Modeling Of Periodic Structures Research Articles

Research on out-of-plane vibration band gap calculation of two-dimensional periodic grillage structures based on spectral element method

The vibration of ship and marine structures directly impacts their structural performance and noise levels. Therefore, the vibration band gap characteristics of two-dimensional periodic grillage structures are investigated based on spectral element method in this article. Firstly, the governing motion equation of out-of-plane vibration of periodic grid structures is established in light of the Bloch theorem, and the shear spring oscillator system is introduced to simulate the first-order vertical shear vibration of bottom plate. As a result, the periodic oscillator coupling grid structure model can be proposed. Based on the periodic grid structures, the influence of material distribution on vibration band gap is obtained. Meanwhile, the dispersion relations and vibration transmission of periodic coupling model are calculated and the coupling effect of local resonance system on the band gap characteristics is analyzed. At last, a general approach for equating periodic grillage unit to numerical model is outlined and summarized on basis of the similarity of dynamic properties. The effectiveness and accuracy of the numerical method in out-of-plane vibration band gap analysis of periodic grillage structures are validated through the computation and model test.

Method of Moments for the Dispersion Modeling of Glide-Symmetric Periodic Structures

Method of Moments for the Dispersion Modeling of Glide-Symmetric Periodic Structures

Study of Rheological-Mechanical Properties and Vibration Mechanics Bandgap of Row Pile Foundation

To analyze the rheological and mechanical properties as well as the vibration-mechanical forbidden zone effect of row pile foundations, this paper employs time-dependent modulus to examine the rheological mechanics of soil. Drawing from viscoelastic theory, we derive the expression of deformation modulus in the frequency domain to analyze the frequency dependence of the shear modulus of rheological soils. We construct a continuous medium dynamics model of the pile-soil periodic structure, taking into account soil rheology, and derive the dispersion equation of shear waves in the periodic structure using the multiple scattering method. The band gap characteristics and parameters that influence the law of shear waves in rheological soil-row pile foundations are studied through the analysis of arithmetic cases. The results show that under the loading condition, the zero-frequency shear modulus of soil is larger than the initial modulus value, and the real part of the shear modulus decreases monotonically with the increase of frequency and finally converges to the initial modulus value; under the unloading condition, the zero-frequency shear modulus of soil is smaller than the initial modulus value, and the real part of the shear modulus increases monotonically with the increase of frequency and finally converges to the initial modulus value; the larger the relaxation time of soil, the faster the convergence rate; the imaginary part of the shear modulus of soil The imaginary part of the soil shear modulus is positive under loading condition and negative under unloading condition, the value of the imaginary part increases and then decreases with increasing frequency and finally converges to 0. The imaginary part reaches the peak at the critical frequency, the larger the relaxation time the smaller the critical frequency, and the peak of the imaginary part is independent of the relaxation time. This study analyzed the dispersion curve of shear waves in a pile-soil periodic structure and found that increasing low-frequency shear wave velocity in rheological soil pile foundation shifts the band gap position to a higher frequency band, resulting in a smaller band gap width than in linear elastic soil. The relaxation time of soil affects the frequency position and width of the band gap, with larger relaxation times resulting in higher frequency positions and smaller widths. Additionally, soil rheology widens the forbidden vibration band gap of the pile periodic structure when the filling rate of the pile foundation is larger.

Non-Uniform TFA reduced multiscale procedure for shell-3D modeling of periodic masonry structures

This work proposes a reduced-order multiscale model for the analysis of masonry elements subjected to in-plane and out-of-plane loading conditions. The Transformation Field Analysis (TFA) is adopted to link the homogeneous shell model at the macroscale with a three-dimensional (3D) representative unit cell (UC) of the masonry material defined at the microscale, accounting for the regular arrangement of bricks/blocks and mortar joints. The UC is modeled considering linear elastic bricks joined by interfaces subjected to possible damage and frictional plasticity mechanisms. An enhanced TFA procedure is proposed, discretizing the interfaces in subsets, where non-uniform distribution of the inelastic quantities is considered and the plastic-damage evolution problem solved. Numerical simulations are developed to assess the advantages and drawbacks of the non-uniform TFA approach compared to previously proposed piece-wise uniform procedure. The results obtained through the proposed numerical approach are compared with both micromechanical and experimental outcomes.

