Buckling of a sandwich symmetrical circular plate with varying mechanical properties of the core

This paper is devoted to analytical and numerical studies of global buckling of a sandwich circular plate. The mechanical properties of the plate core vary along its thickness, remaining constant in the facings. The middle surface of the plate is its symmetrical plane. The mathematical model of the plate is presented. The field of displacements is formulated using the proposed nonlinear hypothesis that generalizes the classical hypotheses. The equations of equilibrium are formulated based on the principle of stationary total potential energy. The proposed mathematical model of the displacements considers the shear effect. The numerical model of the plate is also formulated with a view to verify the analytical one. Numerical calculations are carried out for the chosen family of plates. The values of the critical load obtained by the analytical and numerical methods are compared. The effects of the material properties of the core and the change of the plate radius on the critical load intensity are presented.     

充液挠性航天器俯仰运动 1:1:1 内共振动力学分析

采用已推导的俯仰运动矩形贮箱受控刚-液-弹耦合系统在外力矩作用下的耦合动力 学模型，在刚体上加入控制项，详细分析了系统固有频率的精确解与近似解. 应用多尺 度法对耦合系统1:1:1内共振进行解析分析，与数值解比较验证解析解的正确性. 通过近 似解析分析得到刚-液-弹之间的耦合作用机理：1) 液深影响整个系统的软硬特性，当液体发 生软硬特性转化时，处于液体原多值频率区域的刚体和弹性体幅频曲线分支峰值会减弱，且 具有相同的特性转化趋势；处于液体新多值频率区域的刚体和弹性体幅频曲线分支峰值会增 强，且具有相反的特性转化趋势. 2) 刚体和弹性体幅频曲线的峰值均在以受控刚体和弹性体 为主的耦合系统固有频率处，以液体为主固有频率激励，刚体和弹性体振幅较小.     

Experimental Study and Fractal Analysis of Heterogeneity in Naturally Fractured Rocks

Capillary pressure curves of six low porosity and low permeability core samples from The Geysers geothermal field were measured using the mercury-intrusion approach to characterize the heterogeneity of rock. One high permeability Berea sandstone core sample was analyzed similarly, for comparison. The maximum pressure of mercury intruded into the rock was about 200 MPa to reach the extremely small pores. Experimental data showed that the capillary pressure curves of The Geysers rock are very different from that of the Berea sandstone. It was found that the frequently used capillary pressure models could not be used to represent the data from The Geysers rock samples. This might be because of the fractures in the rock. To this end, a fractal technique was proposed to model the features of the capillary pressure curves and to characterize the difference in heterogeneity between The Geysers rock and Berea sandstone. The results demonstrated that the rock from The Geysers geothermal field was fractal over a scaling range of about five orders of magnitude. The values of the fractal dimension of all the core samples (six from The Geysers and one Berea sandstone) calculated using the proposed approach were in the range from 2 to 3. The results showed that The Geysers rock with a high density of fractures had a greater fractal dimension than Berea sandstone which is almost without fractures. This shows that The Geysers rock has greater heterogeneity, as expected.     

基于局部DQ-RBF不可压缩N-S方程的数值求解

以RBF作为DQ方法的基函数,将迎风机制引入DQ-RBF中,建立了二维不可压缩黏性N-S方程数值求解模型,采用Levenberg-Marquardt算法求解非线性方程组.求解时分析了形状参数对求解精度的影响,改进了边界速度的处理方法.对平板Couette流及有限宽台阶绕流流动问题进行了数值求解.比较了本文方法和FLUE...     

电流变学研究进展

电流变学是近年来新兴的一门学科。本文从电流变学的发展概况，电流变流体，电流变效应的机理和电流变体的应用等４个方面对电流变学的概貌做了阐述，力求能准确地反映国际上电流变学的发展现状。     

考虑油膜力作用的船舶主推进系统冲击研究

舰船推进轴系是舰船动力装置的重要组成部分,它的稳定性是舰船生命力的基本保证.本文以舰船主推进轴系为研究对象,考虑了非线性油膜力的作用,在推进轴的非线性油膜力模型中,考虑了油膜涡动效应和挤压效应以及多个轴承油膜力的耦合影响,并考虑了轴承结构本身的刚度.文中采用弹性体动力学方法对推进轴建模,考虑了在外冲击作用下转速和轴承油膜力对于转轴冲击响应的影响,考虑横向运动与转动耦合作用,导出以非线性偏微分方程描述的舰船主推进轴的动力学方程,并用经典理论对其进行离散,最后采用龙格-库塔法进行数值仿真.实例分析指出转速对于转轴冲击响应的影响不可忽略.     

