Electrophoresis of a 2-particle cluster near a plane boundaryElectrophorèse de deux particules en présence d'une paroi plane

Particle–boundary and particle–particle interactions in Electrophoresis are examined by considering a 2-particle cluster near a plane boundary. The advocated treatment holds for two insulating particles of arbitrary shapes and zeta potential functions and resorts to 13 boundary-integral equations. Preliminary results reveal that, depending upon the addressed velocity nature (translational or angular), wall–particle may be stronger or weaker than particle–particle interactions. To cite this article: A. Sellier, C. R. Mecanique 331 (2003).     

Impact of singularity of Navier-Stokes equation upon atmospheric motion equations

Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navier-Stokes equation are summarized. On the basis of this, by taking the basic system of equations of atmospheric motion via Boussinesq approximation as example to explain in detail that the instability about some simplified models of the basic system of equations for atmospheric motion is caused by the instability of Navier-Stokes equation, thereby, a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations.     

大型沉井结构施工力学模型的研究

大型沉井结构是当今应用较广的基础工程，由于沉井结构的规模大，工区土层复杂，存在有许多不确定性因素。使得施工过程的力学模型比较难确定。迄今尚缺乏可供借鉴的理论研究。由于施工的关键是保证沉井的均匀下沉，控制终沉和防止突沉，为此，建立合适的施工力学模型以预测下沉量和开挖量之间的关系就十分必要，考虑到混凝土沉井在土体中下沉时，其本身的变形很小，可以忽略其影响，本文从多自由度刚体运动的角度，建立沉井下沉过程的动态力学模型。为验证所建模型的正确性，本文对一实际工程进行了数值仿真计算。并将计算结果与实测结果进行了对比。结果表明，所建立的力学模型能较好地反映沉井下沉的工程实际，因而可以应用该模型对沉井下沉进行预测分析。从而有助于指导沉井的实际施工。     

Dynamics of Slider-Crank Mechanisms with Flexible Supports and Non-Ideal Forcing

Transient and steady state dynamic response of a class of slider-crank mechanisms is investigated. Specifically, the class of mechanisms examined involves rigid members but compliant supporting bearings. Moreover, the mechanisms are subjected to non-ideal forcing. Namely, both the driving and the resisting loads are expressed as a function of the angular coordinate describing the crank rotation. First, an appropriate set of equations of motion is derived by applying Lagrange's equations. These equations are strongly nonlinear due to the large rigid body rotation of the crank and the connecting rod, as well as due to the nonlinearities associated with the bearing action and the form of the driving and the resisting loads. Consequently, the dynamics of the resulting dynamical system is examined by solving the equations of motion numerically. More specifically, transient response is captured by direct integration, while determination of complete branches of steady state response is achieved by applying appropriate numerical methodologies. Initially, mechanisms whose crankshaft is supported by bearings with rolling elements and linear stiffness characteristics are examined. Then, numerical results are presented for rolling element bearings with nonlinear stiffness characteristics. Finally, the study is focused on mechanisms supported by hydrodynamic bearings. In all cases, the attention is focused on investigating the influence of the system parameters on its dynamics. Moreover, models with constant crank angular velocity are first analysed, since they provide valuable insight into some aspects of the system dynamics. Eventually, the emphasis is shifted to the general case of non-ideal forcing, originating from the dependence of the driving and the resisting moments on the crankshaft motion.     

两层流体中二维非线性界面波的演化方程

给出两水平固壁间两层不可压缩理想流体中二维非线性界面波的演化方程，首先建立出这个演化方程，并由此方程在一定条件下得到二维非线性界面长波满足的近似方程，然后从理论上证明这个长波近似方程包含了以下两个描述一阶界面升高的著名的浅水孤立波方程；Korteweg-de Vries(KdV)方程和Kadomtsev-Petvishvili(KP)方程，所得特殊结果与前人的一致，表明所建立的二维非线性界面波演化方程正确且具有一般性。     

原位TiC颗粒增强灰铸铁复合材料的组织及其摩擦磨损性能

采用原位反应铸造法制备了TiC颗粒增强灰铸铁复合材料,并考察了复合材料的组织、力学性能和摩擦磨损性能．结果表明：随着合金熔体中Ti含量增加,复合材料中TiC颗粒的数量增加,尺寸减小,而石墨的数量降低,且其形态由片状转化为点状;含有大量TiC颗粒及少量点状石墨的复合材料的力学性能和耐磨性优良,即使在较高载荷下,复合材料中的TiC颗粒和点状石墨仍具有协同减摩抗磨作用,从而使得复合材料的摩擦磨损性能优于普通灰铸铁．     

