阻尼振动方程的一种显式直接积分方法

介绍了一种求解阻尼振动方程的条件稳定的直接积分方法及其逐步求解过程,该方法是显式的,适于分析阻尼系统的动力反应。     

有阻尼振动方程常用显式积分格式稳定性分析

本文主要介绍了用于求解有阻尼振动方程的四种常用显式积分方法，并针对其稳定性和精度进行了分析对比，讨论了其适用范围及阻尼对稳定性的影响。     

地震的概率预报

所谓地震预报，指的是预先知道地震的震中、震级和发生时间。亦可换言之，是在某种前提下，预测地震的发生。把概率用于预测的理由有二：其一，是因为地震现象本身受到不确定因素的影响；其二，是由于我们所掌握的观测预报信息存在着很多的不确定性。因此，进行预报的实际过程，归根结底，是某种条件下的概率预测。由于地震预报具有一定的社会影响，所以，不得不考虑能否将预测结果作为预报公之与众的问题。从这个意义上讲，我们在此将概率预测称之为概率预报。     

内蒙古地震台网与呼和浩特遥测台网ML震级的归一化研究

对内蒙古地震台网和呼和浩特遥测地震台网测定的近震震级ＭＬ的偏差进行了统计研究，结果表明；两者之间的ＭＬ震级标度基本一致。由于ＭＬ震级公式本身的不均匀性，对于网外地震，遥测台网ＭＬ震级需加适量校正值。     

用于不规则界面多层介质的地震波方法比较研究：不规则地形问题

通过研究SH波入射时各种地形的散射，从计算结果的精确性、稳定性和计算效率三个方面研究Aki Larner方法、Bouchon Campillo方法、以及全局广义反-透射矩阵方法（Chen's方法），比较这三种计算具有不规则界面多层介质中理论地震图的离散波数方法. 由于利用了FFT算法，Aki Larner方法速度最快，但由于方法本身受到Rayleigh假设的限制，结果精度最差. Bouchon Campillo方法非常稳定，结果较精确；但其计算效率最低，并且不能正确地处理非常陡峭的地形问题. 全局广义反-透射矩阵方法非常稳定，结果最精确，能够很好地处理非常陡峭的地形问题，并具有适中的计算效率；因此是三种方法中的最佳方法，为计算复杂介质中的地震波动问题提供了十分有效的工具.     

重力滑动过程中蠕滑和松弛因素的作用及其与地震的关系

本文根据岩体自身的力学性质及其变化,讨论了具有挤压特征的正断层的成因。认为这些断层的形成有岩体本身的重力作用,同时也有应力松弛现象。岩体中的应力松弛现象是由流变学因素和非流变学因素引起的。由于松弛后岩体沿断层面滑动过程中,仍受到一定的挤压作用,因此易于出现粘滑现象,从而易于发生地震。     

GECT／T8800滤线器疑难故障一例

作者叙述了ＧＥＣＴ／Ｔ８８００Ｘ线扫描机滤线器的工作原理和检测方法，分析了一次由于控制电路元件的损坏和不稳定而产生的疑难故障．     

风电消纳一直是世界性难题 解读国家能源局《关于做好2015年度风电并网消纳有关工作的通知》

<正>所谓弃风限电,是指在风电发展初期,风机处于正常情况下,由于当地电网接纳能力不足、风电场建设工期不匹配和风电不稳定等自身特点导致的部分风电场风机暂停的现象,这样大量的浪费了风资源。中国的"三北"(华北、东北、西北)是弃风限电重灾区,尤其以河北省张家口、吉林省、内蒙古自治区锡林郭勒盟、呼伦贝尔市和兴安盟等地最     

井下地震计的P波接收函数正演计算及其稳定性研究——以首都圈地区为例

井下地震计波形记录的P波垂向分量存在频谱极小（spectrum null）现象,导致接收函数的结果不稳定.本文以首都圈地区为例,基于平面波入射的传播矩阵理论,发展了用于计算井下地震计的接收函数正演方法.在此基础上,分析了井下地震计波形垂向分量频谱极小现象,研究其对接收函数稳定性的影响.结果表明,井下地震计波形记录垂向分量的频谱极小开始出现的频率和地震计的埋深相关.该现象可造成反卷积提取的接收函数不稳定,且不稳定情况出现在频谱极小附近的频段,可通过选择合适的高斯因子压制其对接收函数的影响.     

