Complex Band Research Articles

Deep-learning-based inverse design of phononic crystals for anticipated wave attenuation

Bandgaps of phononic crystals dominating the propagation of evanescent waves have received significant attention recently, which can be determined and tuned by the topology of a unit cell. Predicting a band structure and designing topological structures with desirable characteristics have become a research hotspot. In this study, a data-driven deep learning framework is applied to arrive at the prediction of the band structure and the inverse design of topology. A convolutional neural network is trained to predict band structures of phononic crystals. After training a generative adversarial network, the generator is concatenated with the convolutional neural network for inverse design. Meanwhile, a complex band structure of phononic crystals is computed by the periodic spectral finite element method to present the spatial decay of evanescent waves. The topology with the greater spatial attenuation is screened from the ground truth topology and the inversely designed topology. Finally, an optimized topological phononic crystal with an anticipated bandgap is obtained, which has the potential for better acoustic insulation and vibration isolation.

Chitosan/Xanthan membrane containing hydroxyapatite/Graphene oxide nanocomposite for guided bone regeneration

ObjectiveTo develop a chitosan-xanthan (CX) membrane associated with Hydroxyapatite (HA) and different concentrations of graphene oxide (GO). MethodologyThe CX complex was associated with the hydroxyapatite-graphene oxide (HAGO) nanocomposite in different concentrations. The experimental groups were:1) CX; 2) Chitosan-Xanthan/Hydroxyapatite (CXHA); 3) Chitosan-Xanthan/Hydroxyapatite-Graphene Oxide 0.5% (CXHAGO 0.5%); 4) CXHAGO 1.0%; 5) CXHAGO 1.5%. The membranes characterizations were performed by X-ray diffraction (XRD), Fourier Transform Infrared Spectroscopy (FTIR), Raman spectroscopy, Scanning Electron Microscopy (SEM), Contact angle, Tensile Strength, in vitro Bioactivity and the in vitro Cell viability (MTT test). The data was submitted to the Normality and Homogeneity tests. In vitro Indirect Cytotoxicity assay data was statistically analyzed by two-way ANOVA and Tukey's test (α = 0.05). Tensile Strength and Contact Angle data were statistically analyzed by one-way ANOVA followed by Tukey's test (α = 0.05). ResultsXRD, FTIR and Raman spectroscopy confirmed the characteristic bands of the CX polymeric complex, the phosphate bands related to HA, and the presence of GO. SEM images demonstrated the non-porous and homogeneous surface of membranes. The contact angle test showed the hydrophilic characteristic of all membranes (p > 0.05). CX showed tensile strength significantly higher than other membranes. The apatite deposition was observed in all membranes after performing the bioactivity test. The cell viability of CXHAGO 1.0% and CXHAGO 1.5% was significantly higher than CX. ConclusionThe addition of HAGO reduced the mechanical strength of membranes, but improved its cell viability. It demonstrated the potential of CXHAGO membranes to be used in guided bone regeneration therapies.

Wave attenuation in viscoelastic hierarchical plates

Phononic crystals (PCs) are periodic structures obtained by the spatial arrangement of materials with contrasting properties, which can be designed to efficiently manipulate mechanical waves. Plate structures can be modeled using the Mindlin–Reissner plate theory and have been extensively used to analyze the dispersion relations of PCs. Although the analysis of the propagating characteristics of PCs may be sufficient for simple elastic structures, analyzing the evanescent wave behavior becomes fundamental if the PC contains viscoelastic components. Another complication is that increasingly intricate material distributions in the unit cell of PCs with hierarchical configuration may render the calculation of the complex band structure (i.e., considering both propagating and evanescent waves) prohibitive due to excessive computational workload. In this work, we propose a new extended plane wave expansion formulation to compute the complex band structure of thick PC plates with arbitrary material distribution using the Mindlin–Reissner plate theory containing constituents with a viscoelastic behavior approximated by a Kelvin–Voigt model. We apply the method to investigate the evanescent behavior of periodic hierarchically structured plates for either (i) a hard purely elastic matrix with soft viscoelastic inclusions or (ii) a soft viscoelastic matrix with hard purely elastic inclusions. Our results show that for (i), an increase in the hierarchical order leads to a weight reduction with relatively preserved attenuation characteristics, including attenuation peaks due to locally resonant modes that present a decrease in attenuation upon increasing viscosity levels. For (ii), changing the hierarchical order implies in opening band gaps in distinct frequency ranges, with an overall attenuation improved by an increase in the viscosity levels.

