Showing papers on "Inertia published in 1996"

Regular and Chaotic Transport in Asymmetric Periodic Potentials: Inertia Ratchets

Abstract: Motivated by recent work on stochastic ratchets, we consider the effect of finite inertia onto the directed motion in a deterministically rocked, periodic potential lacking reflection symmetry. Characterizing the motion by cumulants of the contracted, time-dependent solution of the Liouville equation, we can distinguish regular from chaotic transport. The first cumulant describes a stationary current that exhibits multiple reversals versus increasing driving strength, whereas the second cumulant yields a measure for its variance. Chaotic transport exhibits universal (Gaussian) scaling behavior. [S0031-9007(96)00064-6]

Chaotic motions of a rigid rotor in short journal bearings

Abstract: In the present paper the conditions that give rise to chaotic motions in a rigid rotor on short journal bearings are investigated and determined. A suitable symmetry was given to the rotor, to the supporting system, to the acting system of forces and to the system of initial conditions, in order to restrict the motions of the rotor to translatory whirl. For an assigned distance between the supports, the ratio between the transverse and the polar mass moments of the rotor was selected conveniently small, with the aim of avoiding conical instability. Since the theoretical analysis of a system's chaotic motions can only be carried out by means of numerical investigation, the procedure here adopted by the authors consists of numerical integration of the rotor's equations of motion, with trial and error regarding the three parameters that characterise the theoretical model of the system: m, the half non-dimensional mass of the rotor, σ, the modified Sommerfeld number relating to the lubricated bearings, and ρ, the dimensionless value of rotor unbalance. In the rotor's equations of motion, the forces due to the lubricating film are written under the assumption of isothermal and laminar flow in short bearings. The number of numerical trials needed to find the system's chaotic responses has been greatly reduced by recognition of the fact that chaotic motions become possible when the value of the dimensionless static eccentricity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiabew7aLnaaBaaaleaacaWGZbaabeaaaaa!4046!\[\varepsilon _s \] is greater than 0.4. In these conditions, non-periodic motions can be obtained even when rotor unbalance values are not particularly high (ρ=0.05), whereas higher values (ρ>0.4) make the rotor motion periodic and synchronous with the driving rotation. The present investigation has also identified the route that leads an assigned rotor to chaos when its angular speed is varied with prefixed values of the dimensionless unbalance ρ. The theoretical results obtained have then been compared with experimental data. Both the theoretical and the experimental data have pointed out that in the circumstances investigated chaotic motions deserve more attention, from a technical point of view, than is normally ascribed to behaviours of this sort. This is mainly because such behaviours are usually considered of scarce practical significance owing to the typically bounded nature of chaotic evolution. The present analysis has shown that when the rotor exhibits chaotic motions, the centres of the journals describe orbits that alternate between small and large in an unpredictable and disordered manner. In these conditions the thickness of the lubricating film can assume values that are extremely low and such as to compromise the efficiency of the bearings, whereas the rotor is affected by inertia forces that are so high as to determine severe vibrations of the supports.

A theory of local limiting speed in dynamic fracture

Abstract: A nonlinear continuum analysis is developed to show that stable, steady-state crack motion is limited not only by the macroscopic Rayleigh wave speed as asserted by the established theory of dynamic fracture, but also by a local wave speed governed by the elastic response near the crack tip. The local limiting speed ensures that a subsonic steady-state field can be established in highly nonlinear material regions prior to rupture. A two-dimensional triangular lattice with nearest-neighbor interatomic bonding is studied as a model nonlinear elastic solid that is isotropic under infinitesimal strains, but becomes anisotropic and nonlinear when the lattice is heavily stretched. The local limiting speed is determined by considering the most critical state of deformation on the verge of bond rupture. If the critical state is assumed to be under equibiaxial stressing, the local limiting speed is found to be v 1 = c s σ max μ , where cs is the macroscopic shear wave speed, μ is the shear modulus and σmax is the equibiaxial cohesive strength of the solid (i.e. the maximum equibiaxial tensile stress that a flawless solid can stand without spontaneous rupture). The generality of this result is discussed by relaxing the restrictions in the model problem. It is also shown that lattice dispersion in front of a crack tip can further reduce the speed of bond-breaking stress waves with wavelength on the order of a few atomic spacings. This study lends further support for a viewpoint previously discussed by the author that high speed dynamic fracture involves a competition between a high inertia local crack-tip field and the surrounding low inertia apparent crack field. Motivated by recent molecular dynamics simulations of crack propagation in a 6–12 Lenard-Jones lattice, a variational principle for steady-state deformation is used together with a conjugate gradient minimization algorithm to compute atomistic responses near the tip of a crack moving with constant speed in a similar Lenard-Jones lattice. The computation is performed over a block which moves with the crack and is subjected along the boundary to a low inertia displacement field based on existing solutions for cracks moving in linear elastic solids. The critical velocity at the onset of local crack branching is found to be 0.30cs, in almost exact agreement with the earlier molecular dynamics study. In this case, the local limiting speed is calculated to be v1 = 0.37cs, which is 20% larger than the observed value. This difference can be attributed to the effects of local lattice dispersion. The results are fully supportive of the notion that global-local inertia competition is a key to understanding dynamic fracture instabilities.

