Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.

Nanomechanics of Mg-Gd-Y-Nd-Zn alloy with LPSO and MgRE phases

The mechanical properties of two main precipitating phases(LPSO and MgRE)and matrix in Mg-Gd-Y-Nd-Zn bioalloy were examined using nanoindentation method.A new is suggested for characterizing the elastic-plastic behavior,fracture toughness and strain rate sensitivity(SRS)of materials within micro/nanoscale.Firstly,a nanomechanical model was developed for extracting hardness(H),young’s modulus(E)and yield stress(σY)from the characteristic load points which were subsequently analyzed by atomic force microscope(AFM)images.The elasticity data and AFM data were then utilized for determination of plastic deformation in constituent phases.The displacement of the indentation gets the highest value for Mg matrix and between precipitates,depth is more in LPSO rather than that of MgRE.The serrated flow or the behavior of shear bands may originate from the side effect of the interface region in Mg alloys with precipitates.It can be deduced that the KIC produced by both L method and energy-based calculation are both reliable for KIC approximation.The maximum load in simulation withμ=0.2 friction is marginally lesser than that of the frictionless(μ=0)one while elastic recovery of indentation withμ=0.2 is higher to some extent.

Tungsten nanoparticle-strengthened copper composite prepared by a sol–gel method and in-situ reaction

Tungsten nanoparticle-strengthened Cu composites were prepared from nanopowder synthesized by a sol–gel method and in-situ hydrogen reduction.The tungsten particles in the Cu matrix were well-dispersed with an average size of approximately 100–200 nm.The addition of nanosized W particles remarkably improves the mechanical properties,while the electrical conductivity did not substantially decrease.The Cu–W composite with 6 wt%W has the most comprehensive properties with an ultimate strength of 310 MPa,yield strength of 238 MPa,hardness of HV 108 and electrical conductivity of 90%IACS.The enhanced mechanical property and only a small loss of electrical conductivity demonstrate the potential of this new strategy to prepare W nanoparticle-strengthened Cu composites.

Volumetric lattice Boltzmann method for pore-scale mass diffusionadvection process in geopolymer porous structures

Porous materials present significant advantages for absorbing radioactive isotopes in nuclear waste streams.To improve absorption efficiency in nuclear waste treatment,a thorough understanding of the diffusion-advection process within porous structures is essential for material design.In this study,we present advancements in the volumetric lattice Boltzmann method(VLBM)for modeling and simulating pore-scale diffusion-advection of radioactive isotopes within geopolymer porous structures.These structures are created using the phase field method(PFM)to precisely control pore architectures.In our VLBM approach,we introduce a concentration field of an isotope seamlessly coupled with the velocity field and solve it by the time evolution of its particle population function.To address the computational intensity inherent in the coupled lattice Boltzmann equations for velocity and concentration fields,we implement graphics processing unit(GPU)parallelization.Validation of the developed model involves examining the flow and diffusion fields in porous structures.Remarkably,good agreement is observed for both the velocity field from VLBM and multiphysics object-oriented simulation environment(MOOSE),and the concentration field from VLBM and the finite difference method(FDM).Furthermore,we investigate the effects of background flow,species diffusivity,and porosity on the diffusion-advection behavior by varying the background flow velocity,diffusion coefficient,and pore volume fraction,respectively.Notably,all three parameters exert an influence on the diffusion-advection process.Increased background flow and diffusivity markedly accelerate the process due to increased advection intensity and enhanced diffusion capability,respectively.Conversely,increasing the porosity has a less significant effect,causing a slight slowdown of the diffusion-advection process due to the expanded pore volume.This comprehensive parametric study provides valuable insights into the kinetics of isotope uptake in porous structures,facilitating the development of porous materials for nuclear waste treatment applications.

PHASE EXTENSION AND STRUCTURE ANALYSIS BY THE MAXIMUM ENTROPY METHOD

Excellent results are obtained in structure analysis with jew phases of structure factors by the maximum-entropy method (MEM) for CaGaN PbCO3 and ReBe22 single crystals. The computation time and memory space are minimized by symmetry operations so that structure analysis by the MEM can be carried out with a personal computer.

Noise-induced phase transition in the Vicsek model through eigen microstate methodology

This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of socialanimals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noiseremains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and nonequilibriumstates, the eigen microstate method is employed here for a quantitative examination of the phase transitions inthe Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phasetransitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for thesephase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions withescalation of population density.

