Stability and accuracy of central difference method for real-time dynamic substructure testing considering mass participation coefficient

For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.

Molecular Dynamics, Diffusion Coefficients and Activation Energy of the Electrolyte (Anode) in Lithium (Li and Li+), Sodium (Na and Na+) and Potassium (K and K+)

This work is a simulation modelling with the LAMMPS calculation code of an electrode based on alkali metals (lithium, sodium and potassium) using the MEAM potential. For different multiplicities, two models were studied;with and without gap. In this work, we present the structural, physical and chemical properties of the lithium, sodium and potassium electrodes. For the structural properties, the cohesive energy and the mesh parameters were calculated, revealing that, whatever the chemical element selected, the compact hexagonal hcp structure is the most stable, followed by the face-centred cubic CFC structure, and finally the BCC structure. The most stable structure is lithium, with a cohesion energy of -6570 eV, and the lowest bcc-hcp transition energy of -0.553 eV/atom, followed by sodium. For physical properties, kinetic and potential energies were calculated for each of the sectioned chemical elements, with lithium achieving the highest value. Finally, for the chemical properties, we studied the diffusion coefficient and the activation energy. Only potassium followed an opposite order to the other two, with the quantities with lacunae being greater than those without lacunae, whatever the multiplicity. The order of magnitude of the diffusion coefficients is given by the relationship DLi > DNa > Dk for the multiplicity 6*6*6, while for the activation energy the order is reversed.

Molecular Dynamics, Physical Properties, Diffusion Coefficients and Activation Energy of the Lithium Oxide (Li-O) and Sodium Oxide (Na-O) Electrolyte (Cathode)

This work is a simulation model with the LAMMPS calculation code of an electrode based on alkali metal oxides (lithium, sodium and potassium) using the Lennard Jones potential. For a multiplicity of 8*8*8, we studied a gap-free model using molecular dynamics. Physical quantities such as volume and pressure of the Na-O and Li-O systems exhibit similar behaviors around the thermodynamic ensembles NPT and NVE. However, for the Na2O system, at a minimum temperature value, we observe a range of total energy values;in contrast, for the Li2O system, a minimum energy corresponds to a range of temperatures. Finally, for physicochemical properties, we studied the diffusion coefficient and activation energy of lithium and potassium oxides around their melting temperatures. The order of magnitude of the diffusion coefficients is given by the relation Dli-O >DNa-O for the multiplicity 8*8*8, while for the activation energy, the order is well reversed EaNa-O > EaLi-O.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

Hierarchical Bayesian Calibration and On-line Updating Method for Influence Coefficient of Automatic Dynamic Balancing Machine

Measurement error of unbalance＇s vibration response plays a crucial role in calibration and on-line updating of influence coefficient（IC）. Focusing on the two problems that the moment estimator of data used in calibration process cannot fulfill the accuracy requirement under small sample and the disturbance of measurement error cannot be effectively suppressed in updating process, an IC calibration and on-line updating method based on hierarchical Bayesian method for automatic dynamic balancing machine was proposed. During calibration process, for the repeatedly-measured data obtained from experiments with different trial weights, according to the fact that measurement error of each sensor had the same statistical characteristics, the joint posterior distribution model for the true values of the vibration response under all trial weights and measurement error was established. During the updating process, information obtained from calibration was regarded as prior information, which was utilized to update the posterior distribution of IC combined with the real-time reference information to implement online updating. Moreover, Gibbs sampling method of Markov Chain Monte Carlo（MCMC） was adopted to obtain the maximum posterior estimation of parameters to be estimated. On the independent developed dynamic balancing testbed, prediction was carried out for multiple groups of data through the proposed method and the traditional method respectively, the result indicated that estimator of influence coefficient obtained through the proposed method had higher accuracy; the proposed updating method more effectively guaranteed the measurement accuracy during the whole producing process, and meantime more reasonably compromised between the sensitivity of IC change and suppression of randomness of vibration response.

Critical anomaly and finite size scaling of the self-diffusion coefficient for Lennard Jones fluids by non-equilibrium molecular dynamic simulation

We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with temperature decreases by increasing density. For density ρ＊ = ρσ3 = 0.84 we observe a peak at the value of the self-diffusion coefficient and the critical temperature T＊ = kT/ε = 1.25. The value of the self-diffusion coefficient strongly depends on system size. The data of the self-diffusion coefficient are fitted to a simple analytic relation based on hydrodynamic arguments. This correction scales as N-α, where α is an adjustable parameter and N is the number of particles. It is observed that the values of a 〈 1 provide quite a good correction to the simulation data. The system size dependence is very strong for lower densities, but it is not as strong for higher densities. The self-diffusion coefficient calculated with non-equilibrium molecular dynamic simulations at different temperatures and densities is in good agreement with other calculations fronl the literature.