A First Order Phase Transition Resulting from Finite Inertia in Coupled Oscillator Systems

Abstract: We analyze the collective behavior of a set of coupled damped driven pendula with finite (large) inertia, and show that the synchronization of the oscillators exhibits a first order phase transition synchronization onset, substantially different from the second order transition obtained in the case of no inertia. There is hysteresis between two macroscopic states, a weakly and a strongly coherent synchronized state, depending on the coupling and the initial state of the oscillators. A self-consistent theory is shown to determine these cooperative phenomena and to predict the observed numerical data in specific examples. [S0031-9007(97)02614-8]

Inertia and ion Landau damping of low‐frequency magnetohydrodynamical modes in tokamaks

Abstract: The inertia and Landau damping of low‐frequency magnetohydrodynamical modes are investigated using the drift‐kinetic energy principle for the motion along the magnetic field. Toroidal trapping of the ions decreases the Landau damping and increases the inertia for frequencies below (r/R)1/2vthi/qR. The theory is applied to toroidicity‐induced Alfven eigenmodes and to resistive wall modes in rotating plasmas. An explanation of the beta‐induced Alfven eigenmode is given in terms of the Pfirsch–Schluter‐like enhancement of inertia at low frequency. The toroidal inertia enhancement also increases the effects of plasma rotation on resistive wall modes.

Earthquake nucleation on model faults with rate‐ and state‐dependent friction: Effects of inertia

Abstract: Laboratory studies suggest that earthquake nucleation involves a transition from quasi-static slip when inertial effects are negligible to inertia-driven, dynamic motion. This transition occurs via quasi-dynamic motion, during which the effects of inertia become increasingly important. The characteristics of this transition, which depend on frictional properties of the fault, determine the observability of earthquake nucleation by seismic, geodetic, or other means. By investigating the role of inertia during nucleation, we obtain a quantitative definition of the limiting velocity Vin, which marks the end of quasi-dynamic motion and the onset of instability. For reasonable friction parameters and fault widths, we obtain estimates of Vin for crustal faults. To study the roles of inertia, stiffness, and friction parameters on preseismic motion, we simulate triggered instabilities in a one-dimensional model of a homogeneous fault, with rate and state variable friction. In most of our simulations, triggering is achieved by applying a stress perturbation to an initially creeping fault under steady state friction. We also investigate triggering on faults which are initially locked and overstressed compared to their nominal frictional strength, due to time-dependent healing. We study the amount, Up, and duration, Tp, of preseismic slip as a function of system mass m and other model parameters. For crustal faults, we interpret the relevant mass as a product of density and fault width and find that wider fault zones result in smaller Up and larger Tp. Both Up and Tp are proportional to the system stiffness K, the characteristic slip distance Dc, and the friction constitutive parameter a and inversely proportional to the size of the triggering event. We find greater Up and Tp for constitutive laws which allow strengthening at zero velocity, compared to laws that require slip or a combination of slip and aging for state evolution. In contrast to quasi-static modeling, our simulations suggest a minimum stress perturbation criterion for instability, which may be interpreted in terms of a strain threshold for triggered seismicity.

Segment inertial properties of primates: new techniques for laboratory and field studies of locomotion.

