试论有限差分法模拟电梯悬挂系统横向受迫振动

高层建筑的摇晃给电梯造成位移激励作用,而这种激励是产生电梯悬挂系统横向振动的重要因素。为了提高电梯运行的安全性和舒适度,文章针对有限分差法模拟电梯悬挂系统横向受迫振动展开了研究,基于有限分差法的基本原理和悬挂系统进行了横向振动模型的分析,应用典型案例对振动影响进行了研究。

Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

To speed up three-dimensional （3D） DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method （AGMG）. We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner （AGMG-CG） to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling （3DDCXH）. In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

Application of Padé Approximation in Simulating Photonic Crystals

To save finite-difference time-domain（FDTD） computing time, several methods are proposed to convert the time domain FDTD output into frequency domain. The Pad6 approximation with Baker＇s algorithm and the program are introduced to simulate photonic crystal structures. For a simple pole system with frequency 160THz and quality factor of 5000, the intensity spectrum obtained by the Padé approximation from a 2^8-item sequence output is more exact than that obtained by fast Fourier transformation from a 2^20-item sequence output. The mode frequencies and quality factors are calculated at different wave vectors for the photonic crystal slab from a much shorter FDTD output than that required by the FFT method, and then the band diagrams are obatined. In addition, mode frequencies and Q-factors are calculated for photonic crystal microcavity.

Numerical analysis of multicomponent responses of surface-hole transient electromagnetic method

We calculate the multicomponent responses of surface-hole transient electromagnetic method. The methods and models are unsuitable as geoelectric models of conductive surrounding rocks because they are based on regular local targets. We also propose a calculation and analysis scheme based on numerical simulations of the subsurface transient electromagnetic fields. In the modeling of the electromagnetic fields, the forward modeling simulations are performed by using the finite-difference time-domain method and the discrete image method, which combines the Gaver–Stehfest inverse Laplace transform with the Prony method to solve the initial electromagnetic fields. The precision in the iterative computations is ensured by using the transmission boundary conditions. For the response analysis, we customize geoelectric models consisting of near-borehole targets and conductive wall rocks and implement forward modeling simulations. The observed electric fields are converted into induced electromotive force responses using multicomponent observation devices. By comparing the transient electric fields and multicomponent responses under different conditions, we suggest that the multicomponent-induced electromotive force responses are related to the horizontal and vertical gradient variations of the transient electric field at different times. The characteristics of the response are determined by the varying the subsurface transient electromagnetic fields, i.e., diffusion, attenuation and distortion, under different conditions as well as the electromagnetic fields at the observation positions. The calculation and analysis scheme of the response consider the surrounding rocks and the anomalous field of the local targets. It therefore can account for the geological data better than conventional transient field response analysis of local targets.

Improved absorbing boundary condition based on linear interpolation for ADI-FDTD method

With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.

New numerical algorithm of gas-liquid two-phase flow considering characteristics of liquid metal during mold filling

A new program is developed for gas-liquid two-phase mold filling simulation in casting. The gas fluid, the superheated liquid metal and the liquid metal containing solid grains are assumed to be governed by Navier-Stokes equations and solved through Projection method. The Level set method is used to track the gas-liquid interface boundary. In order to demonstrate the correctness of this new program for simulation of gas-liquid two-phase mold filling in casting, a benchmark filling experiment is simulated （this benchmark test is designed by XU and the filling process is recorded by a 16-mm film camera）. The simulated results agree very well with the experimental results, showing that this new program can be used to properly predicate the gas-liquid two-phase mold filling simulation in casting.

New algorithm for solving 3D incompressible viscous equations based on projection method

A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.

Numerical prediction of the long- term soil temperature variations around shallowsections of cross-river road tunnels