Equivalent plate dynamic modeling of space periodic truss structures

Antenna structures used in spaceflight always contain nonlinear joints distributed along their cross section; hence, an equivalent beam model (EBM) that uses a point to describe the cross section is not ideally suited to depicting connection nonlinearity in the structure. To address this difficulty, a novel orthotropic equivalent plate model (EPM) of a space periodic truss structure is proposed. Firstly, utilizing the Mindlin plate hypothesis, strain in the periodic truss element is expanded into a binary high-order Taylor series, and corrections are introduced to normal strain. Secondly, employing the principle of energy equivalence, the equivalent elastic and inertial matrices of the EPM are calculated for in-plane and out-of-plane vibration. Finally, the static condensation method is utilized to reduce the dimensions of the equivalent model to establish an orthotropic equivalent Mindlin plate dynamic model, and its inherent characteristics are analyzed. The simulations show that when in-plane shear strain is expanded to the third order, the EPM can more accurately represent torsional vibration of the periodic truss structure. By introducing normal strain correction coefficients in the longitudinal direction, lateral bending vibrations of the periodic truss structure can be simulated more precisely. Compared with the EBM, the EPM can more accurately depict mechanical characteristics along the cross section. The EPM broadens the scope of continuum equivalent modeling of periodic trusses, and is more useful in engineering practice. In addition, the frequencies and mode shapes of the analytical EPM are consistent with a model using the finite element method, which supports the accuracy and effectiveness of the EPM. The analytical EPM provides a convenient way to study the nonlinear connections and vibration control of antenna structures with multiple joints along their cross section.

Transmission characteristics of train-induced vibration in buildings based on wave propagation analysis

Various studies have focused on predicting, evaluating, and controlling train-induced building vibrations and radiated noise. This study aimed to clarify the theory of building vibration transmission by investigating the transmission characteristics of vibrations in buildings using wave propagation analysis. First, the building was modelled as a periodic structure, as each floor was similar in layout. Based on the wave propagation method, a periodic structure model was established in which the dynamic stiffness matrix of the cell structure could be derived using the spectral element method. Second, a response transfer function (RTF) database of 140 simplified typical residential buildings was established by wave analysis method. Finally, the transmission laws of train-induced vibration were studied. The results indicated that the vibration transmission laws were related to the mode shapes of structures and the participation of modes, which was affected by the spectral characteristics of the input excitation. With an increase in building height, the natural frequency decreased, which influenced the participation of each mode, and this would cause the transmission characteristics of the total vibration energy to change.

Numerical and experimental analysis of the stiffness and band-gap properties of shell structures with periodically variable cross sections

This paper describes one-dimensional periodic shell structures that have variable cross sections, a new type of periodic shell structures made from photopolymer. This paper will discuss the stiffness of periodic sub-cells that have variable cross sections and the band gaps of Bragg scattering shell structures based on numerical analysis and a series of experiments. This paper uses the Bloch theorem and lumped-mass method to create a band gap model for periodic shell structures. In this paper, an equivalent stiffness model for sub-cells is also created based on the principle of superposition and validated by experiments. Numerical studies and experiments are conducted to examine the effects of geometrical parameters, number of sub-cells, and stiffness of sub-cells on band gaps of one-dimensional periodic shell structures and to test the effectiveness of the models. The findings in this paper prove that by varying the stiffness of sub-cells under a fixed lattice constant, band gaps of one-dimensional periodic shell structures can be decreased. The findings also confirmed that the initial band gap of one-dimensional periodic shell structures can be lowered by increasing the number of sub-cells in a period. Unlike other types of Bragg scattering periodic structures, one-dimensional periodic shell structures allow their longitudinal band gaps to be adjusted under a fixed lattice constant. Those findings serve as a theoretical foundation for the application of Bragg scattering periodic shell structures in low-frequency vibration.

A parametric study on the structural noise radiation characteristics of a steel spring floating slab track

It is a common experience that the interior noise of an underground train vehicle increases suddenly when it just runs into a track section with steel spring floating slabs, significantly reducing passengers’ comfort. This paper investigates the reasons, and control, of such noise through field tests and model simulations. The effect of rail surface irregularity on interior noise was investigated first by analysing data collected from interior noise tests, rail surface irregularity measurement and by analysing the modal behaviour of the slab. Noise radiation of the track slab was then analysed using the acoustic boundary element method while the vibration of the steel spring floating slab track is predicted based on an infinitely long periodic structure model; And finally with the prediction models, a parameter study was performed for the steel spring floating slab, on the purpose of improving the parameters to make the track less noisy. The research presented in this paper may provide a reference for the design of steel spring floating slabs in terms of noise control.