Tomography of the dynamic stress coefficient for stress wave prediction in sedimentary rock layer under the mining additional stress

In this study,the tomography of dynamic stress coefficient(TDSC)was established based on a mechanical model of stress wave propagation in bedding planes and a mathematical model of the stress wave attenuation in rock masses.The reliability of the TDSC was verified by a linear bedding plane model and field monitoring.Generally,the TDSC in the dynamic stress propagation of bedding planes increases with the following conditions:(1)the increase of the normal stiffness of the bedding plane,(2)the increase of the incident angle of the stress wave,(3)the decrease of the incident frequency of the stress wave,or(4)the growth of three ratios(the ratios of rock densities,elastic moduli,and the Poisson’s ratios)of rocks on either side of bedding planes.The additional stress weakens TDSC linearly and slowly during the stress wave propagation in bedding planes,and the weakening effect increases with the growth of the three ratios.Besides,the TDSC decreases exponentially in the rock mass as propagation distance increases.In a field case,the TDSC decreases significantly as vertical and horizontal distances increase and its wave range increases as vertical distance increases in the sedimentary rock layers.

Determination of Water Diffusion Coefficients and Dynamics in Adhesive/Carbon Fiber Reinforced Epoxy Resin Composite Joints

To determinate the water diffusion coefficients and dynamics in adhesive/carben fiber reinforced epoxy resin composite joints, energy dispersive X-ray spectroscopy analysis（EDX） is used to establish the content change of oxy- gen in the adhesive in adhesive/carbon fther reinforced epoxy resin composite joints. As water is made up of oxygen and hydrogen, the water diffusion coefficients and dynamics in adhesive/carben fiber reinforced epoxy resin composite joints can be obtained from the change in the content of oxygen in the adhesive during humidity aging, via EDX analy-sis. The authors have calculated the water diffusion coefficients and dynamics in the adhesive/carbon fiber reinforced epoxy resin composite joints with the aid of beth energy dispersive X-ray spectroscopy and elemental analysis. The de- termined results with EDX analysis are almost the same as those determined with elemental analysis and the results al- so show that the durability of the adhesive/carbon fther reinforced epoxy resin composite joints subjected to silane cou- pling agent treatment is better than those subjected to sand paper burnishing treatment and chemical oxidation treat- ment.

Molecular dynamics simulation of self-diffusion coefficients for liquid metals

The temperature-dependent coefficients of self-diffusion for liquid metals are simulated by molecular dynamics meth ods based on the embedded-atom-method （EAM） potential function. The simulated results show that a good inverse linear relation exists between the natural logarithm of self-diffusion coefficients and temperature, though the results in the litera ture vary somewhat, due to the employment of different potential functions. The estimated activation energy of liquid metals obtained by fitting the Arrhenius formula is close to the experimental data. The temperature-dependent shear-viscosities obtained from the Stokes-Einstein relation in conjunction with the results of molecular dynamics simulation are generally consistent with other values in the literature.

Influence of Structural Parameters of Turbocharger Floating Bearing on Its Dynamic Characteristic Coefficients

The structure parameters in an actual industrial production have a great influence on the coefficient of supercharger floating bearing dynamic characteristics,but there has been little systematic study so far.In this paper,the influence of structural parameters of the turbocharger floating bearing on its dynamic characteristic coefficientsis systematically investigated based on the theories of hydrodynamic lubrication and tribology.The influence of clearance ratio on eccentricity and the influence of internal to external radius ratios,and Sommerfeld number were analyzed.A new formula of responding characteristics of the oil film force caused by the displacement or velocity disturbance was deduced near an equilibrium in the steady state.Applying the newly developed formula,the dynamic characteristic was studied for floating bearings.Regularity for change of oil film stiffness and damping was analyzed with the structural parameters of floating bearing such as radius ratios and eccentricity.It has been found that the clearance ratio increases with eccentricity when the radius ratio is unchanged.The eccentricity decreases with the internal to external radius ratio of floating rings when the clearance ratio is constant.The absolute value of total principal stiffness and total main damping decrease with the clearance ratio and radius ratio of floating rings when the total cross damping is stable.The results and findings in this paper can contribute to nonlinear dynamics designs of turbocharger rotor-bearing systems.

