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Relative Velocities (relative + velocity)
Selected AbstractsDynamics of unsaturated soils using various finite element formulationsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2009Nadarajah Ravichandran Abstract Unsaturated soils are three-phase porous media consisting of a solid skeleton, pore liquid, and pore gas. The coupled mathematical equations representing the dynamics of unsaturated soils can be derived based on the theory of mixtures. Solution of these fully coupled governing equations for unsaturated soils requires tremendous computational resources because three individual phases and interactions between them have to be taken into account. The fully coupled equations governing the dynamics of unsaturated soils are first presented and then two finite element formulations of the governing equations are presented and implemented within a finite element framework. The finite element implementation of all the terms in the governing equations results in the complete formulation and is solved for the first time in this paper. A computationally efficient reduced formulation is obtained by neglecting the relative accelerations and velocities of liquid and gas in the governing equations to investigate the effects of fluid flow in the overall behavior. These two formulations are used to simulate the behavior of an unsaturated silty soil embankment subjected to base shaking and compared with the results from another commonly used partially reduced formulation that neglects the relative accelerations, but takes into account the relative velocities. The stress,strain response of the solid skeleton is modeled as both elastic and elastoplastic in all three analyses. In the elastic analyses no permanent deformations are predicted and the displacements of the partially reduced formulation are in between those of the reduced and complete formulations. The frequency of vibration of the complete formulation in the elastic analysis is closer to the predominant frequency of the base motion and smaller than the frequencies of vibration of the other two analyses. Proper consideration of damping due to fluid flows in the complete formulation is the likely reason for this difference. Permanent deformations are predicted by all three formulations for the elastoplastic analyses. The complete formulation, however, predicts reductions in pore fluid pressures following strong shaking resulting in somewhat smaller displacements than the reduced formulation. The results from complete and reduced formulations are otherwise comparable for elastoplastic analyses. For the elastoplastic analysis, the partially reduced formulation leads to stiffer response than the other two formulations. The likely reason for this stiffer response in the elastoplastic analysis is the interpolation scheme (linear displacement and linear pore fluid pressures) used in the finite element implementation of the partially reduced formulation. Copyright © 2008 John Wiley & Sons, Ltd. [source] A 2-D constitutive model for cyclic interface behaviourINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2002Giuseppe Mortara Abstract The paper concerns a 2-D constitutive model for interface behaviour between sand and solid inclusions under cyclic loading. The model is based on the experimental results obtained from laboratory direct shear interface tests conducted under both constant normal load (CNL) and constant normal stiffness (CNS) conditions. The model is formulated in terms of interface stresses and relative velocities and has been derived by extending an elastoplastic isotropic model previously formulated for monotonic loading to stress reversal paths. Such extension consists in adding to the isotropic hardening mechanism a kinematic rotational one defined by an inner conical surface rotating around the origin of the stress space. This allows one to store the memory of the previous stress and relative displacement history giving to the model the capability to analyse the interface behaviour under cyclic loading. After a brief description of the criteria governing the monotonic model, the paper describes in detail the features of the kinematic hardening. Finally, the predictions of the model are compared with the experimental results obtained from CNL and CNS interface tests. Copyright © 2002 John Wiley & Sons, Ltd. [source] Output feedback control design for station keeping of AUVs under shallow water wave disturbancesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2009Shuyong Liu Abstract In this paper, we consider the problem of autonomous underwater vehicle (AUV) station keeping (SK) in shallow water area. During SK, an AUV is required to maintain position and orientation with respect to a fixed reference point at the sea floor. When AUV operates in shallow water, high-frequency disturbances due to waves will significantly affect the motion of the AUV. In order to derive wave disturbance information for control purposes, a nonlinear observer is first designed to estimate the shallow water wave velocities and AUV relative velocities by using position and attitude measurement. Using the observer estimates, a nonlinear output feedback controller is subsequently synthesized by applying observer backstepping technique. Global exponential stability (GES) of the proposed nonlinear observer,controller design is proved through Lyapunov stability theory. Simulation studies on a model based on an actual AUV were performed to verify the performance of the proposed nonlinear observer and output feedback controller. Copyright © 2008 John Wiley & Sons, Ltd. [source] On some aspects of the stirring rate of planetesimal velocities by a protoplanetMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2007Adrián Brunini ABSTRACT We discuss some aspects of the evolution of the relative velocities of a swarm of planetesimals stirred by a protoplanet. We show that the prescriptions most commonly used in semi-analytical ,oligarchic growth' models overestimate the relative velocities of planetesimals by a non-negligible factor. We discuss the probable origin of this discrepancy, proposing a correction factor that provides good agreement between these prescriptions and the results of numerical experiments. The proposed correction factor can be easily implemented in semi-analytical accretion models. [source] On the relative motions of dense cores and envelopes in star-forming molecular cloudsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2007Ben A. Ayliffe ABSTRACT Hydrodynamical simulations of star formation indicate that the motions of protostars through their natal molecular clouds may be crucial in determining the properties of stars through competitive accretion and dynamical interactions. Walsh, Myers & Burton recently investigated whether such motions might be observable in the earliest stages of star formation