Equilibrium Shapes and Stability of Floating Drops

The problem of the shape and stability of a heavy drop retained on the surface of a less dense liquid by capillary forces is solved numerically and analytically in the plane and three-dimensional variants.     

Degree of Stability of Equilibrium

ABSTRACT

A theoretical study is made of the hysteretic behavior of a portal frame under constant gravity and variable horizontal loading. Special account is taken of the variation of axial forces in the columns, the model simulating the plastic interaction of the overall shearing and bending in tall rectangular frames and battened columns. The assumed elastic-perfectly plastic behavior of columns makes a mathematical formulation feasible, and a detailed examination is given of the cyclic alternate displacement loading with the P-Δ-A effect taken into consideration. This example clarifies characteristic features of repeated loading such as shakedown, incremental collapse, and alternating plasticity under the combined action of bending moment and axial force existing in a frame member.     

受圆柱面约束弹性杆的平衡与稳定性

讨论受圆柱面约束的圆截面弹性杆的平衡与稳定性。以描述截面姿态的欧拉角为变量,建立受约束弹性杆的平衡方程。利用方程的初积分导出约束力、截面内力及挠性线的解析表达式。作为特殊的平衡状态,讨论杆的螺旋线平衡的存在条件。用相平面法分析螺旋线平衡的稳定性,导出解析形式的稳定性条件。     

弹性细杆螺旋线平衡的动态稳定性

本文从动力学观点讨论具有初扭率的非圆截面弹性细杆的螺旋线平衡稳定性。弹性杆平衡的动态稳定性建立在以弧坐标s和时间坐标t为双自变量的离散系统的Lyapunov稳定性概念基础上。对于两端约束状况固定不变的弹性杆,若静态稳定性条件已满足,其与弧坐标对应的本征值可根据端部约束条件确定。则螺旋线平衡的动态稳定性由时间域的本征值判断。在缓慢受扰运动条件下,引入尺度缩小的时间变量T=εt,可将动力学过程视为对平衡状态的摄动。证明在ε^2计算精度范围内,当螺旋线平衡的一次近似静态稳定性条件得到满足时,考虑动力学因素的稳定性条件必也同时满足。     

一种微机电非线性耦合系统奇点稳定性研究

工程中许多微机电系统都采用电容驱动原理，这类结构实际上存在着强烈的静电和机械两个物理场的非线性耦合，因此系统的动态特性比较复杂。本文基于一种扭转微镜系统，通过数值分析方法，研究其非线性动态特性，根据理论分析和数值计算证明该系统在相平面中存在两个奇点，一个是稳定中心，一个是鞍点，且两个奇点位置均随施加电压的变化而逐渐靠近，从而得出系统的静态分叉点；同时分析了有阻尼和无阻尼时电压的变化对相轨道的影响，以及阻尼对吸合电压的影响，吸合电压随阻尼的增大而提高，这些研究结果不仅对扭转微镜的设计和应用提供了理论和方法，而且对用电容驱动的微机电系统的设计亦有参考价值。     

Stability Analysis of Uniform Equilibrium Foam States for EOR Processes

The use of foam for mobility control is a promising mean to improve sweep efficiency in EOR. Experimental studies discovered that foam exhibits three different states (weak foam, intermediate foam, and strong foam). The intermediate-foam state is found to be unstable in the lab whereas the weak- and strong-foam states are stable. The model of Kam (Colloids Surf A Physicochem Eng Asp 318(1–3): 62–77, 2008) is the only mechanistic foam model that can fit a variety of steady-state experimental data including multiple steady states. This model is modified from a previous mechanistic foam model to resolve the intrinsic instability of the strong-foam state. Simple finite-difference simulations have found that an arbitrary perturbation grows for the unstable intermediate foam but diminishes for the strong- and weak-foam states. The issue of the stability of foam states, especially the strong-foam state, is a serious concern in application of foam in EOR. Instabilities may rule out one or more states and consequently have considerable effect on reservoir sweep efficiency and injection pressure. Here, for the first time the stability of the various equilibrium foam states is investigated by an analytical stability-analysis method together with numerical simulations. We demonstrate the instability of most intermediate states, consistent with the laboratory observations. However, our analysis reveals an instability of the strong-foam state. We show that the diffusion, whether introduced artificially by the finite-difference scheme or representing physical dispersion, damps this instability. We obtain good agreement with finite-element simulations with and without additional diffusion. We also prove that all states are unconditionally stable for a local-equilibrium-foam model.     

