated at the same frequency. Measurements of the amplitude values of the piezoconductivity at the same degree of deformation in the dark and under different illumination revealed the presence of a linear relationship between them. The level of the piezosignal also changes linearly depending on the strength of the magnetic field. Thus, TlIn 0. 9 Ga 0. 1 Se2 crystals have a potential prospect of application in the field of highly sensitive magnetic and light sensors. [ABSTRACT FROM AUTHOR]

Bandgaps are intrinsic physical properties of periodic structures, for example, mechanical metamaterials or phononic crystals, which indicate attenuation of wave propagation within a specific frequency range. Bandgap calculation of mechanical metamaterials is realized via discretizing a representative voluame element (RVE) and imposing complex-valued Bloch wave boundary conditions. It is highly desirable to implement Bloch wave analysis in real-valued commercial finite element software. We present and detail an ABAQUS and Python implementation of Bloch wave analysis. Two-dimensional (2D) soft as well three-dimensional (3D) hard mechanical metamaterials are chosen as numerical examples. Material and geometric nonlinearities are tackled properly and the effects of pre-strains are explored. Our numerical results are validated either by similar results reported in the literature or by our experimental measurement. The presented numerical strategy would aid the design, analysis and utilization of mechanical metamaterials for dynamic applications. The codes and data of the paper could be downloaded from https://github.com/XJTU-Zhou-group/Calculating-band-gaps-of-nonlinear-mechanical-metamaterials. [ABSTRACT FROM AUTHOR]

The reduction of the periodicity of phononic crystals (PnCs) usually leads to the decrease of band gap (BG) width. However, a systematic study of the relationship between the unit cell and the supercell in the proposed hybrid stepped PnCs shows that the BG width can be increased in special cases. How the periodicity of PnCs affects the final BG characteristics is important for the design of PnCs with high structural performance. Supercell of PnCs with imperfections from the rotation of the unit cell was used to demonstrate the relationship between the unit cell and the supercell, which was further used for the wave attenuations of the proposed hybrid stepped PnCs. The rotation angle and the number of the rotating scatterers can be controlled for better structural performance for the PnCs. The different changes of the equivalent stiffness corresponding to the starting and the end frequencies lead to the increase of the BG width when the ration angle of the unit cell is 3 5 ∘ in the supercell composed of zigzag scatterers and cross scatterers. The rotation of the unit cell in the supercell leads to the decrease of the starting frequency. [ABSTRACT FROM AUTHOR]

To investigate the properties of elastic waves propagating in the periodic ballasted track, a double-rail phononic crystal (DRPC) model which consists of two parallel rails fastened on equally spaced sleepers supported by ballast is proposed in this study. The presented numerical results show that there are twelve characteristic waves occurring in the DRPC. These waves can be divided into three kinds. Within the calculated frequency range, the first kind of characteristic wave always propagates except an initial lower frequency range. The second kind of characteristic wave has alternative pass bands and stop bands, showing obvious phononic property of the DRPC. The wavenumbers of the third kind of characteristic wave have larger imaginary parts, implying that this kind of wave is evanescent wave and can only propagate a few spans of the track away from the source. The numerical results show more advantages of the DRPC for explaining the elastic wave propagation mechanism in the ballasted track than the single-rail phononic crystal (SRPC) model. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the structural design of beam splitters with high total transmission efficiency in the two-dimensional (2D) GaSb (Gallium Antimonide)-based photonic crystals, and several optimal structures for 1 × 2 and 1 × 4 Y-shaped beam splitters have been provided. Using our proposed alternating iteration algorithm, by introducing several microstructures in the bend and Y-shaped junction areas to achieve topology optimization, the design of Y-shaped beam splitters with high total transmission efficiency at 1550 nm makes great progress. The splitter structures are designed on 2D GaSb-based photonic crystals with a triangular lattice of air holes immersed in the GaSb. All designs are simulated numerically and analyzed by using the finite element method. The optimized structures of 1 × 2 , 1 × 4 Y-shaped beam splitters show that our optimization technique is efficient and simple. And the total transmission efficiencies both over 7 2 % at output ports are obtained, which indicates that our method is relatively efficient to other methods in some related reports. [ABSTRACT FROM AUTHOR]