隔震结构中非经典阻尼影响及最佳阻尼比分析

本文采用双自由度非比例阻尼振动模型描述基础隔震体系,用拉普拉斯变换方法获得其地震时域响应的近似解析解,借助于应谱理论分析了非比例阻尼对隔震体系中的上部结构层间最大剪力及隔震层最大位移等响应值的影响,探寻了隔震系统最佳阻尼比的取值范围。     

Testing density-dependent groundwater models: two-dimensional steady state unstable convection in infinite,finite and inclined porous layers

This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA––A model for saturated–unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4π² and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature.     

TIME-DOMAIN ANALYSIS OF LINEAR HYSTERETIC DAMPING

Two linear-hysteretic-damping models that provide energy dissipation independent of the deformation frequency, are studied in this paper: a hysteretic Kelvin element and a hysteretic Maxwell element. Both models use the Hilbert transform and yield integro–differential equations for the equations of motion of structures when real-valued signals are utilized in the formulation. It is shown that the use of analytic (complex-valued) signals allows the transformation of these integro–differential equations into differential equations with analytic input signals and complex-valued coefficients. These differential equations show both stable and unstable poles. A technique for the solution of these differential equations is presented; it consists of a conventional modal decomposition of the state-space equations and the integration of the differential equations forward in time for the modal co-ordinates associated with stable poles, and backwards in time for the modal co-ordinates associated with unstable poles. Some numerical examples are presented to illustrate the characteristics of the models and the proposed analysis technique.     

Effects of sediment grain size and channel slope on the stability of river bifurcations

Channel bifurcations can be found in river network systems from high gradient gravel-bed rivers to fine-grained low gradient deltas. In these systems, bifurcations often evolve asymmetrically such that one downstream channel silts up and the other deepens and, in most cases, they eventually avulse. Past analytical and numerical studies showed that symmetric bifurcations are unstable in high and low Shields stress conditions resulting in asymmetric bifurcations and avulsion, while they can be stable in the mid-Shields range, but this range is smaller for larger width-to-depth ratio. Here, using a one-dimensional (1D) numerical model, we show that effects of sediment grain size and of channel slope are much larger than expected for low-gradient systems when a sediment transport relation is used that separates between bedload and suspended load transport. We found that the range of Shields stress conditions with unstable symmetric bifurcations expanded for lower channel slopes and for finer sediment. In high sediment mobility, suspended load increasingly dominates the sediment transport, which increases the sediment transport nonlinearity and lowers the relative influence of the stabilizing transverse bedslope-driven flux. Contrary to previous works, we found another stable symmetric solution in high Shields stress, but this only occurs in the systems with small width-to-depth ratio. This indicates that suspended load-dominated bifurcations of lowland rivers are more likely to develop into highly asymmetric channels than previously thought. This explains the tendency of channel avulsion observed in many systems.     

THE STABILITY OF THE SOLUTIONS OF THE POTENTIAL FIELD TRANSFORMATIONS *

The quantitative analysis of the potential fields leads to the solution of some operational equations which sometimes have unstable solutions representing fictitious anomalies. A general method to find numerically stable solutions of such problems is presented in this paper. The subject of the downward analytical continuation is also discussed. The method has been checked on a theoretical model and applied to a gravity map.     

Stability of central difference method for dynamic real‐time substructure testing

This paper studies the stability of the central difference method (CDM) for real‐time substructure test considering specimen mass. Because the standard CDM is implicit in terms of acceleration, to avoid iteration, an explicit acceleration formulation is assumed for its implementation in real‐time dynamic substructure testing. The analytical work shows that the stability of the algorithm decreases with increasing specimen mass if the experimental substructure is a pure inertia specimen. The algorithm becomes unstable however small the time integration interval is, when the mass of specimen equal or greater than that of its numerical counterpart. For the case of dynamic specimen, the algorithm is unstable when there is no damping in the whole test structure; a damping will make the algorithm stable conditionally. Part of the analytical results is validated through an actual test. Copyright © 2009 John Wiley & Sons, Ltd.     

Diffusive destabilisation of the baroclinic circular vortex

Abstract

It is shown that, even for vanishingly small diffusivities of momentum and heat, a rotating stratified zonal shear flow is more unstable to zonally symmetric disturbances than would be indicated by the classical inviscid adiabatic criterion, unless σ, the Prandtl number, = 1. Both monotonic instability, and growing oscillations ("overstability") are involved, the former determining the stability criterion and having the higher growth rates. The more σ differs from 1, the larger the region in parameter space for which the flow is stable by the classical criterion, but actually unstable.

If the baroclinity is sufficiently great for the classical criterion also to indicate instability, the corresponding inviscid adiabatic modes usually have the numerically highest growth rates. An exception is the case of small isotherm slope and small σ.