Considering the coupled heat transfer effect induced by parallel cross-river road tunnels, the long-term soil temperature variations of shallow sections of cross-river tunnels under the river beach are predicted using the finite difference method for numerical simulation. The boundary conditions and the initial values are determined by in situ observations and numerical iterations.The simulation results indicate that the ultimate calculated steady heat transfer time is 68 years, and most of the heat transfer is completed in 20 years.The initial constant temperature soil surrounding the tunnels is transformed to an annually variable one.An obvious temperature-varying region of the surrounding soil is discovered within 5 m from the tunnel exterior, as well as within the entire range of soil between the two tunnels.The maximum temperature increase value reaches 7.14 ℃ and the maximum peak-to-valley value of annual temperature increase reaches 10 ℃.The temperature variation of soils surrounding tunnels below 10 m is completely controlled by the heat transfer from the tunnels.The coupled heat transfer effect is confirmed because the ultimate steady temperature of soil between the two tunnels is higher than the ones along other positions.Moreover, the regression model comprising a series of univariate functions is proposed for the annual soil temperature fluctuation estimation for the locations varied distances around the tunnel.This investigation is beneficial to gain an insight into the long-term variation tendencies of local engineering geological conditions of the river beach above shallow sections of the cross-river road tunnels.

Full Wave Analysis of a Broad Wall Waveguide Slot Coupler

A rigorous analysis of a broad wall slot coupler composed of two crossed rectangular waveguides by using FDTD method is presented. Two types of slots, a longitudinal/transverse slot and a centered-inclined slot, are analyzed. Coupling slot characteristics are obtained, including scattering parameters and the resonant length for different waveguide dimensions and frequencies. The numerical results are all in good agreement with those by the method of moments. A coupler system with a short circuit port is also analyzed to help designing the slot array.

COMPUTER VISUALIZATION OF ELECTROMAGNETIC WAVE INTERACTION WITH STRUCTURES

In this paper, a computer visualization approach is proposed for electromagnetic wave interaction with structures by mains of finite difference-time doain method (F-D) and computer graphics. By visualization of FDTD, Phenomena such as wave propagation, penetration through structures, renection and absorption by structures are observed. Visualization of electromagnetic wave interactions with two wing-shaped structures is demonstrated. These examples indicate that the approach describe in the paper offers an effective way for investigating electromagnetic wave phenomena and is helpful to the engineers in controlling radar signature of the targets.

Improved finite difference method for pressure distribution of aerostatic bearing

An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.

Force analysis of pile foundation in rock slope based on upper-bound theorem of limit

Based on the characteristic that the potential sliding surfaces of rock slope are commonly in the shape of either line or fold line,analysis thought of conventional pile foundation in the flat ground under complex load condition was applied and the upper-bound theorem of limit analysis was used to compute thrust of rock layers with all possible distribution shapes. The interaction of slope and pile was considered design load in terms of slope thrust,and the finite difference method was derived to calculate inner-force and displacement of bridge pile foundation in rock slope under complex load condition. The result of example shows that the distribution model of slope thrust has certain impact on displacement and inner-force of bridge pile foundation. The maximum displacement growth rate reaches 54% and the maximum moment and shear growth rates reach only 15% and 20%,respectively,but the trends of inner-force and displacement of bridge pile foundation are basically the same as those of the conventional pile foundation in the flat ground. When the piles bear the same level lateral thrust,the distribution shapes of slope thrust have different influence on inner-force of pile foundation,especially the rectangle distribution,and the triangle thrust has the smallest displacement and inner-force of pile foundation.

3D finite-difference modeling algorithm and anomaly features of ZTEM

The Z-Axis tiPPer eiectromagnetic （ZTEM） technique is based on a frequency-domain airbome electromagnetic system that measures the natural magnetic field. A survey area was divided into several blocks by using the Maxwell＇s equations, and the magnetic components at the center of each edge of the grid cell are evaluated by applying the staggered-grid finite-difference method. The tipper and its divergence are derived to complete the 3D ZTEM forward modeling algorithm. A synthetic model is then used to compare the responses with those of 2D finite-element forward modeling to verify the accuracy of the algorithm. ZTEM offers high horizontal resolution to both simple and complex distributions of conductivity. This work is the theoretical foundation for the interpretation of ZTEM data and the study of 3D ZTEM inversion.

Finite difference method for dynamic response analysis of anchorage system

Based on some assumptions, the dynamic analysis model of anchorage system is established. The dynamic governing equation is expressed as finite difference format and programmed by using MATLAB language. Compared with theoretical method, the finite difference method has been verified to be feasible by a case study. It is found that under seismic loading, the dynamic response of anchorage system is synchronously fluctuated with the seismic vibration. The change of displacement amplitude of material points is slight, and comparatively speaking, the displacement amplitude of the outside point is a little larger than that of the inside point, which shows amplification effect of surface. While the axial force amplitude transforms considerably from the inside to the outside. It increases first and reaches the peak value in the intersection between the anchoring section and free section, then decreases slowly in the free section. When considering damping effect of anchorage system, the finite difference method can reflect the time attenuation characteristic better, and the calculating result would be safer and more reasonable than the dynamic steady-state theoretical method. What is more, the finite difference method can be applied to the dynamic response analysis of harmonic and seismic random vibration for all kinds of anchor, and hence has a broad application prospect.