The Response of an Oscillator Moving along a Parabola to an External Excitation

The behavior of a mass point moving along a parabola under theeffect of an external periodic excitation in resonance with the naturalfrequency of the oscillator is studied. The asymptotic perturbationmethod based on temporal rescaling and balancing of the harmonic termswith a simple iteration is used in order to determine the nonlinearmodulation equations for the amplitude and the phase of the oscillation.External force-response curves are shown and moreover jump phenomena arealso observed. In certain cases a second low frequency appears inaddition to the forcing frequency and then stable two-periodquasi-periodic motions are present with amplitudes depending on theinitial conditions. The value of the low frequency depends on theamplitude of the external excitation. A higher order perturbationanalysis is developed and the validity of the method is highlighted bycomparing the leading order and the higher order approximate analyticsolutions to numerical results.     

大型桩基础动力特性及地震反应分析

本文针对大型桩基础的地震反应问题,以上海“东方明珠”广播电视塔桩基础为工程背景,采用梁单元模拟桩的运动,用8节点块体单元对土体进行离散,通过凝聚法消去桩（梁）节点的转动自由度,建立了“东方明珠”电视塔中央部位桩基础的三维有限元分析模型,对桩基础的动力特性进行了计算与分析。在此基础上,以文献[1]根据地震危险性分析和土层反应分析后获得的桩尖处加速度时程作为输入,对桩基础的动力反应进行时程分析,探讨了桩－土动力相互作用和上部结构等因素对地震地面运动和桩承台反应的影响,得到了一些有应用价值的结果。     

On stability of stationary motion of a nonconservative nonholonomic rheonomic system

One considers, in this paper, the motion of a mechanical system in a nonstationary field of potential and positional forces, subject to the action of rheonomic holonomic and nonholonomic linear homogeneous constraints. Assuming that differential equations of motion of the system considered satisfy the conditions for the existence of Painlevé's integral of energy, formulated in [Painlevé, P., 1897. Leçons sur l'intégration des équations de la Mécanique, Paris] and [Appell, P., 1911. Traité de mécanique rationnelle, T. II, Dynamique des systémes – Mécanique analitique, Gauthier-Villars, Paris] and generalized in [Čović, V., Vesković, M., 2004. On stability of motion of a rheonomic system in the field of potential and positional forces, BAMM-1720/2004, No-2233, 93–100] and [Čović, V., Vesković, M., 2005. Hagedorn's theorem in some special cases of rheonomic systems. Mechanics Research Communications 32 (3), 265–280], the original mechanical system is substituted by an equivalent one whose Lagrangian function, nontransformed with respect to nonholonomic constraints, does not depend on time explicitly. Using the properties of the equivalent system, which, in contrast to the original one, moves in a stationary field of potential forces and in a nonstationary field of gyroscopic forces, the definition of cyclic coordinates is generalized, as well as sufficient conditions for the existence of (cyclic) first integrals, corresponding to coordinates mentioned and linear in velocities are established. Further, the conditions for the existence of steady motion of the system considered are found. In the case of existence of such a motion of the system, the Theorem of Routh's type on stability of that motion, based on the minimum of reduced potential for which it is shown that, in contrast to known cases (see, for example, [Gantmacher, F., 1975. Lectures in Analytical Mechanics. Mir Publisher, Moscow; Neimark, J., Fufaev, N., 1972. Dynamics of Nonholonomic Systems. Amer. Math. Soc., Providence, RI; Pars, L., 1962. An Introduction to Calculus of Variations. Heinemann, London; Karapetyan, A., Rumyantsev, V., 1983. Stability of conservative and dissipative systems. In: Itogi Nauki I Tekhniki: Obschaya Mekh., vol. 6, VINITI, Moscow, pp. 3–128 (in Russian)]), it includes the influence of the positional forces field, is formulated. Thus, the Routh's Theorem on stability of steady motion of a conservative mechanical system is extended to the case of a nonconservative system.     

Dynamics of a Fluid in a Rotating Horizontal Cylinder

The behavior of a low-viscosity fluid in a rotating horizontal circular cylinder is investigated experimentally. The stability of the centrifuged layer, the motion of the fluid with respect to the cavity, the excitation of inertial waves on the fluid surface, and the effect of the waves on the stability and flow structure are studied over a wide region of relative occupancy of the cavity. The results are analyzed from the viewpoint of vibrational mechanics in which the motion is generated by the oscillations of the fluid with respect to the cavity and the gravity force plays the role of the force oscillating in the cavity reference system.