A Dynamic Model of Capillary Hysteresis in Immiscible Fluid Displacement

The capillary hysteresis in a dynamic and quasi-static two-fluid flow in a porous medium is discussed. Thermodynamic background is presented. It is shown that physically acceptable constitutive relations satisfying the thermodynamic conditions can be constructed in terms of Preisach hysteresis operators.     

The Stability of the Equilibrium of Planar Hamiltonian and Reversible Systems

In this paper, we study the stability of the equilibrium of planar systems

介电弹性球膜的动力稳定性分析

介电弹性体结构具有卓越的力电性能,然而由于其大变形特性,在动态工作模式下极易出现各类失效问题,这极大阻碍了其工程应用.论文研究与力电失稳行为直接相关的理想介电弹性球膜动力稳定性问题.首先据虚功原理建立电压及压力共同作用下关于伸长比的动力学方程,系统自由能由弹性应变能与静电能组成,而前者基于Mooney-Rivlin模型表出.通过系统首次积分解析给出稳态响应峰值与阶跃电压/阶跃压力的关系曲线,其与静态平衡曲线的交点决定了临界电压/临界压力.研究表明:给定任意电压,材料参数存在某阈值,当超过该值后系统始终保持稳定;对于任意非零压力值,存在类似材料参数阈值;而当压力恰为零时,则始终存在临界电压值,超过该值则系统动力不稳定.     

非圆截面弹性细杆的螺旋线平衡及稳定性

本文研究端部受力和力矩作用，且存在初曲率和初扭率的非圆截面弹性细杆的螺旋线平衡及其稳定性。描述弹性细杆平衡状态的Kirchhoff方程存在与杆的螺旋线平衡状态相对应的特解。直杆和圆环杆为螺旋线状态的两种特例。文中分析了螺旋线的几何特性与作用力和力矩之间的相互关系，并导出螺旋线平衡的一次近似解析形式稳定性判据。分析表明，松弛状态下弹性杆可处于螺旋线状态，直杆只有在轴向压力的作用下才能保持螺旋线平衡。无初曲率和初扭率弹性杆的螺旋线平衡稳定性必要条件是杆截面绕副法线轴的抗弯刚度大于或等于绕法线轴的抗弯刚度。此条件也适用于带初扭率的圆环杆及更普遍情形。无初曲率和初扭率的圆截面杆的螺旋线平衡恒稳定。     

Estimation of Dynamic Relative Permeability and Capillary Pressure from Countercurrent Imbibition Experiments

Direct laboratory measurements of in situ water-phase saturation history are used to estimate relative permeability and capillary pressure functions. The magnitude of so-called nonequilibrium effects during spontaneous imbibition is quantified and, if significant, these effects are incorporated within the estimation technique. The primary constraint employed is that curves must increase or decrease monotonically; otherwise, no predetermined functionality is assumed. The technique is demonstrated using water saturation profile histories obtained for diatomite (a low-permeability and high-porosity rock). Results indicate that nonequilibrium effects detected at laboratory scale in low-permeability rocks influence the estimation of unsteady-state relative permeability and capillary pressure.     

非圆截面弹性细杆的平衡稳定性与分岔

本文研究存在初始曲率或挠率的非圆截面弹性细杆的平衡及稳定性问题,在两端受力矩单儿作用的条件下,杆的平衡微分方程可转换为用欧拉角表述的一阶自治系统,并有可能利用相平面的奇点理论分析弹性细杆平衡状态的稳定性,文中对杆截面的对称性,以及杆的初始曲率和挠率对平衡状态性的影响进行了定性分析,导出了解析形式的稳定性判据,揭示了杆平衡状态的列态分岔现象。     