Phase composition,conductivity,and sensor properties of cerium-doped indium oxide

The hydrothermal synthesis of In_(2)O_(3)and CeO_(2)–In_(2)O_(3)is investigated as well as the properties of sensor layers based on these compounds.During the synthesis of In_(2)O_(3),intermediate products In(OH)_(3)and InOOH are formed,which are the precursors of stable cubic(c-In_(2)O_(3))and metastable rhombohedral(rh-In_(2)O_(3))phases,respectively.A transition from c-In_(2)O_(3)to rh-In_(2)O_(3)is observed with the addition of CeO_(2).The introduction of cerium into rh-In_(2)O_(3)results in a decrease in the sensor response to hydrogen,while it increases in composites based on c-In_(2)O_(3).The data on the sensor activity of the composites correlate with XPS results in which CeO_(2)causes a decrease in the concentrations of chemisorbed oxygen and oxygen vacancies in rh-In_(2)O_(3).The reverse situation is observed in composites based on c-In_(2)O_(3).Compared to In_(2)O_(3)and CeO_(2)–In_(2)O_(3)obtained by other methods,the synthesized composites demonstrate maximum response to H_(2)at low temperatures by 70–100℃,and have short response time(0.2–0.5 s),short recovery time(6–7 s),and long-term stability.A model is proposed for the dependence of sensitivity on the direction of electron transfer between In_(2)O_(3)and CeO_(2).

Effect of microalloying on wettability and interface characteristics of Zr-based bulk metallic glasses with W substrate

The infiltration casting method is widely employed for the preparation of ex-situ composite materials.However,the production of composite materials using this method must necessitates a comprehensive understanding of the wettability and interface characteristics between the reinforcing phase and the bulk metallic glasses(BMGs).This work optimized the composition of Zr-based BMGs through microalloying methods,resulting in a new set of Zr-based BMGs with excellent glass-forming ability.Wetting experiments between the Zr-based BMGs melts and W substrates were conducted using the traditional sessile drop method,and the interfaces were characterized utilizing a scanning electron microscope(SEM)equipped with energy dispersive X-ray spectroscopy(EDS).The work demonstrates that the microalloying method substantially enhances the wettability of the Zr-based BMGs melt.Additionally,the incorporation of Nb element impedes the formation of W-Zr phases,but the introduction of Nb element does not alter the extent of interdiffusion between the constituent elements of the amorphous matrix and W element,indicating that the influence of Nb element on the diffusion of individual elements is minute.

Phase equilibrium data prediction and process optimizationin butadiene extraction process

In response to the lack of reliable physical parameters in the process simulation of the butadiene extraction,a large amount of phase equilibrium data were collected in the context of the actual process of butadiene production by acetonitrile.The accuracy of five prediction methods,UNIFAC(UNIQUAC Functional-group Activity Coefficients),UNIFAC-LL,UNIFAC-LBY,UNIFAC-DMD and COSMO-RS,applied to the butadiene extraction process was verified using partial phase equilibrium data.The results showed that the UNIFAC-DMD method had the highest accuracy in predicting phase equilibrium data for the missing system.COSMO-RS-predicted multiple systems showed good accuracy,and a large number of missing phase equilibrium data were estimated using the UNIFAC-DMD method and COSMO-RS method.The predicted phase equilibrium data were checked for consistency.The NRTL-RK(non-Random Two Liquid-Redlich-Kwong Equation of State)and UNIQUAC thermodynamic models were used to correlate the phase equilibrium data.Industrial device simulations were used to verify the accuracy of the thermodynamic model applied to the butadiene extraction process.The simulation results showed that the average deviations of the simulated results using the correlated thermodynamic model from the actual values were less than 2%compared to that using the commercial simulation software,Aspen Plus and its database.The average deviation was much smaller than that of the simulations using the Aspen Plus database(>10%),indicating that the obtained phase equilibrium data are highly accurate and reliable.The best phase equilibrium data and thermodynamic model parameters for butadiene extraction are provided.This improves the accuracy and reliability of the design,optimization and control of the process,and provides a basis and guarantee for developing a more environmentally friendly and economical butadiene extraction process.