Metamaterial beams with graded two-stage inertial amplification and elastic foundation

In this study, a novel local resonant metamaterial (LRM) beam with elastic foundation is proposed by introducing grounded local resonators based on the two-stage inertial amplification structure with adjustable large inertia. The complex band structure is calculated by using the extended plane wave expansion method, and it is found that bandgaps of the novel LRM beam are lower and wider than that of the existing inertant LRM beam. The formation mechanisms of such bandgaps are revealed, and the effects of structural parameters on bandgap characteristics are discussed. Numerical analysis and experimental measurement of vibration transmission characteristics of finite beam structure verify the accuracy of the theoretical results. Furthermore, three kinds of bandgap widening methods based on the structure tunability of local resonator are proposed by setting graded structural parameters. The regularities of bandgap variation with different parameter spacings are given, and the effectiveness of the method is verified by numerical analysis of the finite graded LRM beam under different boundary conditions. These results are expected to provide certain guidance for low and ultra-low frequency broadband flexural waves and vibration control.

Evanescent Lamb waves in viscoelastic phononic metastrip

In this paper, the propagation of evanescent Lamb waves in the one-dimensional viscoelastic phononic metastrip is studied. Complex band structures and transmission spectra are calculated by using the finite element method. The effect of viscosity is included according to the Kelvin–Voigt model. Two types (namely H-type and I-type) of metastrips are fabricated in either steel or epoxy. A theoretical model is developed to predict the distribution of the displacements of evanescent waves in the finite metastrip. The effect of different cutting forms on the complex band structure is also investigated. It is found that the spatial attenuation of evanescent waves is clearly observed in both simulation and measurement. Numerical and experimental results agree well for steel metastrips when only the elastic stiffness matrix is considered, whereas good agreement for epoxy metastrips is achieved when viscoelasticity is taken into account. The displacement distribution of evanescent waves can be accurately predicted from the two least evanescent waves identified in the complex band structure. Different slicing forms for the metastrip result in the reconstruction of evanescent waves, leading to the opening or closing of bandgaps. The present work lays the numerical and experimental foundation for practical application of phononic metastrips.

Studying the Possibility of Application ir Spectroscopy for Raw Material Identification <I>Valeriana wolgensis</I> Kazak. and <I>Valeriana dudia</I> L.