A Full-Wave Generalized PEEC Model for Periodic Metallic Structure With Arbitrary Shape

In this work, a full-wave partial element equivalent circuit (PEEC) model for 2-D periodic metallic structures is proposed. The mixed potential integral equations (MPIEs) with periodic Green’s function (GF) are interpreted as loop equations following Kirchhoff’s voltage law (KVL) in a circuit domain. The impact of gauge freedom in the MPIE on the corresponding PEEC model is discussed. A tailored gauge function is introduced to form a generalized PEEC model for periodic structures, which demonstrates superior passivity and frequency stability. With the proposed PEEC model, lumped and active elements can be easily integrated with conducting bodies for field-circuit co-simulation. Through the distributed circuit including coupling elements, the PEEC model provides a clear physical insight into the electromagnetic behavior of the physical models for design and optimization. Three numerical examples, including frequency-selective surface (FSS), array antenna, and pixelwise meta-atom, are given to illustrate the accuracy and efficiency of the proposed PEEC model.

Interaction mechanism between CO and H2S over CuFe2O4 oxygen carrier during chemical-looping combustion: A DFT study

During the chemical-looping combustion process, CO as an important part of syngas and H2S as a common sulfur compound inevitably coexist in the fuel. Based on the density functional theory and periodic structure model, the interaction mechanism between CO and H2S over the O-defective CuFe2O4 surface was comprehensively investigated. The results show that the adsorption energies of adsorbates on the O-defective surface are in the order of S* (−205.42 kJ/mol) > HS* (−191.37 kJ/mol) > CO (−44.88 kJ/mol) > H2S* (−28.97 kJ/mol). CO adsorption over the O-defective surface is dominant as compared to H2S adsorption. The adsorption energies of CO in the presence of H2S, HS* and S* are − 73.21, −255.98 and − 105.35 kJ/mol, respectively. The adsorption strength of CO over the O-defective surface was enhanced in the presence of HS* or S*. The presence of CO* will greatly limit the H2S dehydrogenation process, especially for the second dehydrogenation step. The energy barriers of CO oxidation with the participation of H2S*, HS* and S* are 69.66, 51.42 and 14.19 kJ/mol, respectively. COS may be produced form the reaction between CO and S* with an energy barrier of 27.13 kJ/mol, following the Eley–Rideal reaction mechanism. CuFe2O4 oxygen carrier exhibits good anti-sulfur ability because the reaction of CuFe2O4 with CO and H2S kinetically prefers the CO oxidation pathway rather than the COS formation pathway.

Chemical looping combustion of sulfur paste to SO2 by phosphogypsum oxygen carrier for sulfur acid production

Sulfur paste is the side product of coal chemical engineering, with its main component being elemental sulfur. Sulfuric acid production via Chemical Looping Combustion (CLC) of sulfur paste is a novel technology to generate SO2 that are highly concentrated in combustion products, by means of circulating oxygen carrier particles. The objective of the present work is investigating reaction kinetics and mechanism of CLC application using sulfur paste as fuel by a phosphogypsum oxygen carrier, which is also one kind of solid waste with large stock. Thermodynamics analysis, experiments and reaction kinetics model validation were performed to evaluate the sulfur paste conversion behavior. Then, based on density functional theory and periodic structure model, the microscopic reaction mechanism of the interaction between S2 and CaSO4(010) oxygen carrier surface was studied at the molecular level. CaSO4 has the strong chemical affinity with sulfur to produce SO2, but thermodynamic limitation of S conversion to SO2 with CaSO4 oxygen carrier exits in the process. The intrinsic reduction kinetics of phosphogypsum oxygen carrier with sulfur paste focusing on the dominant reaction CaSO4 + 2S = CaS + 2SO2 was described well by the Anti-Jander function model, which agrees well with the experimental data. The formation of two SO2 molecules needs to overcome the reaction energy barrier of 124 kJ/mol.

Optimization of second-order nonlinear optical susceptibilities in 1D GaN photonic crystal

We report the modeling and optimization of 1D periodic structures for second-order nonlinear effects. We present the work done in modeling to determine the location of the electromagnetic field in periodic structures. This modeling, carried out in a simple one dimension, makes it possible to mastery the properties of these structures and to study the influence of the different physical parameters on these properties. It allowed us to optimize structures for second-order nonlinear effects by focusing on the two essential factors of nonlinear polarization intensity and phase matching. This study, carried out in 1D structures, was extended to 1D planar structures (called 1.5D) used in guided optics and applied to the design of a 1.5D photonic crystal structure made in a Gallium Nitride layer for the second harmonic generation.