Sonic crystals (SCs) are unique periodic structures designed to attenuate acoustic waves in tunable frequency bands known as bandgaps. Though previous works on conventional uniform SCs show good insertion loss (IL) inside the bandgaps, this work is focused on widening their bandgaps and achieving better IL inside the bandgaps by using a gradient-based sonic crystal (GBSC). The GBSC applies property gradient to the conventional SC array by varying its basic properties, i.e., the distance between the scatterers/resonators (lattice constant), and resonator dimensions between the columns and hence the name GBSC. The design of the GBSC is backed by the results of acoustic beamforming experiments conducted over the uniform SCs of hollow scatterers and Helmholtz resonators (HRs) having two-dimensional (2D) periodicity prepared by using Polyvinyl chloride (PVC) pipes without any property gradient and their respective 2D finite element (FE) studies. The experimental and FE simulation results of the uniform SCs were found to be in good agreement and therefore, the GBSC was modeled and analyzed using FE method considering the viscothermal losses inside the resonators. The results indicated that the property gradient improves both Bragg scattering and Helmholtz resonance compared to that of the uniform SCs and therefore, the GBSC exhibits wider attenuation gaps and higher attenuation levels. An array of 30 microphones was used to conduct acoustic beamforming experiments on the uniform SCs. Beamforming was found to be an advanced and fast method to perform quick measurements on the SCs. [ABSTRACT FROM AUTHOR]

We have employed the Oguchi approximation (OA) to investigate the effects of a random crystal field which is active (inactive) with probability p (1 − p) for given lattice sites on the thermodynamic properties of the mixed spin- (5 2 , 1 2) anisotropic Heisenberg model in the presence of an external magnetic field. By exploiting the thermal variations of the order parameters, interesting phase diagrams are produced on various planes. The phase diagrams show first- and second-order transition lines and also tricritical points. In addition to the reentrant behavior which is localized in a certain range of p at very low temperature, the magnetic exponent β calculated near the critical point exhibits interesting behaviors depending on the crystal field interaction. The hysteresis behavior of the model is also investigated and it reveals that the width of hysteresis loop decreases or increases, respectively, for negative or positive crystal field region as the probability p increases. [ABSTRACT FROM AUTHOR]

In this paper, a novel phoxonic crystal (PxC) structure composed of silicon, with optimal dual phononic band gap (PNBG) and photonic band gap (PTBG), is presented. Using the finite element analysis method, both the transmission characteristics and dispersion relation of PNBG and PTBG are calculated, and the existence of dual BGs is demonstrated by the means of the analysis of transmission for the PxC structure. The influences of structural parameters on the dual forbidden band characteristics are further explored, the sensitive structure parameters can be determined: the width of elastic beams, the length of square silicon, and the length of square hole. Using the orthogonal test, 25 experimental runs based on 3-factor and 5-level experiment are performed to finish the numerical experimental design and analysis. Four functional relationships can be acquired between the three sensitive parameters and dual BGs. Finally, the unified objective function method is employed to perform the construction of the single objective optimization model for the purpose of obtaining the optimal dual BGs and the corresponding optimal parameter combinations of the PxC structure. Such scheme can be used as the potential optimization way, which may find wide application in the development and design of PxCs. [ABSTRACT FROM AUTHOR]