A feedback control method for phase signal demodulation in fber-optic hydrophones

In the realm of acoustic signal detection,the identification of weak signals,particularly in the presence of negative signal-to-noise ratios,poses a significant challenge.This challenge is further heightened when signals are acquired through fiber-optic hydrophones,as these signals often lack physical significance and resist clear systematic modeling.Conventional processing methods,e.g.,low-pass filter(LPF),require a thorough understanding of the effective signal bandwidth for noise reduction,and may introduce undesirable time lags.This paper introduces an innovative feedback control method with dual Kalman filters for the demodulation of phase signals with noises in fiber-optic hydrophones.A mathematical model of the closed-loop system is established to guide the design of the feedback control,aiming to achieve a balance with the input phase signal.The dual Kalman filters are instrumental in mitigating the effects of signal noise,observation noise,and control execution noise,thereby enabling precise estimation for the input phase signals.The effectiveness of this feedback control method is demonstrated through examples,showcasing the restoration of low-noise signals,negative signal-to-noise ratio signals,and multi-frequency signals.This research contributes to the technical advancement of high-performance devices,including fiber-optic hydrophones and phase-locked amplifiers.

Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictions[Phys.Rev.A 72053604(2005)]and[arXiv:0706.1609]indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering.However,due to ergodic difficulties faced by Monte Carlo methods at low temperatures,this topological phase has not been numerically explored.We propose a linear cluster updating Monte Carlo method,which flips spins without rejection in the anisotropy limit but does not change the energy.Using this scheme and conventional Monte Carlo methods,we succeed in revealing the nature of topological phases with half-vortices and domain walls.In the constructed global phase diagram,Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier.We also propose and explore a wide range of quantities,including magnetism,superfluidity,specific heat,susceptibility,and even percolation susceptibility,and obtain consistent and reliable results.Furthermore,we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes,as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections.The critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

Dual-phase coexistence enables to alleviate resistance drift in phase-change films

The amorphous phase-change materials with spontaneous structural relaxation leads to the resistance drift with the time for phase-change neuron synaptic devices. Here, we modify the phase change properties of the conventional Ge_2Sb_2Te_5(GST) material by introducing an SnS phase. It is found that the resistance drift coefficient of SnS-doped GST was decreased from 0.06 to 0.01. It can be proposed that the origin originates from the precipitation of GST nanocrystals accompanied by the precipitation of SnS crystals compared to single-phase GST compound systems. We also found that the decrease in resistance drift can be attributed to the narrowed bandgap from 0.65 to 0.43 eV after SnS-doping. Thus, this study reveals the quantitative relationship between the resistance drift and the band gap and proposes a new idea for alleviating the resistance drift by composition optimization, which is of great significance for finding a promising phase change material.

Frost heaving and crack initiation characteristics of tunnel rock mass in cold regions under low-temperature degradation

Water freezing in rock fractures causes volumetric expansion and fracture development through frost heaving.This study introduces a novel analytical model to investigate how uneven freezing force and surrounding rock pressure influence fracture initiation,based on mass conservation,elasticity,and water-ice phase transition principles.A model for rock fracture initiation considering freezing temperature,uneven freezing expansion,in-situ stress,and lateral pressure was proposed based on fracture mechanics.Equations for stress intensity factors were developed and validated using the phase field method.The effects of rock elastic modulus anisotropy and critical fracture energy density on fracture initiation were also discussed.The results show that the values of KI and KII exhibit an upward trend as the freezing temperature,uneven expansion,in-situ stress,and lateral pressure increase.The uneven freezing expansion has the most significant influence on KI and KII values among these parameters.As the uneven freezing expansion coefficient increases to 0.5,the fracture initiation mode shifts from tensile fracture to shear fracture.As the lateral pressure coefficient increases to 1,the fracture initiation mode shifts from tensile fracture to shear fracture.Rock elastic modulus anisotropy causes fractures to propagate in a clockwise direction,forming a'butterfly'pattern.Critical fracture energy density an isotropy causes counterclockwise deviation in propagation direction,resulting in branching paths and an'H'-shaped pattern.

Stress-corrosion coupled damage localization induced by secondary phases in bio-degradable Mg alloys:phase-field modeling

In this study,a phase-field scheme that rigorously obeys conservation laws and irreversible thermodynamics is developed for modeling stress-corrosion coupled damage(SCCD).The coupling constitutive relationships of the deformation,phase-field damage,mass transfer,and electrostatic field are derived from the entropy inequality.The SCCD localization induced by secondary phases in Mg is numerically simulated using the implicit iterative algorithm of the self-defined finite elements.The quantitative evaluation of the SCCD of a C-ring is in good agreement with the experimental results.To capture the damage localization,a micro-galvanic corrosion domain is defined,and the buffering effect on charge migration is explored.Three cases are investigated to reveal the effect of localization on corrosion acceleration and provide guidance for the design for resistance to SCCD at the crystal scale.

