Finite difference computation of the dynamic motion of cylindrical shells including the effect of rotatory inertia and transverse shear

The accuracy of finite difference computations for the dynamic motion of cylindrical shells, including transverse shear and rotatory inertia, has been assessed by comparison with Fourier series solutions. The finite difference models were based upon either the differential equations or upon control volume concepts, with the results of the latter being less sensitive to mesh size and in better agreement with the Fourier series results. A frequency analysis of all of the finite difference algorithms and the Fourier series demonstrated that for shells with clamped ends the finite difference spectra had a very considerable gap which closed slowly as the mesh size decreased, with the spectra being most complete for the best algorithm. A new algorithm was based upon these spectra and is shown to yield good results while permitting increases in the computational speed by the factor of mesh size/shell thickness.     

拱结构动力稳定实用判别方法

在总结和借鉴已有动力稳定判别准则的基础上,提出了两种拱结构动力稳定性分析的实用判别方法。方法1通过提取发生最大位移响应时刻的刚度矩阵的特征根符号来判断,方法2通过荷载-位移曲线的斜率变化来判断。通过对不同荷载类型、不同计算条件下拱结构的动力失稳特征的分析对比,指出结构整体刚度矩阵出现负的特征值是结构失稳的必要条件,可依此判断结构动力失稳临界荷载的下限值,位移时程曲线发散、性质发生改变或发生跳跃,荷载-位移曲线出现不规则现象,是拱结构动力失稳的重要判断依据。     

The nonlinear stabilization of a zonal shear flow instability

Abstract

The development of initially small perturbations in a weakly supercritical zonal shear flow on a β-plane is studied. Two different scenarios of evolution are possible. If the supercriticality is sufficiently small, the growth of a perturbation is stopped in the viscous critical layer regime; for this case the evolution equation (corrected by the inclusion of a quintic nonlinearity) is derived. At greater supercriticality the nonlinearity cannot stop the growth of the perturbation in a linear (viscous or unsteady) critical layer regime, and the evolution is more complicated. Transition to a nonlinear critical layer regime leads to a reduction in the growth rate and to a slowing (but not a stopping) of the increase in amplitude, A. These are connected to the formation of a plateau (S=constant) of width L=O(A ^½) in the profile of absolute vorticity, S. Careful analysis reveals that the growth in amplitude ceases only when the whole instability domain (where the slope of unperturbed S-profile is positive) becomes covered again by the plateau.     

The nonlinear development of disturbances in a zonal shear flow

Abstract

A study is made of the nonlinear stability of a weakly supercritical zonal shear flow in the β-plane approximation. The dynamics of initially small disturbances are examined. The main nonlinear effects are associated with the rearrangement of the critical layer. It is shown that as the wave grows in amplitude, linear regimes of the critical layer (viscous and nonstationary) change over to a nonlinear regime while the exponential law of disturbance growth becomes a power-law.     

Seismic evaluation of the shear behavior in reinforced concrete bridge columns including effect of vertical accelerations

The effect of vertical excitation on shear capacity of reinforced concrete columns is important. Field evidences, analytical studies and static or hybrid simulations suggested that excessive tension or tensile strain of the column may lead to shear strength degradation, and therefore vertical excitation can be one of the causes of shear failure. This paper describes an experimental study consisting of shaking table tests on reduced‐scale bridge columns. Results of the tests indicate that tension in the columns has the potential to degrade the shear capacity, which is mainly due to the degradation of the concrete contribution to this capacity. The presented computational results and code evaluations also support this shear strength degradation. The presented dynamic tests contribute to better understanding of the effect of vertical excitation on the shear failure, which is one of the most critical brittle failure mechanisms. Copyright © 2013 John Wiley & Sons, Ltd.     

Impact of the surface temperature and vertical shear of zonal wind on the dynamics of a simple two-layer model of the atmosphere

The paper presents and analyzes, from the point of view of smooth dynamic systems theory, a two-layer baroclinic model of the troposphere in geostrophic approximation. The model describes airflow in β-channel within the tropospheric part of the main Hadley circulation cell. It enables to obtain, after application of the Galerkin method, a fairly simple low-parametric dynamic system describing the phenomena of non-linear interactions, bifurcations and blocking in the atmosphere. This enables to take into consideration such basic factors influencing the atmospheric dynamics like the heat exchange within the surface, orography, vertical variability of zonal wind and hydrostatic stability. Impact of zonal thermal variability of the surface and vertical shear of zonal wind in the troposphere on the orographic bifurcation was investigated and the oscillation character in the dynamic system after Hopf bifurcation of the second kind was analyzed. Additionally, the model dynamics was investigated in conditions including momentum forcing in the upper and lower parts of the troposphere and excluding orographic interaction, as well as in the conditions of thermal interaction between the troposphere and the surface for the vertical shear of zonal wind in both tropospheric layers. Impact of the mean zonal wind in the troposphere on the properties of model dynamics was assessed. It was proved that zonally varied surface temperature and layered mean zonal wind in the atmosphere are the parameters that have basic influence on the model dynamics. They cause numerous bifurcations and strongly influence the periods of oscillations of the model variables. They are often Hopf bifurcations of the second kind during which tropospheric states fairly distant from the ones before the bifurcations are generated. This significantly influences the model predictability.     

