Motion Planning for a Wheeled Robot (Kinematic Approximation)

The motion-planning problem for a wheeled robot is solved in kinematic approximation. The solution is given for robots with one and two steering wheels. The results of solving the problem for a specific system are compared with the results obtained by other authors__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 91–102, February 2005.     

Nonlinear rheological behavior of a concentrated spherical silica suspension

Linear and nonlinear viscoelastic properties were examined for a 50 wt% suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G^* obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus G(t) was obtained for small step strain (0.2) while the nonlinear relaxation modulus G(t, ) characterizing strong stress damping behavior was obtained for large (>0.2). G(t, ) obeyed the time-strain separability at long time scales, and the damping function h() (–G(t, )/G(t)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity () for small shear rates (< ^–1; = linear viscoelastic relaxation time) and shear-thickening for larger (>^–1). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, + (t, ) and _– (t, ). In the shear-thinning regime, the and dependence of ₊(t,) and _–(t,) as well as the dependence of () were well described by a BKZ-type constitutive equation using the G(t) and h() data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shearthinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.Dedicated to the memory of Prof. Dale S. Parson     

Stability of Navier-Stokes equation (I)

In this paper we give an example of non-uniqueness of local solution for some kinds of boundary value problem of Navier-Stokes equation.     

Stability of the Sliding Mode in Nonstationary Automatic-Control Systems with Variable Structure

The paper addresses the stability of the sliding mode in nonstationary automatic-control systems of variable structure. The parameters of dynamic states are assumed to vary arbitrarily and continuously within a given bounded domain. The existence and stability conditions for the sliding mode on the switching hyperplane are established. They define nonstationary sets that contain phase velocity vectors directed away from the sliding hyperplane. The sets do not have common points with the switching hyperplane, except for the origin, for the known extreme values of the discontinuous coefficients of logical controls. This is the essence of the necessary and sufficient conditions for the stable sliding mode of the automatic-control system. The general results are used to analyze the stability conditions for the sliding mode in a nonstationary automatic-control system with a variable structure of the third order     

三维离散网格中的弹性波动

本文采用形式解法研究三维有限元离散模型中波动的传播规律。文中由波动方程得到它的特征方程，进而给出了三维离散网格中波的频散关系，分析了三维网格中平面波、非匀匀波、寄生振荡及其它可能存在的运动形式的基本特点；详细讨论了平面波的频散、截止频率及偏振漂移等重要的不同于连续介质中的波动传播性质的特点，提示了其中不同于低维网格中 波动的现象。     

紊动流场中悬浮颗粒分布的随机理论

通过分析固体颗粒在紊动流场中的随机运动,建立了二维流场中垂直于时均流动的方向上颗粒随机位移的概率密度分布函数所满足的方程。由该方程解出的分布函数在一定条件下即相当于颗粒浓度分布函数。运用这一方法研究了[1]、[2]中报道的壁面附近颗粒浓度降低的现象。     

GENERALIZATION OF STEINER FORMULAFOR THE HOMOTHETIC MOTIONS ONTHE PLANAR KINEMATICS

The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.     

Capillary Imbibition and Pore Characterisation in Cement Pastes

The kinetics of capillary imbibition in ordinary Portland cement pastes has been studied experimentally and theoretically. Nuclear magnetic resonance stray field imaging (STRAFI) has been used to record water concentration profiles for various ingress times. The profiles follow a t law and thus a master curve can be formed using the Boltzmann transformation. The distribution of pore sizes within the sample as measured by NMR cryoporometry shows a prominent peak at 100Å. A computer model of the pore structure was developed consisting of a lattice of interconnecting pores with a size distribution consistent with the cryoporometry results. The Hagen–Poiseuille law was used to describe the kinetics of the water in this pore structure. The best agreement between the computer simulations and the experimental master curve was obtained by using a narrower range of pore sizes than indicated by the cryoporometry results.     

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.     

Stability of a shallow arch with one end moving at constant speed

In this paper we consider a shallow arch with rise parameter h, free of lateral loading, but subject to prescribed end motion e with constant speed c. Attention is focused on finding out whether dynamic snap-through will occur. Quasi-static analysis is first performed to identify all equilibrium configurations and their stability properties when e and h are specified. If the arch is stretched quasi-statically, it will be straightened up and no snap-through will occur. However, when the speed c is not negligible it is possible for the arch to snap to the other side dynamically. Careful analysis shows that the only possible situation when dynamic snap-through may occur is and . In this case, to prevent dynamic snap-through to occur the end speed c must not exceed a critical speed, which is a function of e and h. The minimum critical stretching speed is found to be 25.9 for all possible combinations of e and h.