Construction of Pingdingshan coal molecular model based on FT-IR and 13C-NMR

To construct a molecular model of coal and study the adsorption characteristics from the perspective of microscopic molecules, the microstructure of coal samples from Pingdingshan mining area in China was studied by means of Fourier transform infrared spectroscopy (FT-IR) and carbon-13 nuclear magnetic resonance spectroscopy (13C-NMR). The coal mainly possesses an aromatic molecular structure with fa (aromaticity), faH and XBP (the ratio of aromatic bridge carbon to surrounding carbon) being 0.86, 0.29 and 0.54, respectively. According to the results, the aromatic structure, with a high degree of condensation, is mainly dominated by pyrene and chrysene, while the aliphatic structure is mainly composed of methyl and methylene whose ratio is about 0.52. Furthermore, it contains a small amount of oxygen-containing functional groups such as carbonyl group, phenolic hydroxyl group and ether bond. In light of the above-mentioned molecular structure characteristics, the periodic structure model of Pingdingshan coal with the molecular formula C108H71O4N was constructed based on molecular mechanics and molecular dynamics by using the Materials Studio software. The model has a density of 1.3 g/cm3, a porosity of 4.1% and a specific surface area of 614.5 m2/g, faithfully reflecting the structural information of coal sample. Moreover, methane isothermal adsorption curves were simulated by the model at the temperatures of 318, 333 and 348 K. The experimentally measured and simulated isothermal methane adsorption curves both exhibit an error of smaller than 5% under high pressure. The results verify rationality and accuracy of the model structure. The study provides a model basis for further research on coal on the microscopic level.

Fast statistical energy analysis modelling of periodic box-like structures

This paper proposes a fast way to create a base Statistical Energy Analysis (SEA) model for periodic box-like structures, for which further refining and modification can be conducted with simplicity. A novel numbering system is introduced which enables the model builder to build, locate and change the property of each subsystem as well as to specify the connections between different subsystems in a 3D coordinate system. Two numerical SEA models are studied with the aid of the new method. It greatly decreases the time in model building and increases the simplicity of studying the acoustic attenuation by changing the properties of different subsystems. The results show that when increasing the internal loss factors (ILF) of all structural elements from 0.015 to 0.12, a 13.5 dB sound insulation improvement can be observed for the 2-room system at 1000 Hz and that for the 24-room system is 10.9 dB. This method serves as a promising way to investigate the acoustic transmission in heavily damped periodic box-like structures.Article HighlightsA fast SEA model building method is proposed.A 3D coordinate based numbering system is developed for subsystem location and identification.Application of damping on structural elements results in better sound insulation.

Crystal cleavage, periodic nanostructure and surface modification of SiC ablated by femtosecond laser in different media

SiC , as one typical 3rd generation semiconductor, has high potential to be used as the substrate for harsh environment sensors. However, the etching of this material is still challenging. Femtosecond laser has been demonstrated to have great potential in SiC etching, but the material removal mechanisms need further investigation. Herein, the two-temperature model considering carrier concentration is utilized to illustrate the microscopic mechanism of carrier concentration and temperature change in SiC caused by femtosecond laser irradiation. An 800 nm, 50 fs, 10 Hz Ti: sapphire femtosecond laser was used to process SiC in different media including air, HF and water. The ablation threshold of SiC in the three media is calculated. The highest ablation threshold (4.98 J/cm 2 ) is obtained when the pulse number N = 50, in air. The lowest ablation threshold (0.53 J/cm 2 ) is obtained when the pulse number N = 300, in HF. Results indicate that ablation threshold is strongly dependent on the laser pulse number and processing medium. Based on the cleavage phenomenon of SiC crystal structure observed by micro-nano characterization, the mechanism model of femtosecond laser-induced periodic structure of SiC surface based on material lattice cleavage is established, and the relationship between the intrinsic texture and the evolution of periodic structure of ablation surface is revealed. This will provide a new way to understand the ablation mechanism of femtosecond laser. In addition, the processing media has significant effect on surface roughness and chemical bond characteristics of SiC. Liquid processing media can reduce the surface roughness and avoid oxidation, which is helpful to manufacture SiC devices with specific surface requirements using femtosecond laser as an auxiliary method. • The mechanism of femtosecond laser ablating SiC in different media are studied systematically. • The ablation threshold of SiC in different media (air, water, HF) are experimentally obtained. • The femtosecond laser-induced periodic structure is closely related to intrinsic structure cleavage.