Coupled horizontal–vertical stability of bearings under dynamic loading

In this study, the coupled horizontal–vertical behavior of elastomeric bearings subjected to dynamic loading is studied in detail. Under extreme dynamic loading, elastomeric bearings exhibit unstable behavior and an instantaneous loss of horizontal stiffness that is recoverable. Building on an earlier study where the authors developed an analytical model for the horizontal behavior of bearings under dynamic loads, in this study, a new analytical model for the coupled horizontal–vertical behavior of the bearings is developed. The coupled behavior of the bearing is first studied for quasi‐static loading, and later, the behavior of the bearings under dynamic loading is studied. A clear distinction is made between different types of deformation the bearing undergoes in the vertical direction. Based on experimental results, it is observed that the behavior of the bearings under dynamic loading differs markedly from that observed under static loading. A new analytical model is proposed that can account for the coupled horizontal–vertical behavior of the bearings under dynamic loading. The proposed analytical model for predicting the post‐stability vertical behavior of the bearings is verified using experimental results. The model proposed is found to successfully predict the coupled horizontal–vertical behavior of elastomeric bearings. Copyright © 2015 John Wiley & Sons, Ltd.     

考虑抗震墙剪切变形情况下对框架-抗震墙协同工作分析探讨

通过建立框架-抗震墙结构单元模型，采用在楼层处有集中力而在楼层之间有分布力的地震作用模式并考虑抗震墙剪切变形的影响，得到了结构内力和变形之间的公式。根据实例分析可得抗震墙剪切变形对整体结构变形影响很小，因此一般情况下在计算框架-抗震墙结构时忽略剪切变形是合理的；同时发现框架剪切刚度越大，抗震墙剪切变形对框架-抗震墙结构整体变形的影响就越大，反之则越小。     

亚热带山地垂直地带土壤的磁性特征及其环境响应

土壤中磁性矿物的形成转化对环境变化具有指示意义,定量分析土壤磁性对环境因子的响应机制是目前该领域的重要问题.本文综合相关研究及野外实地考察,采集福建南部亚热带地区戴云山垂直地带相同母质的土壤剖面进行环境磁学和漫反射光谱测试分析.结果表明：研究区土壤剖面中磁铁矿和磁赤铁矿主导其磁性变化,当海拔至1320 m以上,土壤中出现次生纤铁矿.当排除地形的影响后,相关磁学参数指示磁畴颗粒在低海拔区域以SP颗粒为主,而较高海拔区域土壤中以粗SD颗粒为主.漫反射光谱结果表明,研究区土壤中赤铁矿和针铁矿对气候梯度变化较为敏感,其中赤铁矿含量随海拔增加显示出降低趋势,并且至海拔1320 m以上赤铁矿消失而主要以针铁矿和纤铁矿为主.对比加热前后针铁矿和赤铁矿特征峰变化,并进行半定量分析认为,当年均降水量超过1900 mm且年均温低于13℃时达到赤铁矿形成的临界值,而针铁矿和纤铁矿则继续呈增加趋势.本研究论证了赤铁矿、针铁矿及纤铁矿对气候梯度具较强的敏感性,可作为研究低纬区域古环境变化的重要指标.

     

亚热带山地垂直地带土壤的磁性特征及其环境响应

土壤中磁性矿物的形成转化对环境变化具有指示意义,定量分析土壤磁性对环境因子的响应机制是目前该领域的重要问题.本文综合相关研究及野外实地考察,采集福建南部亚热带地区戴云山垂直地带相同母质的土壤剖面进行环境磁学和漫反射光谱测试分析.结果表明：研究区土壤剖面中磁铁矿和磁赤铁矿主导其磁性变化,当海拔至1320 m以上,土壤中出现次生纤铁矿.当排除地形的影响后,相关磁学参数指示磁畴颗粒在低海拔区域以SP颗粒为主,而较高海拔区域土壤中以粗SD颗粒为主.漫反射光谱结果表明,研究区土壤中赤铁矿和针铁矿对气候梯度变化较为敏感,其中赤铁矿含量随海拔增加显示出降低趋势,并且至海拔1320 m以上赤铁矿消失而主要以针铁矿和纤铁矿为主.对比加热前后针铁矿和赤铁矿特征峰变化,并进行半定量分析认为,当年均降水量超过1900 mm且年均温低于13℃时达到赤铁矿形成的临界值,而针铁矿和纤铁矿则继续呈增加趋势.本研究论证了赤铁矿、针铁矿及纤铁矿对气候梯度具较强的敏感性,可作为研究低纬区域古环境变化的重要指标.     