This paper designs a thermal waveguide using thermal phonon insulators, to manipulate the loss of thermal radiation. Two-dimensional (2D) photonic crystals with dielectric background and air holes have been used in the waveguide clad to suppress thermal radiation so that thermal radiation cannot escape out from the waveguide clad. The photonic crystals may reduce the loss of thermal radiation through waveguide clad which surges the thermal energy confinement in the waveguide core and propagation along the longitudinal axis. The photonic crystals have been designed with the bandgap covering the thermal phonon frequency range and thus can be used to construct thermal phonon insulators to suppress or trap thermal emission generated through phonon wave propagation. The finite-difference-time-domain simulation results demonstrate that electromagnetic bandgap in photonic crystals has enough width in the thermal phonon frequency range to confine the thermal energy within the core of the waveguide and effective transmission of thermal radiation can be conquered within the waveguide core. [ABSTRACT FROM AUTHOR]

A calculation of the phonon contribution to the coherent transport between two-dimensional (2D) lattices is presented in this paper. The model structure is obtained by the juxtaposition of semi-infinites square (S) and triangular (T) leads, which thus define the nanojunction S / T and its inverse T / S. We determine, numerically and by simulation, the 2D interface observables for different values of masses and elastic coupling in the nanojunction zone. The local dynamics and atomic nanojunction response to the microscopic changes, in the interfacial domain, are subjects to our investigation. The theoretical formalism based on the matching technique is applied to describe the lattice dynamics and the evanescent phonon modes, in the two studied 2D interfaces. We mainly analyze the vibration spectra, the coherent phonon transmission/reflection and the phononic transmittance through the interface, as elements of a Landauer–Büttiker type scattering matrix. The obtained results show that the nanojunction domain is an effective phonon splitter and suggest that its characteristics may be controlled by varying its nanometric parameters. The observed fluctuations are due to the coherent coupling between continuum modes and the phonons' discrete states induced by the connected atomic sites. [ABSTRACT FROM AUTHOR]

A proper lattice structure consisting of homogeneous material is designed in this paper to investigate the maximum bandwidth of perfect lattice structures and tunable property of waveguide with linear geometric defect by means of selecting optimal geometric lattice cell. A simulation model based on finite element method is used to calculate dispersion curves and transmission spectrums of lattice structures with different geometric parameters. Meanwhile, a simplified theoretical model of unit cell, which considers the mass of grid bar and stiffness of node area, is applied to validate the accuracy of simulation result and may provide an effective approach for prediction of band gap lower boundary. Then, the validated numerical results show different orders of widest band gap that can be realized by different optimal geometric structures. Moreover, waveguide property can be effectively controlled and manipulated by changing defect parameters. The present study may establish theoretical and simulation foundation to control and manipulate band structures and other acoustic propagation characteristics of waveguide devices. [ABSTRACT FROM AUTHOR]

In this study, we have scrutinized the frequency gap generation by changing the geometrical parameters of a one-dimensional phononic crystal. For this purpose, we have calculated the transmission coefficient of an incident acoustic wave by using the transfer matrix method. We have retained and fixed the total length of the system and changed the system internal geometry not to increase the system length too much. Another reason was to adjust the phononic band gaps and get the desired transmission properties by finding the optimum internal geometry without increasing or decreasing the total length of phononic crystals. In addition, we also propose few structures with the opportunity of applications in acoustical devices such as sonic reflectors. Our results can also be of high interest to design acoustic filters in the case that transmission of certain frequencies is necessary. [ABSTRACT FROM AUTHOR]

Convergent beam electron diffraction (CBED) performed on two-dimensional (2D) materials recently emerged as a powerful tool to study structural and stacking defects, adsorbates, atomic 3D displacements in the layers, and the interlayer distances. The formation of the interference patterns in individual CBED spots of 2D crystals can be considered as a hologram, thus the CBED patterns can be directly reconstructed by conventional reconstruction methods adapted from holography. In this study, we review recent results applying CBED to 2D crystals and their heterostructures: holographic CBED on bilayers with the reconstruction of defects and the determination of interlayer distance, CBED on 2D crystal monolayers to reveal adsorbates, and CBED on multilayered van der Waals systems with moiré patterns for local structural determination. [ABSTRACT FROM AUTHOR]