Nonlinear Dynamic Stability of Normal and Arthritic Greyhounds

In this paper the dynamic stability of greyhound gait was analyzed within the framework of nonlinear dynamics theory. A video based motion analysis system was utilized to obtain the kinematic data of the hindlimb joints of greyhounds at trot. Phase plane portraits and first return maps for the coxofemoral, femorotibial, and the tarsal joints were calculated from averaged kinematic data for each dog. The analysis was based on the assumption that the steady state dog locomotion could be represented as a nonlinear periodic system. Using the Floquet theory, the dynamic stability of gait was quantified by computing the characteristic multipliers from experimental data. A stability index based on multipliers was used for comparison between normal and arthritic dogs. Phase plane portraits and first return maps of the dogs with transient synovitis were compared with the averaged portraits of the normal dogs. It was observed that the coxofemoral angle exhibited the maximum difference while the femorotibial and the tarsal joints showed little or no difference from those of the normals. Comparison of the Floquet multipliers indicated that the dogs with synovitis had a less stable gait than that of the normal dogs.     

A Numerical Study of Two-Phase Flow Models with Dynamic Capillary Pressure and Hysteresis

Saturation overshoot and pressure overshoot are studied by incorporating dynamic capillary pressure, capillary pressure hysteresis and hysteretic dynamic coefficient with a traditional fractional flow equation in one-dimensional space. Using the method of lines, the discretizations are constructed by applying the Castillo–Grone’s mimetic operators in the space direction and a semi-implicit integrator in the time direction. Convergence tests and conservation properties of the schemes are presented. Computed profiles capture both the saturation overshoot and pressure overshoot phenomena. Comparisons between numerical results and experiments illustrate the effectiveness and different features of the models.     

Technical Stability of Dynamic States of Controlled Elastic Aircraft

Sufficient conditions are obtained for the technical stability of the controlled longitudinal vertical motion of elongated elastic aircraft. These aircraft are considered to have a variable cross-section and to be subject to significant transverse deformations and vibrations. The technical-stability criteria formulated depend on a small positive parameter. This parameter is a function of key parameters of the controlled dynamic process such as the increment in the transverse load due to the curvature of the system axis and the aerodynamic forces     

Symmetry-Breaking Bifurcations of Charged Drops

It has been observed experimentally that an electrically charged spherical drop of a conducting fluid becomes nonspherical (in fact, a spheroid) when a dimensionless number X inversely proportional to the surface tension coefficient is larger than some critical value (i.e., when <_c). In this paper we prove that bifurcation branches of nonspherical shapes originate from each of a sequence of surface-tension coefficients ), where ₂=_c. We further prove that the spherical drop is stable for any >₂, that is, the solution to the system of fluid equations coupled with the equation for the electrostatic potential created by the charged drop converges to the spherical solution as t provided the initial drop is nearly spherical. We finally show that the part of the bifurcation branch at =₂ which gives rise to oblate spheroids is linearly stable, whereas the part of the branch corresponding to prolate spheroids is linearly unstable.     

非均质土层下基桩的动力稳定性研究

本文根据桩在轴向谐振力作用下，探讨了非均质层下基桩的动力稳定性问题，分析了各种地基土横向抗力系数K以及桩的几何特征，激振频率，桩土阻尼对桩动力稳定性的影响，结果表明，随地基土层的不同，基桩的动力不稳定区域将发生不同的变化，随桩径，桩长的增大，基桩的动力不稳定区域将逐渐减小，表明地基土的横向抗力对桩的动力稳定性起加强作用，桩土阻尼对基桩的动力稳定性影响较大，得出了一些有价值的结论，可为工程设计提供参考依据。     

具有封严蓖齿转子系统的动力稳定性分析

封严蓖齿的气弹力对转子系统的稳定性起重要作用，本文建立了具有封严蓖齿的转子系统动力稳定性的分析方法，该方法利用传递矩阵法建立系统的主导方程，将封严蓖齿的气弹力以等效刚度及等效阻尼系数的方式引入转子系统的主导方程，用数值积分法解主导方程，求得系统的动力特性，根据扰动解判断系统的稳定性。本文所建立的分析软件，也可计算转子系统的不平衡响应、临界转速、突加不平衡响应等。文中对一模型转子进行了算例分析。     

自由正交异性矩形厚板的动态稳定

对在一条边上作用着均匀分布的非保守跟随力的四边自由正交异性矩形厚板的动态稳定进行了分析，通过把位移和剪力展成重傅立叶级数解，把微分方程简化成了代数方程。计算表明厚度的微小变化会引起颤振载荷明显的减小。这个明显减小是因为存在剪切变形。