Diagnosing vertical motion in the Equatorial Atlantic

Estimating the vertical velocity (w) in the oceanic upper-layers is a key issue for understanding the cold tongue development in the Eastern Equatorial Atlantic. In this methodological paper, we develop an expanded and general formulation of the vertical velocity equation based on the primitive equation (PE) system, in order to gain new insight into the physical processes responsible for the Equatorial and Angola upwellings. This approach is more accurate for describing the real ocean than simpler considerations based on just the wind-driven patterns of surface layer divergence. The w-sources/forcings are derived from the PE w-equation and diagnosed from a realistic ocean simulation of the Equatorial Atlantic. Sources of w are numerous and express the high complexity of terms related to the turbulent momentum flux, to the circulation and to the mass fields, some of them depending explicitly on w and others not. The equatorial upwelling is found to be mainly induced by the (i) the zonal turbulent momentum flux, (ii) the curl of turbulent momentum flux and (iii) the imbalance between the circulation and the pressure fields. The Angola upwelling in the eastern part of the basin is controlled by strong curl of turbulent momentum flux. A strong cross-regulation is evidenced between the w-forcings independent of w and dependent on w, which suggests an equatorial balanced-dynamics. The w-forcing depending on w represents the negative feedback of the ocean to the w-forcing independent of w: in the equatorial band, this adjustment is led by non-linear processes and by vortex stretching outside.     

竖向地裂缝附近的地面运动

针对均匀弹性半空间不同深度(20m,40m,80m)的细裂缝,由下向上分别垂直和斜(30°)入射一脉冲波,计算裂缝附近地面运动的时程反应和传递函数的幅值谱。计算结果与均匀半空间自由场做了对比,以说明竖向地裂缝对地震波传播和附近地面运动的影响。此外,对断裂周边一般结构抗震设计是否要考虑它的影响,提供了一点参考意见。     

竖向断层对场地地面运动的影响

本文采用二维显式有限元结合透射边界的数值方法,考虑均匀弹性半空间内存在着不同宽度及深度的断层,由下向上分别垂直和斜(30°)入射一个脉冲波,研究非发震断层地面运动的一些特点。通过计算断层内外地震地面运动传递函数的幅值谱,并与自由场反应对比,以说明竖向断层对地震波传播和附近地面运动的影响,在此基础上进一步对断层周边一般结构抗震设计是否要考虑断层影响提出了几点建议。     

Large scale vertical eddies in the atmosphere and the energy of the mean zonal flow

Summary The zonal eddy stress across horizontal surfaces due to large scale vertical motions was evaluated for two months from data for the northern hemisphere for a number of levels up to 50 mb. From this information and from the corresponding distributions for each of the two months of the mean zonal winds, the rate of transformation of kinetic energy from eddy to mean zonal form was calculated. The two sets of data gave rather small values for the hemisphere which were of opposite sign.     

The effects of vertical shear and stratification on stationary rossby waves

Abstract

The generation of stationary Rossby waves by sources of potential vorticity in a westerly flow is examined here in the context of a two-layer, quasi-geostrophic, β-plane model. The response in each layer consists of a combination of a barotropic Rossby wave disturbance that extends far downstream of the source, and a baroclinic disturbance which is evanescent or wave-like in character, depending on the shear and degree of stratification. Contributions from each of these modes in each layer are strongly dependent on the basic flows in each layer; the degree of stratification; and the depths of the two layers. The lower layer response is dominated by an evanescent baroclinic mode when the upper layer westerlies are much larger than those in the lower layer. In this case, weak stationary Rossby waves of large wavelengths are confined to the upper layer and the disturbance in the lower layer is confined to the source region.

Increasing the upper layer flow (with the lower layer flow fixed) increases the Rossby wavelength and decreases the amplitude. Decreasing the lower layer flow (with the upper layer flow fixed) decreases the wavelength and increases the amplitude. Stratification increases the contribution from the barotropic wave-like mode and causes the response to be confined to the lower layer.