In this paper, two-dimensional phononic bandgap materials are designed through multiobjective optimization using the genetic algorithm. Two cases are given. In Case I, 2D phononic crystals (PnCs) with maximum bandgap and minimum mass are optimized. The optimal results show that the third-order relative bandgaps become large, along with the increase in mass. In Case II, 2D local resonance phononic crystals (LRPnCs) simultaneously maximizing the third and sixth relative bandgap widths (RBWs) are designed. The frequency response function of the optimized structures shows that the attenuation of elastic waves is most remarkable at the beginning frequency of the bandgap. Finally, an integrated structure, which accumulates the bandgaps of three optimized substructures, is proposed. These results provide a new approach for bandgap design. [ABSTRACT FROM AUTHOR]

Locally resonant phononic crystal (LRPC) has the extraordinary property to prohibit the wave propagation in specific low-frequency ranges, however it exists limitation in engineering application due to narrow band gap width. Extensive achievements have been obtained on the locally resonant band gap (LRBG) tunability, whereas existing investigations mainly concern the independent primitive cells structure, which have the limitation in obtaining low-frequency and broadband simultaneously. In this paper, the composited locally resonant phononic crystals (CLRPC) are proposed and the effects of primitive cells contact state on the LRBG properties are investigated. The dispersion curves are applied to obtain the LRBG, and the corresponding modal features are analyzed to explain the band gap formation mechanism. The band structure indicates the design of composite primitive cells is able to increase the band gap number and obtain lower band gap, which is verified by the frequency response function (FRF). For the band gap formation mechanism, the asymmetric vibration due to primitive cells contact leads to diverse and strong coupling response, which generates more band gaps and reduces the band gap starting frequency, therefore the band gaps can be tuned by designing carefully the geometry structure of CLRPC. Further researches on band gap optimization demonstrate that the smaller cell spacing, smaller lattice constant and larger damping of coating layer should be satisfied to obtain broader LRBG and considerable attenuation synchronously. This investigation can provide references for the locally resonant isolation structure design in the low-frequency vibration control field. [ABSTRACT FROM AUTHOR]

In this paper, a windmill-like phononic crystal (PC) structure with optimal locally resonant bandgaps (LRBGs) is proposed. By analyzing the variation trend of BGs, three geometric parameters (the side length and height of cuboid scatterer, and the width of elastic beams) are found to be key factors for the determination of BGs. Using response surface methodology (RSM), 3-factor and 7-level experiment are designed to obtain experimental data with the help of finite element simulations. Three relationships (fitting equations) between the three factors and the second BGs terminating frequency, the first BGs bandwidth, and the second BGs bandwidth, are further obtained by fitting the simulation data. Based on the three fitting equations, the optimal LRBGs are finally obtained using a simple optimization method. The proposed windmill-like structure PC is demonstrated to possess an optimal range of BG. [ABSTRACT FROM AUTHOR]

The current topological edge states lack dynamical modulation and the intense field localization effect. To solve these problems, we construct a topological edge state structure based on two-dimensional photonic crystals with lattice shrink. Through the optimization of structure parameters, a nearly flat edge state dispersion curve occurs in a wide bandgap. The topological edge states with intense field localization take on some unique properties such that the transport directions can be controlled by both the source spin and the source position. The transport modes can be dynamically switched between the two opposite unidirectional channels just through moving the source position. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) magnonic crystal (MC) with an asymmetric complex basis is proposed in this paper, and its band structures are calculated in the whole area of the first Brillouin zone (BZ). This kind of MCs is composed of two different atoms in the unit cell, and the symmetry of the unit cell is broken due to changes in the position of the second atom, so the irreducible part of the BZ is no longer the small area (Γ X M) for square lattice, and it must be expanded to the whole first BZ. Only by investigating the whole first BZ, can we get the true full band-gap for this kind of MCs. [ABSTRACT FROM AUTHOR]