The Precise Finite Difference Method for Seismic Modeling

D seismic modeling can be used to study the propagation of seismic wave exactly and it is also a tool of 3-D seismic data processing and interpretation. In this paper the arbitrary difference and precise integration are used to solve seismic wave equation, which means difference scheme for space domain and analytic integration for time domain. Both the principle and algorithm of this method are introduced in the paper. Based on the theory, the numerical examples prove that this hybrid method can lead to higher accuracy than the traditional finite difference method and the solution is very close to the exact one. Also the seismic modeling examples show the good performance of this method even in the case of complex surface conditions and complicated structures.

The Numerical Modeling of 3-D Elastic Wave Equation Using a High-Order,Staggered-Grid, Finite Difference Scheme

This article provides the application of the high-order, staggered-grid, finite-difference scheme to model elastic wave propagation in 3-D isotropic media. Here, we use second-order, tempo- ral- and high-order spatial finite-difference formulations with a staggered grid for discretization of the 3-D elastic wave equations of motion. The set of absorbing boundary conditions based on paraxial approximations of 3-D elastic wave equations are applied to the numerical boundaries. The trial re- sults for the salt model show that the numerical dispersion is decreased to a minimum extent, the accuracy high and diffracted waves abundant. It also shows that this method can be used for modeling wave propagation in complex media with the lateral variation of velocity.

ulti-azimuth three-component surface seismic modeling for viscoelastic cracked monoclinic media

In this article, a method of high order, staggered grid, finite difference was used to model snapshots of seismic wave propagation and multi-azimuth surface seismic records in viscoelastic cracked monoclinic media. The modeling results clearly show the anisotropy caused by the crack fill material and the viscoelastic wave field through the monoclinic media. Summarizing the regularity of seismic records for different azimuths, this study is a significant attempt to understand the wave fields propagated in real media and to propose a more rational theoretical model for the future.

3-D acoustic wave equation forward modeling with topography

In order to model the seismic wave field with surface topography, we present a method of transforming curved grids into rectangular grids in two different coordinate systems. Then the 3D wave equation in the transformed coordinate system is derived. The wave field is modeled using the finite-difference method in the transformed coordinate system. The model calculation shows that this method is able to model the seismic wave field with fluctuating surface topography and achieve good results. Finally, the energy curves of the direct and reflected waves are analyzed to show that surface topography has a great influence on the seismic wave＇s dynamic properties.

Investigation on temperature field of unidirectional carbon fiber/epoxy composites during drilling process

The phenomenon of heat accumulation and transportation in the composite materials is a very typical and critical issue during drilling process.In this study,a three-dimensional temperature field prediction model is proposed using finite difference method,based on the partly homogenization hypothesis of material,to predict temperature field in the process of drilling unidirectional carbon fiber/epoxy(C/E)composites.According to the drilling feed motion,drilling process is divided into four stages to study the temperature distributing characteristics.The results show that the temperature distribution predicted by numerical study has a good agreement with the experimental results.The temperature increases with increasing the drilling depth,and the burn phenomena is observed due to the heat accumulation,especially at the drill exit.Due to the fiber orientation,an elliptical shape of the temperature field along the direction is found for both numerical and experimental studies of C/E composites drilling process.

Failure mechanism of large-diameter shield tunnels and its effects on ground surface settlements

A new technique for the analysis of the three-dimensional collapse failure mechanism and the ground surface settlements for the large-diameter shield tunnels were presented.The technique is based on a velocity field model using more different truncated solid conical blocks to clarify the multiblock failure mechanism.Furthermore,the shape of blocks between the failure surface and the tunnel face was considered as an entire circle,and the supporting pressure was assumed as non-uniform distribution on the tunnel face and increased with the tunnel embedded depth.The ground surface settlements and failure mechanism above large-diameter shield tunnels were also investigated under different supporting pressures by the finite difference method.