Rate Coefficients of Roaming Reaction H+MgH Using Ring Polymer Molecular Dynamics

The ring-polymer molecular dynamics(RPMD)was used to calculate the thermal rate coefficients of the multi-channel roaming reaction H+MgH→Mg+H_(2).Two reaction channels,tight and roaming,are explicitly considered.This is a pioneering attempt of exerting RPMD method to multichannel reactions.With the help of a newly developed optimization-interpolation protocol for preparing the initial structures and adaptive protocol for choosing the force constants,we have successfully obtained the thermal rate coefficients.The results are consistent with those from other theoretical methods,such as variational transition state theory and quantum dynamics.Especially,RPMD results exhibit negative temperature dependence,which is similar to the results from variational transition state theory but different from the ones from ground state quantum dynamics calculations.

Dynamic model of saturator based on a global heat and mass transfer coefficient

Saturator is one of the core components of humid air turbine （HAT） and is the main feature of HAT making it different from other gas turbine cycles. Due to the lack of sufficient experience in commercial plant operation, HAT cycle has a great demand for modeling and simulation of the system and its components, especially the saturator, to provide reference for system design and optimization. The conventional saturator models are usually based on the theory of heat and mass transfer, which need two accurate coefficients to ensure convincing results. This work proposes a global heat and mass transfer coefficient based on cooling tower technology to model the saturator in small-scale HAT cycle. Compared with the experimental data, the simulation results show that the proposed model well predicts the dynamic humidity and temperature distribution characteristics of saturator at low air pressure and temperature.

Identification Method of Dynamic Coefficients of Fluid Film Bearings for HDD Spindle Motors

Fluid film bearings are widely used as support elements of rotating shaft for HDD （hard disk drive） spindle motors. Recently, the opportunity for the HDD spindle motors exposed to external vibration has been increasing because the HDDs are used for various information related equipments such as mobile PCs, car navigation systems. Hence, the rotating shaft has a possibility to come in contact with the bearing and it causes wear or seizure to the bearing surface. In order to avoid the problems, it is extremely important to enhance the dynamic characteristics of the fluid film bearings for spindles. However, verification from both theory and experiment of dynamic characteristics such as spring coefficients and damping coefficients is rare and few. In this paper, the bearing vibration characteristics when the HDD spindle is oscillated are investigated theoretically and experimentally. And then the identification method ofoil film coefficients of fluid film bearing spindles is described.

Dynamic Characteristics of Planar Deployable Structure Based on ScissorLike Element Using Influence Coefficient Method

In order to execute geometric analysis for planar deployable mechanism of scissors unit,the dynamic analysis model of scissor planar deployable structure is created based on the Cartesian coordinate system,the influence coefficient is acquired by means of the coordinate transformation,combining the D 'Alembert 's principle with Dynamic-Static method,the dynamic characteristic analysis is completed finally. Moreover,specific calculating examples are adopted to verify the effectiveness of proposed method,and the result shows that the movement of each component of scissors unit mechanism is more smooth during initial deployment stage,however,when the configuration angle θ of unit mechanism is approaching π,some comparative large variations would appear on movement parameters and hinge constraint force.

DETERMINATION OF STATIC AND DYNAMIC DIFFUSION COEFFICIENTS OF MOISTURE IN PARTICLEBOARDS

The static and dynamic diffusion coefficients are important coefficients to describe the moisture transfer processes in particleboard. In this paper, the formula of culculating the static and dynamic diffusion coefficients were deduced. At first, the static diffusion coefficients of four kinds of particleboards were determined by using diffusion cup method. The results demonstrated that the static diffusion coefficients parallel to panel surface were 10-20 times as large as that of perpendicular to panel surface for test boards. To determine both dynamic diffusion coefficients and surface emission coefficients of moisture in particleboards in one experimental period, specimens in four different thicknesses of each kind of particleboard were used in the experiment. Then the method of regression was used and the dynamic diffusion coefficients and surface emission coefficients were determined based on the slope and intercept of the regressive line.