Influence of diffusion and kinetic characteristics on the combustion of a carbon particle

The spherically symmetric steady-state problem of heterogeneous combustion for a carbon particle is discussed. The exact solution of this problem is obtained. The dimensionless mass flux through the particle surface is graphically represented as a function of oxygen concentration in the external domain. The rate ratio for the diffusion process and the kinetic process is introduced as a dimensionless characteristic of the combustion process. The dimensionless mass fluxes through the particle surface are graphically represented as functions of external constitutive parameters. The resulting solution is approximated. The diffusion and kinetic modes of combustion are considered as limiting cases.     

西气东输管道工程中卫黄河穿越隧道场地工程地质条件评价

西气东输工程中卫黄河穿越隧道长1197.77m,高4.3m,宽5.6m。隧道入口高于黄河水位28m,出口高于黄河水位45m。隧道顶板高程为1130m。位于黄河水下100m。隧道场地围岩为寒武系磨盘井组灰绿色、银灰色浅变质中厚层细粒长石石英砂岩、千枚状板岩、绢云母化千枚岩。围岩为弱风化Ⅲ～Ⅳ类岩石。透水率为4～67Lu,纵波波速为500～3300m.s^-1。BQ为300～400。变形模量为6.11～9.22GPa。泊松比（μ）0.14～0.24。内摩擦角（ψ）为42.1°～44.7°。地下水为基岩裂隙水。含水层为寒武系浅变质岩,受大气降水渗入补给,单井涌水量为1.0～50m³.d^-1。隧道轴线穿越区岩体较完整—较破碎,未有全新活动断层。隧道位置选择和开挖深度设计是可行的。施工和长期运营是安全的。     

水平弹性支撑圆拱的动力特性研究

用柔度法建立了水平弹性支撑拱结构的自由振动方程,考虑了拱脚处集中质量的附加惯性力. 计算分析了水平弹性支撑对两铰圆拱固有特性的影响,水平弹性支撑会使拱结构的自振频率减小,当拱结构的矢跨比为0.1 左右时影响最为显著,同时还会改变拱结构的振动形态,尤其在高阶振型中将完全按照梁的特点振动.分析了圆弧梁与两铰圆拱的振动内力特点,提出了柔度系数的概念,经过计算得到了水平弹性支撑拱转化为两铰圆拱和圆弧梁的临界柔度系数以及对应的临界刚度系数.     

Darcy-Forchheimer flow by rotating disk with partial slip

The viscous dissipation and heat transfer in the Darcy-Forchheimer flow by a rotating disk are examined. The partial slip conditions are invoked. The optimal series solutions are computed via the optimal homotopic analysis method(OHAM). The thermophoresis and Brownian motions are studied. The Darcy-Forchheimer relation characterizes the porous space. The roles of influential variables on the physical quantities are graphically examined. A reduction in the local Nusselt number is observed through thermophoresis and thermal slip parameters. The local Sherwood number depicts an increasing trend for the higher Brownian motion and concentration slip parameters.     

Three-dimensional flow of Oldroyd-B fluid over surface with convective boundary conditions

The present study addresses the three-dimensional flow of an Oldroyd-B fluid over a stretching surface with convective boundary conditions. The problem formulation is presented using the conservation laws of mass, momentum, and energy. The solutions to the dimensionless problems are computed. The convergence of series solutions by the homotopy analysis method (HAM) is discussed graphically and numerically. The graphs are plotted for various parameters of the temperature profile. The series solutions are verified by providing a comparison in a limiting case. The numerical values of the local Nusselt number are analyzed.     

大学物理《力学》中的自由度分析

对《力学》中的物体自由度进行多方面分析,以深化教学、提高学生正 确分析物理问题的能力.使用实际教学分析的研究方法,在《力学》范围内讨论自由度与坐标、 自由与约束的关系并得以下结论: (1) 同一物体的自由度随其所在的``空间'不同而不同, 不因坐标系的选取不同而 异, 在同类参考系中不因参考系的动静而有别;(2)自由度遵循叠加原理. 讨论了质点系的总自由度及相关计算问题,并指出研究《力学》中自由度的意义.     