Numerical Simulation Study of Oil-Water Emulsion Separation in an Ultrasonic Field:Effect of Coupling between Acoustic and Flow Field Parameters

In this study,the separation and coalescence of oil-in-water emulsions are explored in an ultrasonic field using the lattice Boltzmann method.By simulating the propagation of ultrasonic waves,this study focuses on examining the effects of acoustic wave frequency,the ratio of oil to water components,and the aspect ratio of the boundary on the emulsification and separation processes of oil-water mixtures.The following conclusions are drawn.①Frequency affects the speed of oil droplet separation,leading to an increase in droplet size over time.Larger droplets are found near the source,while smaller droplets are distributed throughout the wave web.②As the boundary aspect ratio increases,the emulsification efficiency of the droplets weakens,and the system takes longer to stabilize.③Emulsions with a higher component of oil can better resist acoustic waves.④At the same acoustic frequency,longer wavelength ultrasonic fields promote the formation of uniformly distributed,smaller oil droplets,which is beneficial to the storage of emulsions.These numerical simulation results offer insights for optimizing conditions for oil-in-water separation and serve as a numerical reference for the study of oil-in-water emulsion separation in ultrasonic environments.

Weak and Strong Convergence of Self Adaptive Inertial Subgradient Extragradient Algorithms for Solving Variational Inequality Problems

Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.

Investigation on the temperature-dependent diffusion growth of intermetallic compounds in the Mg-Al-Zn system:Experiment and modeling

With the rapid development of Mg alloys,deeper understanding to the thermodynamic and diffusional kinetic behavior of intermetallic compounds(IMCs)is important for studying the effect of alloying elements to the microstructure evolution.Specially,a systematic quantitative investigation on the diffusional growth of IMCs is of great necessity.However,the works studying the elemental diffusion behaviors of multiple-element IMCs are rare in magnesium alloy systems.The current work takes the ternary Mg-Al-Zn system as research target,and combines the diffusion couple technique,phase stability diagrams,in-situ observation technique and numerical inverse method to investigate the temperature-dependent kinetic coefficients.The parabolic growth constant(PGC)and interdiffusion coefficients for Mg solid-solution phase andγ-Mg_(17)Al_(12),β-Mg_(2)Al_(3),ε-Mg_(23)Al_(30),MgZn_(2),Mg_(2)Zn_(3),τ-Mg_(32)(Zn,Al)49 andφ-Mg_(5)Zn_(2)Al_(2) IMCs in the Mg-Al-Zn alloy system are determined.By comparing the current experimental with calculation results,the rate-controlling factor of the temperature-dependent diffusion growth ofφ,τandεternary IMCs in the Mg-Al-Zn system is further discussed in detail.

Three-Dimensional Phase Field Simulations of Hysteresis and Butterfly Loops by the Finite Volume Method

Three-dimensional simulations of ferroelectric hysteresis and butterfly loops are carried out based on solving the time dependent Ginzburg-Landau equations using a finite volume method. The influence of externally mechanical loadings with a tensile strain and a compressive strain on the hysteresis and butterfly loops is studied numerically. Different from the traditional finite element and finite difference methods, the finite volume method is applicable to simulate the ferroelectric phase transitions and properties of ferroelectric materials even for more realistic and physical problems.

三步接骨法治疗Sanders Ⅱ型跟骨骨折的有限元研究

目的量化评估三步接骨法治疗Sanders Ⅱ型跟骨骨折效能指标,阐明其科学机制。方法利用健康成年男性踝关节CT数据,构建正常足踝模型与Sanders Ⅱ型跟骨骨折模型,在骨折模型上进行三步接骨法的力学加载,模拟拔伸牵引、提按顶复、端挤捏骨等手法,评估跟骨复位情况并求解不同手法作用下力学的变化。结果建立正常足部模型与Sanders Ⅱ A/B/C型跟骨骨折模型;三步接骨法加载复位后跟骨长、高、宽、Gissane’s角及Bohler’s角得到明显纠正;求解不同手法的力学趋势,发现拔伸牵引法能有效纠正重叠位移,提按顶复法侧重纠正前后侧移位,端挤捏骨法致力纠正内外侧移位。结论三步接骨法通过依次纠正骨折位移,能恢复跟骨解剖结构,有效治疗跟骨SandersⅡ型损伤,具有有效性及科学性。