Introduction. Recently, IR spectroscopy has been increasingly used to identify various groups of biologically active substances (BAS) in plant objects. It is known that plants are capable of accumulating various BAS. Currently, there is no reliable, complete and accessible database of IR spectra of medicinal plant raw materials (MPR), which has a multicomponent composition, which is necessary for solving specific practical problems. It is of interest to use express methods of non-destructive testing for the purpose of identifying medicinal plant raw materials, as well as differential diagnostics of closely related species and various varieties of medicinal plants, which allow the analysis of raw materials in the shortest possible time, while maintaining the possibility of further vegetation. These types of difficult to distinguish raw materials include 9–14 (according to various sources) closely related plant species of the genus Valeriana, included, according to the accepted classification of V. I. Grubov with additions and changes by V. N. Voroshilov in the collection cycle (V. officinalis L.) of the Officinales Grub. series, and are characterized by an extremely similar composition of the metabolome.Aim. The purpose of this study was to study the possibility of using IR spectroscopy for the identification of MPR of Valeriana wolgensis Kazak. and Valeriana dudia L.Materials and methods. The objects of the study were rhizomes with roots, grass of Valeriana wolgensis Kazak. and Valeriana dudia L. Samples were col-lected in the Voronezh region in 2019 on the banks of the Ikorets river in the village of Sredny Ikorets, Liskinsky district and in the vicinity of the village of Belogorye, Podgorensky district. IR spectra were obtained without preliminary sample preparation on a IR Fourier spectrometer VERTEX 70 (Bruker, Germany) by the disturbed total internal reflection method and subsequent pro-cessing with the OMNIC or GRAMS 4/32 program.Results and discussion. In all spectra of the studied samples, absorption bands reflecting the general chemical composition were found. Similar absorption bands were observed, differing only in intensity. The spectra of similar groups of raw materials (herbs and rhizomes with roots) of the studied species of Valeriana were especially close to each other. In the IR spectra of the powders of the medicinal product under study, one can distinguish absorption bands characteristic of the hydroxyl groups of the cyclopentanepyrane skeleton of valepotriates: 3296–3280 cm-1. The complex absorption band in the region of 2958–2844 cm-1 is due to stretching vibrations of numerous methyl and methylene groups. Bending vibrations of the same groups give characteristic peaks at 1751–1407 cm-1 and about 700 cm-1 (790–720 cm-1 – pendulum vibrations of methylene groups). At the same time, among the main BAS of this medicinal product, the dominant compounds are those in which the methylene groups are closed in unstressed rings, which is manifested in bands in the range of 1420–1400 cm-1. The absorption bands in the range of 3296–3280 cm-1 in the IR spectra of the medicinal product of the studied species are due to stretching vibrations of the hydroxyl group in intermolecular hydrogen bonds. Based on the data obtained, the thermodynamic characteristics of the identified bonds, such as energy (EH) and length (R), were calculated. Valepotriates containing a cyclopentanepyran skeleton with five hydroxyl groups – polyhydrooxycyclo-pentanepyrane, in the studied medicinal plant, according to IR data, polyassociates are formed with characteristic absorption frequencies at 3400–3200 cm-1. The specific frequencies identified in the spectrum can be considered characteristic for a certain type of raw material of Valeriana and can be used as markers in determining the authenticity and species by the IRS method.Conclusion. The studies have shown that the IR Fourier spectroscopy of the disturbed total internal reflection can be used to obtain individual IR spectra of MPR of various morphological groups. The data obtained, in general, indicate the similarity of the chemical composition of two closely related species of valerian harvested in the Voronezh region, which, in addition to other studies of the metabolome composition, justifies the possibility of their use along with the official raw material of Valeriana officinalis L. The formation of hydrogen bonds and their character between BAS molecules in the studied medicinal product was established by IR spectroscopy. The results obtained indicate that the method used is promising for the rapid assessment of the medicinal product authenticity.

Tunable asymmetric transmission of Lamb waves in piezoelectric bimorph plates by electric boundary design

The multi-mode and dispersion natures of elastic guided waves bring big challenges for wave manipulation, and also provide more possibilities for smart device design. In this study, a piezoelectric bimorph plate connected to a periodic arrangement of electric circuits is proposed, and both propagating and evanescent guided Lamb waves are investigated through the complex band structure resulting form using different shunting capacitor or inductor distributions. Results show that keeping and breaking the symmetry of the electric boundary condition can, respectively, lead to decoupling or hybridizing of multi-mode Lamb waves. Accordingly, the asymmetric transmission at a desired frequency can be realized by combining the symmetric and asymmetric electric boundary conditions. Harmonic analysis shows that numerical results are in good agreement with the prediction of complex band structure. Actively changing the electric boundary conditions can be used for guided wave propagation in piezoelectric bimorph plates to easily control the system without changing the structure’s geometry. The framework presented herein offers enhanced capabilities for controlling guided wave propagation for engineering applications and to develop nondestructive testing techniques.