偶应力理论下拉力型锚固体的受力特性

锚固体的受力特征及其影响因素是锚固体设计的重要依据,直接影响锚固效果。传统的经典弹性理论没有考虑应变梯度的影响。偶应力理论引进弯曲曲率,考虑了弯曲效应对介质变形特性的影响。基于偶应力理论,建立了平面应变问题的有限元计算模型,研究锚固体锚固段界面上的剪应力分布、锚固体轴力分布、偶应力的尺度效应以及弹性模量和围压对锚固力的影响,并将偶应力理论的计算结果和经典弹性理论的计算结果进行了比较。结果表明,在偶应力理论下,锚固体锚固段界面的剪应力有所减小,特别是峰值处的剪应力减小明显;岩土的弹性模量越大,锚固界面局部剪应力越大;锚固力随着围压的增大而增大,偶应力尺度效应明显。     

非线性粘弹性板的失稳条件

研究了给定面内周期激励作用下简支各向同性均匀粘弹性板平衡失稀问题,板的材料特性由Leaderman非线性本构关系描述,将板的动力学方程进行（Galerkin截断得到简化数学模型为弱非线性系统,采用平均法得到系统的平均化方程,对平均化方程进行稳定性分析得到了板平衡失稳的解析条件,对原系统用数值仿真进行研究,数值结果表明,随着激励幅值的增加或粘弹性材料系数的减少,系统平衡点推失稳,激励幅值和粘弹性材料系数的临界值均与解析结果接近。     

Slip and induced magnetic field effects on peristaltic transport of Johnson-Segalman fluid

The peristaltic flow of a Johnson-Segalman fluid in a planar channel is investigated in an induced magnetic field with the slip condition.The symmetric nature of the flow in a channel is utilized.The velocity slip condition in terms of shear stresses is considered.The mathematical formulation is presented,and the equations are solved under long wavelength and low Reynolds number approximations.The perturbation solutions are established for the pressure,the axial velocity,the micro-rotation component,the stream function,the magnetic-force function,the axial induced magnetic field,and the current distribution across the channel.The solution expressions for small Weissenberg numbers are derived.The flow quantities of interest are sketched and analyzed.     

Dynamics of Sutterby fluid flow due to a spinning stretching disk with non-Fourier/Fick heat and mass flux models

The magnetohydrodynamic Sutterby fluid flow instigated by a spinning stretchable disk is modeled in this study. The Stefan blowing and heat and mass flux aspects are incorporated in the thermal phenomenon. The conventional models for heat and mass flux, i.e., Fourier and Fick models, are modified using the Cattaneo-Christov(CC)model for the more accurate modeling of the process. The boundary layer equations that govern this problem are solved using the apt similarity variables. The subsequent system of equations is tackled by the Runge-Kutta-Fehlberg(RKF) scheme. The graphical visualizations of the results are discussed with the physical significance. The rates of mass and heat transmission are evaluated for the augmentation in the pertinent parameters. The Stefan blowing leads to more species diffusion which in turn increases the concentration field of the fluid. The external magnetism is observed to decrease the velocity field. Also,more thermal relaxation leads to a lower thermal field which is due to the increased time required to transfer the heat among fluid particles. The heat transport is enhanced by the stretching of the rotating disk.     

电磁对偶有限元及在波导计算中的应用

力学中的Hamilton体系采用对偶变量描述问题。电磁场采用电场和磁场两类变量描述问题。将力学中的Hamilton体系引入到电磁场问题中，电场变量和磁场变量构成对偶变量，把频域电磁场的基本方程导向对偶方程形式，建立电磁场有限元所需的对偶变量变分原理，由此推导出电磁对偶有限元。将电磁对偶有限元应用于电磁波导计算中，可确定电磁波导的传播常数。文中给出了用电磁对偶有限元方法，计算矩形波导不同模式对应的传播常数的数值计算结果。     

飞行Ma12条件超燃发动机流场及燃烧特征分析

为提升针对高马赫数发动机的模拟能力,对计算方法进行了可压缩性修正,并针对飞行Ma12条件下超燃冲压发动机进行了多状态三维数值模拟,分析了发动机内波系、参数以及燃烧性能特征.研究结果表明:(1)修正后的方法计算所得激波位置及强度与试验值吻合,在激波串模拟、高马赫数发动机模拟上均展现了更优的能力.(2)发动机内形成激波与反...     

考虑不确定性因素的有限元屈曲模型验证

研究了考虑不确定性因素的有限元屈曲模型验证和确认方法,提出了不确定参数选择的相关性和敏度分析方法以及基于面积度量的模型评估方法.针对化铣整体壁板,开展了有限元屈曲模型验证研究,首先利用8件试验件,获得了壁板屈曲载荷的试验值,然后依据试验加载情况,建立了考虑试验台的壁板有限元模型,最后利用面积度量方法对有限元模型进行了验证和确认.本文的模型验证和确认方法可为其他工程结构开展类似的工作提供借鉴.