The finite amplitude response to westerly flow over two sources of potential vorticity is also considered. In this case stationary Rossby waves induced by both sources interact to reinforce or diminish the downstream wave pattern depending on the separation distance of the sources relative to the Rossby wavelength. For fixed separation distance, enhancement of the downstreatm Rossby waves will only occur for a narrow range of flow variables and stratification.     

Microfracture processes in the breakdown zone during dynamic shear rupture inferred from laboratory observation of near-fault high-frequency strong motion

High-frequency velocities are measured during stick-slip motion in the immediate vicinity of a fault in a granite sample to reveal the microscopic process taking place in the breakdown zone defined in the slip-weakening model. It is found that 1) the onset time of the observed strong motion approximately coincides with the local rupture onset time, 2) the observed near-fault high-frequency strong-motion duration is approximately proportional to the local breakdown time, and 3) the power spectra of strong motions exhibit significant amplitudes at frequencies above the value off _max, wheref _max is a cut-off frequency relevant to rupturing the breakdown zone. These observations suggest that the high-frequency motion would be due to the incoherent brittle microfracture whose characteristic scale is much shorter than the breakdown zone size. We present a stochastic fault model to synthesize the near-fault high-frequency velocity waveforms. In the model, a number of small circular subfaults are distributed randomly on the fault and the rupture onset time of an individual subfault is assumed to be random. The main features of the observed velocity waveforms are well explained by this numerical modeling. It is concluded that approximately half of the total energy of high-frequency elastic waves observed at a point is radiated from the propagating breakdown zone. We emphasize the importance of the observation of near-fault high-frequency strong motions for large shallow earthquakes.     

On the stability properties of the nongeostrophic disturbances in a barotropic zonal current

Summary The stability properties of the nongeostrophic disturbances are studied in a barotropic zonal current. The growth rate of the nongeostrophic disturbances is increased and the instability is generally shifted towards shorter wavelengths. Even in the structure of the nongeostrophic disturbances large differences are found as compared to geostrophic disturbances.On leave from Physical Research Laboratory, Ahmedabad, India.     

Assessment of the vertical distribution on seismic ground motion

It is very important for the facilities such as nuclear power plants to infer seismic force loading on the earthquake stability assessment of the building foundation and the surrounding slope. The purpose of this paper was to propose a method to evaluate underground seismic coefficients, taking into account dynamic response along the depth in horizontally multi-layered ground. The dynamic property of the seismic coefficient was analyzed on the basis of earthquake records observed at hard and soft rock sites mostly found in Tertiary deposits and sedimentary ground sites of the Pleistocene and Holocene epoch. The evaluation methods of a vertical distribution on underground seismic coefficients were proposed for a few calculation methods on the classified layered ground. Extended evaluation for underground seismic coefficients was confirmed with respect to some multi-layered ground during strong motion.     

竖向地震动特征研究

本文以国内外数十次地震(ML≥5)的近场自由地表加速度记录为基础数据，进行近场加速度峰值比的统计分析，并着重对1999年台湾集集地震竖向地震动反应谱特征进行研究。统计结果表明，竖向与水平向(V／H)加速度峰值比与震源距相关，随震源距增加，比值降低；竖向反应谱及竖向与水平向加速度反应谱比是周期的函数、并与场地条件及震源距相关。     

风的垂直切变对滞弹性大气中静力适应过程的影响

本文基于描写滞弹性大气静力适应过程的线性方程组,从波动频散关系、气团运动规律和能量转换的角度出发,研究了水平基流及其垂直切变对该模式大气静力适应过程的影响.构造四种水平基流垂直分布模型进行比较,分别为常数型、线性切变型、反气旋切变型和气旋切变型,得到结论：（1）具有重力波性质的波动是滞弹性大气静力适应过程中扰动能量传播的方式,当垂直折射指数大于零时,基本气流及其垂直切变的存在,不仅改变了波动频率的大小,而且改变波动传播的方向;（2）在静力适应过程中气块的运动轨迹呈椭圆形,水平基流及其垂直切变影响椭圆的扁率,同时也影响扰动物理量之间的偏振关系;（3）水平基流的垂直切变是扰动能量和水平基流能量发生转换的媒介,当存在垂直向上的动量输送时,正的垂直风切变对应扰动能量的衰减,水平基流能量的增加,负的垂直风切变对应扰动能量的增加,水平基流能量的衰减;（4）不同的风的垂直切变模型,对静力适应过程的影响不同;对于水平基流呈反气旋切变型和气旋切变型,扰动发展的波动垂直结构为,急流轴上方波动等相位线自下而上向西倾斜,急流轴下方波动等相位线自下而上向东倾斜,反之亦然.