2-aminopyrimidine-oxalic acid liquid–liquid charge-transfer interactions: Synthesis, spectroscopic characterizations, and the effect of temperature

The intermolecular charge-transfer (CT) interaction of 2-aminopyrimidine (2AP) (as an electron donor) with oxalic acid (OA) (as a typical σ-electron acceptor) has been studied at multiple temperatures in methanol solvent. The stoichiometry of the generated CT complex (2AP-OA) was determined using the Benesi-Hildebrand method (BHM). The molecular interaction of 2AP donor with OA acceptor has been discussed as a function of temperature. The crystal structure and space group of the 1:1 adduct has been determined using the single-crystal X-ray crystallographic technique. The 1H NMR spectrum of 2AP-OA indicates the formation of N+H∙∙∙O− intermolecular hydrogen bonding. The FTIR spectrum of 2AP-OA also well resolved the complex absorption bands in the region where 2AP and OA bands have been observed. The thermal stability and composition of 2AP-OA were analyzed to compare with 2AP donor and OA acceptor using thermogravimetric (TGA) and differential thermal analysis (DTA). The Van’t Hoff equation was employed to calculate various important thermodynamic parameters (i.e., entropy; ΔS, enthalpy; ΔH, and Gibbs free energy; ΔG). The reaction between 2AP and OA was spontaneous and exothermic in nature, as indicated by the negative values of ΔG and ΔH.

First-principles study of the structural, electronic, dynamical, and mechanical properties of Pd–Nb binary systems

We study the structural, electronic, dynamical, and mechanical properties of the whole Pd–Nb binary systems based on first-principles density functional theory calculations. Using the variable-composition evolutionary structure search algorithm, we predict five new ground-state phases (cI32-Pd15Nb, oF60-Pd13Nb2, mC24-Pd5Nb, oC16-PdNb7, and oC32-PdNb15) and nine metastable phases (oC24-Pd11Nb, mC18-Pd8Nb, hP9-Pd8Nb, mC12-Pd5Nb, tP2-PdNb, oC20-PdNb, tI10-Pd2Nb3, oC20-Pd2Nb3, and mP10-PdNb4) that have not yet been either experimentally reported or theoretically predicted. All the predicted phases are dynamically stable in the absence of soft phonon modes in calculated phonon dispersions. The elastic properties calculations show that all these compounds are also mechanically stable. We find that the Young’s modulus, bulk modulus as well as shear modulus exhibit similar convex variations with respect to the Nb concentrations, while the Poisson’s ratio shows the opposite trend. These trends are found to be highly correlated with the atomic arrangement in crystal structures and associated chemical bondings. Among all the predicted PdxNby compounds, tI8-Pd3Nb exhibits the largest elastic moduli due to its relatively close-packed structure induced near homogeneous chemical bondings. The electronic structure calculations reveal that all predicted Pd–Nb compounds are metallic with complex band structures. Interestingly, the oI6-Pd2Nb compound hosts nontrivial Dirac nodal lines around the Fermi energy and exhibits topological nodal line surface states on the (001) plane. This work provides the first complete survey on the whole Pd–Nb systems, paving the way to exploring potential candidates for Pd-based electrocatalysts.

A Mechanical Model for Elastic Wave Propagation in Nacre-Like Materials With Brick-and-Mortar Microstructures

Abstract Many biological materials have outstanding properties unparalleled by artificial materials because of their periodic and/or hierarchical structures. In this paper, the longitudinal elastic wave propagation in nacre-like materials with brick-and-mortar microstructures has been studied theoretically by taking the different deformation mechanisms into account. A viscoelastic model in relation to the sacrificial bond behavior for the organic matrix has been developed. The shear-lag model is adopted to simulate the deformation of the brick-mortar structure. Complex band structures have been analyzed and the mechanical model has been validated by finite element method. Results have shown that bandgaps with lower edge close to vanishing frequency may arise in such bio-inspired periodic structures and attenuated propagation of elastic waves may be dominant in the range of higher frequencies. It may cast light on the dynamic strengthening mechanisms in nacre-like materials and provide a scientific basis for the design of bio-inspired metamaterials with low-frequency bandgaps.