A multi-scale model order reduction scheme for transient modelling of periodic structures

In this paper, a Floquet Model Order Reduction (MOR) method is proposed for the modelling of finite periodic structures subjected to harmonic or transient loads. This Floquet MOR generates frequency-independent projection matrices of the full-scale structure using a Floquet expansion of the local state-vectors computed on a single unit-cell with the Forced Wave Finite Element framework. This two-step MOR method can handle large multi-scale waveguides regardless of the scale and the number of unit-cells. A comparison with a standard sub-structuring approach based on unit-cell wave-mode reduction demonstrates that Floquet MOR is able to create reduced models of finite periodic structures with an unequalled computational efficiency. The method’s ability to produce small and accurate models suitable for time-domain simulations presents a high potential for virtual sensing, real-time Structural Health Monitoring (SHM) and digital twins for large periodic structures and metamaterials.

Mechanistic study of the effect of oxygen vacancy and sulfur poisoning on the reaction of copper ferrite spinel with CO during chemical-looping combustion

The surface structure has a great influence on the chemistry property and performance of oxygen carrier used for chemical-looping combustion. Based on density functional theory and periodic structure model, the effect of oxygen vacancy and sulfur poisoning on the reaction of copper ferrite spinel with CO during chemical-looping combustion was systematically studied. The results show that Cu–O2 bridging site shows better activity towards CO adsorption on the O-defective and sulfur-poisoned copper ferrite surfaces. The adsorption energies of CO follow the order of Eads (perfect surface) > Eads (sulfur-poisoned surface) > Eads (O-defective surface). The energy barriers of CO oxidation over different surfaces are in the order of O-defective surface (Ea = 22.68 kJ/mol) > sulfur-poisoned surface (Ea = 14.19 kJ/mol) > perfect surface (Ea = 4.85 kJ/mol). The oxygen vacancy and sulfur poisoning not only weaken the reactivity towards CO adsorption, but also have a disadvantageous impact on the CO oxidation process. For the sulfur-poisoned surface, the COS formation is kinetically unfavorable as compared to CO oxidation due to the higher energy barrier (27.13 kJ/mol).

Numerical homogenization of second gradient, linear elastic constitutive models for cubic 3D beam-lattice metamaterials

Generalized continuum mechanical theories such as second gradient elasticity can consider size and localization effects, which motivates their use for multiscale modeling of periodic lattice structures and metamaterials. For this purpose, a numerical homogenization method for computing the effective second gradient constitutive models of cubic lattice metamaterials in the infinitesimal deformation regime is introduced here. Based on the modeling of lattice unit cells as shear-deformable 3D beam structures, the relationship between effective macroscopic strain and stress measures and the microscopic boundary deformations and rotations is derived. From this Hill–Mandel condition, admissible kinematic boundary conditions for the homogenization are concluded. The method is numerically verified and applied to various lattice unit cell types, where the influence of cell type, cell size and aspect ratio on the effective constitutive parameters of the linear elastic second gradient model is investigated and discussed. To facilitate their use in multiscale simulations with second gradient linear elasticity, these effective constitutive coefficients are parameterized in terms of the aspect ratio of the lattices structures.

Finite-Difference Time-Domain Modeling of Periodic Structures: A review of constant wave vector techniques

This article reviews state-of-the-art periodic boundary conditions (PBCs) in finite difference time-domain (FDTD) simulations that operate by enforcing constant wave vector components. The mathematical principles and 3D FDTD implementation details are systematically outlined. Techniques for extracting scattering parameters, Brillouin diagrams, and attenuation constants are presented along with the array scanning method (ASM) used to model the interaction of nonperiodic sources with periodic structures. Through these techniques, the robustness, utility, and efficiency of PBCs are demonstrated and a unified view of the various approaches to the FDTD implementation of PBCs is presented.

Simulation analysis of plasma grating based on PDMS thin films

In order to measure the resonance wavelength of plasma grating, the sensitivity of grating parameters to stress is studied, a new type of stress-sensitive polydimethylsiloxane (PDMS) thin film plasma grating is proposed. Based on the principle of finite difference time domain (FDTD), a simulation model of periodic plasma grating structure is established. With the help of periodic boundary conditions, by applying stress to the grating and changing the parameters of the plasma grating (i.e. period, duty cycle and Au film thickness) to achieve the measurement of the resonance wavelength, the sensitivity of the grating parameters to the force is studied; and compare the simulation result with the theoretical value to get the relative error. The relative error is calculated by comparing the simulation result with the theoretical value. The results show that when the grating period is 0.7 μm, the duty cycle is 55%, and the gold film thickness is 0.02 μm, the response to force is most sensitive at this time; Secondly, comparing the resonance peak wavelength at different periods obtained by simulation with the theoretical calculation value, the results of the two are consistent; When the period is 0.7 μm, the wavelength of the resonance peak is 1.251 μm, and the relative error obtained by theory and simulation is less than 2%, and the result is more accurate. This method plays an important role in the fields of monochromator, spectrometer and sensor.