In this paper, we consider the discrete electrical lattice with nonlinear dispersion described by Salerno equation, Fig. 1. Stability of equilibrium points, limit cycles and flip and Hopf bifurcations of the system are discussed. New exact solutions of a continuous approximation of the discrete system in the upper forbidden band gap are obtained by two methods, namely, exp (− χ (ξ)) -expansion function method and Θ ′ (ξ) Θ 2 (ξ) expansion method. Numerical simulation is used to follow the dynamics of the system and to investigate its physical properties. [ABSTRACT FROM AUTHOR]

In this study, we carry out a simulation of the surface band structures for face-centered cubic (fcc) leads that end up in (100), (110) and (111) surfaces. The surface Hamiltonian matrix is constructed from tight-binding approach and the secular equations of the surface eigenvalue problem. The solution of the problem is performed by integrating the Landauer–Büttiker formalism (LBF) in the phase field matching approach (PFMA). The LBF provides the quantum scattering properties and the PFMA connects the bulk modes to those of the surface based on the quantum scattering coefficients. The combination of these methods allows calculating the electronic bands in the three directions mentioned above. We report the results of ordered slabs for Ag, described as s -like orbital and Ni given as d -type orbitals. To show the impact of expanding the crystal wavefunction, we reveal the calculation of the localized states for Rh, Cu, Pt given as d -type orbitals as first calculation then d 9. 5 s 1. 5 -coupling orbitals as second calculation. The results of the nonordered slabs are applied to Pd and Ir. Cutting the crystals affects the internal energy of the surface atoms, which will be subject to a relaxation effect until equilibrium is achieved. [ABSTRACT FROM AUTHOR]

By applying non-local elasticity theory and plane wave expansion (PWE) method to Timoshenko beam, the calculation method of band structure of a non-local piezoelectric phononic crystal (PC) Timoshenko nanobeam is proposed and formulized. In order to investigate the properties of wave propagating in the nanobeam in detail, bandgaps of first four orders are picked, and the corresponding influence rules of thermo-electro-mechanical coupling fields, non-local effect and geometric parameters on bandgaps are studied. During the research works, temperature variation, external electrical voltage and axial force are chosen as the influencing parameters related to the thermo-electro-mechanical coupling fields. Scale coefficient is chosen as the influencing parameter corresponding to non-local effect. Length ratio between materials PZT-4 and epoxy and height-width ratio are chosen as the influencing parameters of geometric parameters. Moreover, all the band structures and influence rules of Timoshenko nanobeam are compared to those of Euler nanobeam. The results are expected to be of help for the design of micro and nanodevices based on piezoelectric periodic nanobeams. [ABSTRACT FROM AUTHOR]

The interface state in two-dimensional (2D) sonic crystals (SCs) was obtained based on trying or cutting approach, which greatly limits its practical applications. In this paper, we theoretically demonstrate that one category of interface states can deterministically exist at the boundary of two square-lattice SCs due to the geometric phase transitions of bulk bands. First, we derive a tight-binding formalism for acoustic waves and introduce it into the 2D case. Furthermore, the extended 2D Zak phase is employed to characterize the topological phase transitions of bulk bands. Moreover, the topological interface states can be deterministically found in the nontrivial bandgap. Finally, two kinds of SCs with the C 4 v symmetry closely resembling the 2D Su–Schrieffer–Heeger (SSH) model are proposed to realize the deterministic interface states. We find that tuning the strength of intermolecular coupling by contacting or expanding the scatterers can effectively induce the bulk band inversion between the trivial and nontrivial crystals. The presence of acoustic interface states for both cases is further demonstrated. These deterministic interface states in 2D acoustic systems will be a great candidate for future waveguide applications. [ABSTRACT FROM AUTHOR]