Enhanced tunneling magnetoresistance and spin filtering in perovskite magnetic tunnel junctions via oxygen octahedral tilting

Oxygen octahedral tilting significantly reduces the symmetry of perovskites and changes the transport properties of perovskite magnetic tunnel junctions (MTJs). We investigated ${\mathrm{SrRuO}}_{3}/{\mathrm{CaTiO}}_{3}/{\mathrm{SrRuO}}_{3}$ MTJs by first-principles simulation and predicted an intriguing coupling between oxygen octahedral tilting and tunneling magnetoresistance. We obtained higher spin polarization at the Fermi level for the ${\mathrm{SrRuO}}_{3}$ electrodes with tilted octahedra, which increases the tunneling magnetoresistance value. Transmission and complex band structure analysis shows that the majority spin tunneling current in the ${\mathrm{CaTiO}}_{3}$ barrier with tilted octahedra is suppressed by wave function symmetry filtering, thus producing a negative spin filtering with an efficiency close to \ensuremath{-}100% and further enhancing the TMR effect. Both phenomena disappear in the junction without oxygen octahedral tilting, hence they have resulted from lattice distortions. The effective control of the tunneling magnetoresistance via oxygen octahedral tilting could act as a way to improve the performances of perovskite spintronic devices.

Complex Band Structure of 2D Piezoelectric Local Resonant Phononic Crystal with Finite Out-Of Plane Extension

In this study, a new type of 2D piezoelectric phononic crystal with a square hollow and convex structures is designed and established. A theoretical study of the piezoelectric phononic crystal is presented in this article to investigate the transmission properties of waves in terms of complex dispersion relations. Based on the finite discretization technique and plane wave expansion, the formula derivation of the real band structure is achieved as well as the complex band diagrams are obtained. The numerical results are presented to demonstrate the multiple broadband complete bandgaps produced by the designed piezoelectric phononic crystal and the propagation characteristics of the elastic waves for different directions. In addition, the transmission loss in the ΓX direction is calculated to verify the band structure. Finally, the effects of the thickness and the square hollow side length on the band structure are discussed.

Non-Hermitian skin effect in a phononic beam based on piezoelectric feedback control

Non-Hermitian systems have gained a great deal of interest in various wave problems due their ability of exhibiting unprecedented phenomena such as invisibility, cloaking, enhanced sensing, or the skin effect. The latter manifests itself by the localization of all bulk modes in a specific frequency range at a given boundary, with an unconventional bulk-boundary correspondence. In this work, we propose to realize the skin effect for flexural waves in a non-Hermitian piezoelectric phononic beam with feedback control between a sensor and an actuator in each unit cell. By implementing a non-Hermitian parameter, effective gain and loss can be achieved in the phononic beam characterized by complex eigen frequencies, and non-reciprocal pass bands are obtained. We highlight that the split point separating the gain and loss areas can occur not only at the edges of the Brillouin zones but also inside the same Brillouin zone. We further analyze the influence of the geometric and non-Hermitian parameters on the complex dispersions and the split point. The topology of the complex bands is characterized by the winding number, which supports the skin effect together with the non-reciprocity. The localization degree of the skin mode manifested by the enhanced beam's vibration energy at one boundary is related to the strength of the non-reciprocity, and the skin mode can be always excited regardless of the source position. Our results provide a potential platform to introduce non-Hermiticity into phononic or metamaterial systems with novel functions for elastic waves such as topological insulators, vibration attenuation or amplification, and energy harvesting.