The Application of Ridge Regression in Dynamic Balancing of Flexible Rotors Based on Influence Coefficient Method

Based on the model structure of the influence coefficient method analyzed in depth by matrix theory ,it is explained the reason why the unreasonable and instable correction masses with bigger MSE are obtained by LS influence coefficient method when there are correlation planes in the dynamic balancing. It also presencd the new ridge regression method for solving correction masses according to the Tikhonov regularization theory, and described the reason why the ridge regression can eliminate the disadvantage of the LS method. Applying this new method to dynamic balancing of gas turbine, it is found that this method is superior to the LS method when influence coefficient matrix is ill-conditioned,the minimal correction masses and residual vibration are obtained in the dynamic balancing of rotors.

RELATION BETWEEN DYNAMIC LOSS MODULUS AND DIFFUSION COEFFICIENT IN A MODIFIED PET FIBER

The mobility of polymer chain segments is shown to play a major role in the diffusion ofdisperse dyes in a copolymerization modified PET system, monoepoxy compoundCH_3 (CH_3),OCH_2CH--CH_2 modified PET. The rate of dye diffusion (diffusion coefficient D) hasbeen related to the time-dependent mechanical property, dynamic loss modulus E', which iscontrolled by the mobility of chain segments. In this modified copolyester system, the variance ofamount of modifier in the copolyester fibers causes the change in disperse dye diffusion coefficientto fiber, and in the dynamic loss modulus of the fibers, but the relationship between the diffusionand the dynamic loss modulus is in agreement with the theoretical relation derived by Bell andDumbleton. The relation obtained in this paper is:Ln D=-2. 28Ln E'+26. 81

Translocation of Polymer Through a Nanopore Studied by Langevin Dynamics:Effect of the Friction Coefficient

The driven polymer translocation through a nanopore with unbiased initial configuration has been studied by using Langevin dynamics(LD) simulations.It is found that the scaling relationship between translocation time and the polymer chain length is strongly affected by the friction coefficient in LD and the driving force.However,there is no scaling relationship between the translocation time and the friction coefficient.The translocation time is almost inversely proportional to the driving force,which is in agreement with those obtained in biased translocation.The scaling relationship between gyration radius(R g) of subchain at the trans side with the subchain length(L) is R g ～L 0.33 that is in good agreement with the limiting value for molten globule state,while the curve of R g of subchain at the cis side has two distinct stages.During translocation,the subchain at the cis side is being stretched gradually,and the structure of the subchain transforms from sphere-like to rod-like.When the effect of stretching reaches the tail end,the subchain is at the most stretched state.Finally the subchain will rapidly restore to coil structure.According to the results of force analysis,the retarding force at the trans side is more crucial during the practical translocation.

Molecular Dynamics Simulations of Self-diffusion Coefficients of Exponential-six Fluids

Self-diffusion coefficients of exponential-six fluids are studied using equilibrium molecular dynamics simulation technique. Mean-square displacements and velocity autocorrelation functions are used to calculate self-diffusion coefficients through Einstein equation and Green-Kubo formula. It has been found that simulation results are in good agreement with experimental data for liquid argon which is taken as exponential-six fluid. The effects of density, temperature and steepness factor for repulsive part of exponential-six potential on self-diffusion coefficients are also investigated. The simulation results indicate that the self-diffusion coefficient of exponential-six fluid increases as temperature increases and density decreases. In addition, the larger self-diffusion coefficients are obtained as the steepness factor increases at the same temperature and density condition.

Parametric Study by Dynamic Simulation of the Influence of the Air Infiltration Rate and the Convective Thermal Transfer Coefficient on the Thermal Behavior of Residential Buildings Built with Cut Lateritic Blocks

Sustainable building design in dry tropical areas recommends reducing exposure of buildings to solar radiation and/or designing efficient enclosures with satisfactory thermal inertia.We propose in this paper a study of the influence of the infiltration rate in the building and the coefficient of thermal transfer by convection of the walls, on the thermal comfort using TRNSYS software. All the models carried out were validated by recognized scientific criteria, namely correlation （R） and determination （R2） coefficients on the one hand and NBME and CVRMSE coefficients defined by ASHARE, 2002 on the other hand. The results obtained indicate that the modulation of the air infiltration rate allows the simulations on TRNSYS to be compared to in-situ measurements, with an annual average relative difference of 2.86% on the temperature difference. Furthermore, depending on the parameterization of the heat transfer coefficients by convection of the internal and external walls of walls used in the STD, the average annual difference can be reduced by 1% to 4% between the predictions and the measurements.