A single normal mode of the linearized theory is also, formally, a finite amplitude solution; however, no theoretical attempt is made to assess the effect of finite amplitude in general. But, in a following paper, viscous overturning (the mechanism giving rise to the sub‐classical monotonic instability when σ > 1) is shown to play an important role at finite amplitude in certain examples of nonlinear steady thermally‐driven axisymmetric flow of water in a rotating annulus. Irrespective of whether analogous mechanisms turn out to be identifiable and important in large‐scale nature, it appears then that a Prandtl‐type parameter should enter the discussion of any attempt to make laboratory or numerical models of zonally‐symmetric baroclinic geophysical or astrophysical flows.     

Development of instability of a rock mass studied by the method of active geophysical monitoring

Results of five-year electromagnetic monitoring of a rock mass of the Tashtagol mine are presented. The introduction of the interval intensity parameter for disintegration zones is shown to be instrumental in the numerical classification of the rock mass state in terms of three gradations: stable, unstable, and intermediate. Disintegration zones of stable and unstable rock masses are shown to differ in spatial dynamics.     

Influence of Boundary Condition Types on Unstable Density‐Dependent Flow

Boundary conditions are required to close the mathematical formulation of unstable density‐dependent flow systems. Proper implementation of boundary conditions, for both flow and transport equations, in numerical simulation are critical. In this paper, numerical simulations using the FEFLOW model are employed to study the influence of the different boundary conditions for unstable density‐dependent flow systems. A similar set up to the Elder problem is studied. It is well known that the numerical simulation results of the standard Elder problem are strongly dependent on spatial discretization. This work shows that for the cases where a solute mass flux boundary condition is employed instead of a specified concentration boundary condition at the solute source, the numerical simulation results do not vary between different convective solution modes (i.e., plume configurations) due to the spatial discretization. Also, the influence of various boundary condition types for nonsource boundaries was studied. It is shown that in addition to other factors such as spatial and temporal discretization, the forms of the solute transport equation such as divergent and convective forms as well as the type of boundary condition employed in the nonsource boundary conditions influence the convective solution mode in coarser meshes. On basis of the numerical experiments performed here, higher sensitivities regarding the numerical solution stability are observed for the Adams‐Bashford/Backward Trapezoidal time integration approach in comparison to the Euler‐Backward/Euler‐Forward time marching approach. The results of this study emphasize the significant consequences of boundary condition choice in the numerical modeling of unstable density‐dependent flow.     

Estimation of Salt Water Upconing Using a Steady‐State Solution for Partial Completion of a Pumped Well

A new steady‐state analytical solution to the two‐dimensional radial‐flow equation was developed for drawdown (head) conditions in an aquifer with constant transmissivity, no‐flow conditions at the top and bottom, constant head conditions at a known radial distance, and a partially completed pumping well. The solution was evaluated for accuracy by comparison to numerical simulations using MODFLOW. The solution was then used to estimate the rise of the salt water‐fresh water interface (upconing) that occurs under a pumping well, and to calculate the critical pumping rate at which the interface becomes unstable, allowing salt water to enter the pumping well. The analysis of salt water‐fresh water interface rise assumed no significant effect on upconing by recharge; this assumption was tested and supported using results from a new steady‐state analytical solution developed for recharge under two‐dimensional radial‐flow conditions. The upconing analysis results were evaluated for accuracy by comparison to those from numerical simulations using SEAWAT for salt water‐fresh water interface positions under mild pumping conditions. The results from the equation were also compared with those of a published numerical sharp‐interface model applied to a case on Cape Cod, Massachusetts. This comparison indicates that estimating the interface rise and maximum allowable pumping rate using the analytical method will likely be less conservative than the maximum allowable pumping rate and maximum stable interface rise from a numerical sharp‐interface model.     

Positive solution of two-dimensional solute transport in heterogeneous aquifers

The transport of contaminants in aquifers is usually represented by a convection-dispersion equation. There are several well-known problems of oscillation and artificial dispersion that affect the numerical solution of this equation. For example, several studies have shown that standard treatment of the cross-dispersion terms always leads to a negative concentration. It is also well known that the numerical solution of the convective term is affected by spurious oscillations or substantial numerical dispersion. These difficulties are especially significant for solute transport in nonuniform flow in heterogeneous aquifers. For the case of coupled reactive-transport models, even small negative concentration values can become amplified through nonlinear reaction source/sink terms and thus result in physically erroneous and unstable results. This paper includes a brief discussion about how nonpositive concentrations arise from numerical solution of the convection and cross-dispersion terms. We demonstrate the effectiveness of directional splitting with one-dimensional flux limiters for the convection term. Also, a new numerical scheme for the dispersion term that preserves positivity is presented. The results of the proposed convection scheme and the solution given by the new method to compute dispersion are compared with standard numerical methods as used in MT3DMS.