Geoecological assessment and environmental monitoring within the boundaries of the impact of the development of gold deposits using GIS technologies

An interdisciplinary approach is used in the study of this problem. Well-known methods are used in the work. The ground-based phase of the research consisted of sampling. The results indicate intense pollution. High concentrations of compounds of mercury, arsenic, copper, lead, zinc were recorded. Deciphering the Landsat 8 (GloVis) images made it possible to supplement the mining and environmental monitoring by studying the dynamics of changes in the areas of placer gold mining. Data processing was carried out on the basis of the open geoinformation system Qgis. Image processing methods: False Color Composite (FCC) images in artificial colors; Band Ratio (BR) creates complex band ratios. Digitization of the images showed increasing areas of disturbed land. For the first time, a geo-ecological assessment using GIS technologies was carried out. Over a long period of time, ground monitoring data are entered into the Qgis database. The practical significance of the work is confirmed by the Patent of the Russian Federation and substantiated by the creation of a method to ensure the environmental safety of technogenically polluted areas using bioremediation.

Influences of defects on the propagation of transverse waves in periodic piezoelectric laminate structure with nanoscaled layers

By the stiffness matrix method based on the nonlocal elastic continuum theory, the transmission spectra of the transverse elastic waves propagating normally in nanoscaled periodic piezoelectric laminates with defects are investigated in detail in this paper. Defect is introduced by replacing a constituent layer or inserting another layer in a unit-cell. The thicknesses of all sub-layers and defect layer are at the nanoscale. Simultaneously, complex band structures and localization factors are calculated and employed to verify the band structures described by the transmission spectra. The influences of the defect type, the defect material, the volume fraction of the defect layer in the unit-cell, the piezoelectric constants of the defect layer, and the nanoscale size-effect on the transmission spectra are analyzed and discussed in detail. The present study provides a theoretical guide for the design and applications of the nanoscaled acoustic filters or transducers with defects.

Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices

Due to the fundamental position of spin-orbit coupled ultracold atoms in the simulation of topological insulators, the gain/loss effects on these systems should be evaluated when considering the measurement or the coupling to the environment. Here, incorporating the mature gain/loss techniques into the experimentally realized spin-orbit coupled ultracold atoms in two-dimensional optical lattices, we investigate the corresponding non-Hermitian tight-binding model and evaluate the gain/loss effects on various properties of the system, revealing the interplay of the non-Hermiticity and the spin-orbit coupling. Under periodic boundary conditions, we analytically obtain the topological phase diagram, which undergoes a non-Hermitian gapless interval instead of a point that the Hermitian counterpart encounters for a topological phase transition. We also unveil that the band inversion is just a necessary but not sufficient condition for a topological phase in two-level spin-orbit coupled non-Hermitian systems. Because the nodal loops of the upper or lower two dressed bands of the Hermitian counterpart can be split into exceptional loops in this non-Hermitian model, a gauge-independent Wilson-loop method is developed for numerically calculating the Chern number of multiple degenerate complex bands. Under open boundary conditions, we find that the conventional bulk-boundary correspondence does not break down with only on-site gain/loss due to the lack of non-Hermitian skin effect, but the dissipation of chiral edge states depends on the boundary selection, which may be used in the control of edge-state dynamics. Given the technical accessibility of state-dependent atom loss, this model could be realized in current cold-atom experiments.

P‐82: Prediction Methodology for the Optical Properties of QDs with Arbitrary 3D Shape

Recently, researchers have strived to enhance the optical characteristics of Quantum Dots (QDs) by carefully tailoring the QD material composition, shape and size. In this endeavor, simulation proves an invaluable tool to assess and optimize the QD structure. In this paper, the optical properties of QD structures are explored, taking into account the complex band structure of the QD and its geometric structure, as well as the probability of quantum state transitions. In order to perform this analysis the In‐house Simulator (DaVinci_QD), based on 3D FEM, was developed and applied. We demonstrate that the DaVinci_QD simulator exhibits good agreement with experiment, providing confidence that the tool be applied to predict optical characteristics with accuracy. The simulator is applied to state‐of�the‐art QDs that are currently under development, offering additional insight to aid in the analysis of optical measurements and revealing paths to further performance enhancement. In this way, simulation can replace experiment and QD structures can be optimized rapidly.