by measuring the relative shifts of line-centre velocities of low- and high-density tracers of low-mass star-forming cores. They found very small (,0.1 km s,1) relative motions. In this paper, we analyse the hydrodynamical simulation of Bate, Bonnell & Bromm and find that it also gives small relative velocities between high-density cores and low-density envelopes, despite the fact that competitive accretion and dynamical interactions occur between protostars in the simulation. Thus, the simulation is consistent with the observations in this respect. However, we also find some differences between the simulation and the observations. Overall, we find that the high-density gas has a higher velocity dispersion than that observed by Walsh et al. We explore this by examining the dependence of the gas velocity dispersion on density and its evolution with time during the simulation. We find that early in the simulation the gas velocity dispersion decreases monotonically with increasing density, while later in the simulation, when the dense cores have formed multiple objects, the velocity dispersion of the high-density gas increases. Thus, the simulation is in best agreement with the observations early on, before many objects have formed in each dense core. [source] Two-dimensional modeling for stability analysis of two-phase stratified flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2010Ghassem Heidarinejad Abstract The effect of wavelength and relative velocity on the disturbed interface of two-phase stratified regime is modeled and discussed. To analyze the stability, a small perturbation is imposed on the interface. Growth or decline of the disturbed wave, relative velocity, and surface tension with respect to time will be discussed numerically. Newly developed scheme applied to a two-dimensional flow field and the governing Navier,Stokes equations in laminar regime are solved. Finite volume method together with non-staggered curvilinear grid is a very effective approach to capture interface shape with time. Because of the interface shape, for any time advancement, a new grid is performed separately on each stratified field, liquid, and gas regime. The results are compared with the analytical characteristics method and one-dimensional modeling. This comparison shows that solving the momentum equation including viscosity term leads to physically more realistic results. In addition, the newly developed method is capable of predicting two-phase stratified flow behavior more precisely than one-dimensional modeling. It was perceived that the surface tension has an inevitable role in dissipation of interface instability and convergence of the two-phase flow model. Copyright © 2009 John Wiley & Sons, Ltd. [source] Toward Deterministic Material Removal and Surface Figure During Fused Silica Pad PolishingJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 5 2010Tayyab I. Suratwala The material removal and surface figure after ceria pad polishing of fused silica glass have been measured and analyzed as a function of kinematics, loading conditions, and polishing time. Also, the friction at the workpiece/lap interface, the slope of the workpiece relative to the lap plane, and lap viscoelastic properties have been measured and correlated to material removal. The results show that the relative velocity between the workpiece and the lap (i.e., the kinematics) and the pressure distribution determine the spatial and temporal material removal, and hence the final surface figure of the workpiece. In cases where the applied loading and relative velocity distribution over the workpiece are spatially uniform, a significant nonuniformity in material removal, and thus surface figure, is observed. This is due to a nonuniform pressure distribution resulting from: (1) a moment caused by a pivot point and interface friction forces; (2) viscoelastic relaxation of the polyurethane lap; and (3) a physical workpiece/lap interface mismatch. Both the kinematics and these nonuniformities in the pressure distribution are quantitatively described, and have been combined to develop a spatial and temporal model, based on Preston's equation, called Surface Figure or SurF. The surface figure simulations are consistent with the experiment for a wide variety of polishing conditions. This study is an important step toward deterministic full-aperture polishing, allowing optical glass fabrication to be performed in a more repeatable, less iterative, and hence more economical manner. [source] Laboratory simulation of impacts on aluminum foils of the Stardust spacecraft: Calibration of dust particle size from comet Wild-2METEORITICS & PLANETARY SCIENCE, Issue 2 2006A. T. Kearsley The ability of soft aluminum alloy to record hypervelocity impacts as bowl-shaped craters offers an opportunistic substrate for recognition of impacts by particles of a potentially wide size range. In contrast to impact surveys conducted on samples from low Earth orbit, the simple encounter geometry for Stardust and Wild-2, with a known and constant spacecraft-particle relative velocity and effective surface-perpendicular impact trajectories, permits closely comparable simulation in laboratory experiments. For a detailed calibration program, we have selected a suite of spherical glass projectiles of uniform density and hardness characteristics, with well-documented particle size range from 10 ,m to nearly 100 ,m. Light gas gun buckshot firings of these particles at approximately 6 km s,1 onto samples of the same foil as employed on Stardust have yielded large numbers of craters. Scanning electron microscopy of both projectiles and impact features has allowed construction of a calibration plot, showing a linear relationship between impacting particle size and impact crater diameter. The close match between our experimental conditions and the Stardust mission encounter parameters should provide another opportunity to measure particle size distributions and fluxes close to the nucleus of Wild-2, independent of the active impact detector instruments aboard the Stardust spacecraft. [source] A linear differential game with bounded controls and two information delaysOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 2 2009Valery Y. Glizer Abstract The problem of intercepting a maneuvering target by a guided interceptor is considered. It is assumed that the interceptor gets the information on the relative velocity and the target lateral acceleration with time delays. This problem is formulated as a zero-sum differential game with information delays. By using the uncertainty set concept, this differential game is transformed to a new perfect information differential game with a delayed dynamics. The solution of this game is derived, yielding the interception strategy. Illustrative examples are presented. Copyright © 2008 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||||||||