Fe- and Co-based magnetic tunnel junctions with AlN and ZnO spacers

AlN and ZnO, two wide band-gap semiconductors extensively used in the display industry, crystallise in the wurtzite structure, which can favour the formation of epitaxial interfaces to close-packed common ferromagnets. Here we explore these semiconductors as material for insulating barriers in magnetic tunnel junctions. In particular, the {\it ab initio} quantum transport code {\it Smeagol} is used to model the $X$[111]/$Y$[0001]/$X$[111] ($X=$ Co and Fe, $Y=$ AlN and ZnO) family of junctions. Both semiconductors display a valance-band top with $p$-orbital character, while the conduction band bottom exhibits $s$-type symmetry. The smallest complex-band decay coefficient in the forbidden energy-gap along the [0001] direction is associated with the $\Delta_1$ symmetry, and connects across the band gap at the $\Gamma$ point in 2D Brillouin zones. This feature enables spin filtering and may result in a large tunnelling magnetoresistance. In general, we find that Co-based junctions present limited spin filtering and little magnetoresistance at low bias, since both spin sub-bands cross the Fermi level with $\Delta_1$ symmetry. This contrasts the situation of Fe, where only the minority $\Delta_1$ band is available. However, even in the case of Fe the magnitude of the magnetoresistance at low bias remains relatively small, mostly due to conduction away from the $\Gamma$ point and through complex bands with symmetry different than $\Delta_1$. The only exception is for the Fe/AlN/Fe junction, where we predict a magnetoresitance of around 1,000\% at low bias.

Longitudinal Wave Locally Resonant Band Gaps in Metamaterial-Based Elastic Rods Comprising Multi-Degree-of-Freedom DAVI Resonators

The wave propagation and vibration transmission in metamaterial-based elastic rods with periodically attached multi-degree-of-freedom (MDOF) dynamic anti-resonant vibration isolator (DAVI) resonators are investigated. A methodology based on a combination of the transfer matrix (TM) method and the Bloch theorem is developed, yielding an explicit formulation for the complex band structure calculation. The bandgap behavior of the periodic structure arrayed with single-degree-of-freedom (SDOF) DAVI resonators and two-degree-of-freedom (2DOF) DAVI resonators are investigated, respectively. A comparative study indicates that the structure consisting of SDOF DAVI resonators periodically jointed on the metamaterial-based elastic rod can obtain an initial locally resonant band gap 500 Hz smaller than the one given in the published literature. The periodic structure containing 2DOF DAVI resonators has an advantage over the periodic structure with SDOF DAVI resonators in achieving two resonance band gaps. By analyzing the equivalent dynamic mass of a DAVI resonator, the underlying mechanism of achieving a lower initial locally resonant band gap by this periodic structure is revealed. The parameters of the 2DOF DAVI resonator are optimized to obtain the lowest band gap of the periodic structure. The numerical results show that, with the optimal 2DOF DAVI parameters, the periodic structure can generate a much lower initial locally resonant band gap compared with the case before the optimization.

The effect of viscosity of saturated soil on the surface wave attenuation by periodic in-filled trench

Investigations on the ambient vibration reduction by periodic wave barriers have been received more and more attention in recent years. However, the role of energy dissipation caused by the viscosity of soil is usually ignored in most of the previous studies. The surface wave attenuation in saturated viscoelastic soil by periodic in-filled trench is investigated in this study. Firstly, the constitutive model of saturated viscoelastic soil is constructed by introducing Kelvin viscoelastic model into the Biot's theory. Secondly, the complex band structure of surface waves propagating in periodic in-filled trench is calculated. A finite model for analyzing ambient vibration isolation is built, and the responses of the site under external excitation are numerically solved both in frequency domain and time domain. The roles of the viscosity of soil and the periodic barrier in the surface wave attenuation are comprehensively discussed, and some findings are obtained. Soil's viscosity reinforces the attenuation when the frequencies of surface waves fall in the attenuation zone. However, the contribution of the viscosity is not obvious. Contrary to the attenuation zone, soil's viscosity plays a key role in the attenuation when the frequencies of surface waves are out of the attenuation zone.