Abstract: Studies of the dynamics of locomotor performances depend on knowledge of the distribution of body mass within and between limb segments. However, these data are difficult to derive. Segment mass properties have generally been estimated by modelling limbs as truncated cones, but this approach fails to take into account that some segments are of elliptical, not circular, cross section; and further, the profiles of real segments are generally curved. Thus, they are more appropriately modelled as solids of revolution, described by the rotation in space of convex or concave curves, and the possibility of an elliptical cross section needs to be taken into account. In this project we have set out to develop a general geometric model which can take these factors into account, and permit segment inertial properties to be derived from cadavers by segmentation, and from living individuals using linear external measurements. We present a model which may be described by up to four parameters, depending o the profile and serial cross section (circular or ellipsoidal) of the individual segments. The parameters are obtained from cadavers using a simplified complex-pendulum technique, and from intact specimens by calculation from measurements of segment diameters and lengths. From the parameters, the center of mass, moments of inertia, and radii of gyration may be derived, using simultaneous equations. Inertial properties of the body segments of four Pan troglodytes and a single Pongo were determined, and contrasted to comparable findings for humans. Using our approach, the mass distribution characteristics of any individual or species may be represented by a rigid-link segment model or “android.” If this is made to move according to motion functions derived from a real performance of the individual represented, we show that recordings of resulting ground reaction forces may be quite closely simulated by predictive dynamic modelling. © 1996 Wiley-Liss, Inc.

A new architecture of planar three-degree-of-freedom parallel manipulator

Abstract: In this paper a new architecture of a planar three-degree-of-freedom (3-dof) parallel manipulator is presented. In the proposed mechanism, the prismatic actuators are fixed to the base which leads to a reduction of the inertia of the moving links and hence makes it attractive, particularly when high speeds are required and electric actuation is considered. After introducing the mechanism, a kinematic analysis is reported. Then, velocity and acceleration equations are derived. Based on the geometry of the manipulator a workspace analysis is performed and a description of the boundaries of the workspace is provided. This manipulator can be used in robotic applications involving the positioning and orientation of a rigid body on the plane with high stiffness or accuracy. Additionally, the mechanism can find applications in motion simulators or other high-precision or high-speed devices.

Forces in pile foundations under seismic loading

Abstract: The purpose of this paper is to study the relative significance of kinematic and inertial interaction on the magnitude of forces induced in pile foundations by a seismic disturbance. The structure is modeled as a single-degree-of-freedom (SDOF) oscillator and the foundation is a typical pile group embedded in a homogeneous half-space. A three-dimensional Green’s function-based formulation, which rigorously models the pile-soil-pile interaction, is used to calculate the forces in the piles during the seismic kinematic- and inertial-interaction phases. Different structures, represented by their aspect ratios and natural frequencies, and different pile foundations, characterized by their pile rigidities and spacings, are considered in this study. The results show that the seismic shear force and bending moment in a pile are strongly contributed by the kinematic seismic interaction, except in a band approaching the natural frequency of the pile-soil-structure system. In this frequency band, the inertial interaction dominates the pile forces. The extent of contribution from the inertial interaction is governed by the damping of the foundation.

Nonlinear behaviour of contained inertia waves

Abstract: Rotating fluid-filled containers are systems which admit inertial oscillations, which at appropriate frequencies can be represented as inertia wave modes. When forced by a time-dependent perturbation, systems of contained inertia waves have been shown, in a number of experimental studies, to exhibit complex and varied breakdown phenomena. It is particularly hard to determine a forcing amplitude below which breakdowns do not occur but at which linear wave behaviour is still measurable. In this paper, experiments are presented where modes of higher order than the fundamental are forced. These modes exhibit more complex departures from linear inviscid behaviour than the fundamental mode. However, the experiments on higher-order modes show that instabilities begin at nodal planes. It is shown that even a weakly nonlinear contained inertia-wave system is one in which unexpectedly efficient interactions with higher-order modes can occur, leading to ubiquitous breakdowns. An experiment with the fundamental mode illustrates the system's preference for complex transitions to chaos.

The motion of an ellipsoid in tube flow at low Reynolds numbers

Abstract: The motion of a rigid ellipsoidal particle freely suspended in a Poiseuille flow of an incompressible Newtonian fluid through a narrow tube is studied numerically in the zero-Reynolds-number limit. It is assumed that the effect of inertia forces on the motion of the particle and the fluid can be neglected and that no forces or torques act on the particle. The Stokes equation is solved by a finite element method for various positions and orientations of the particle to yield the instantaneous velocity of the particle as well as the flow field around it, and the particle trajectories are determined for different initial configurations. A prolate spheroid is found to either tumble or oscillate in rotation, depending on the particle–tube size ratio, the axis ratio of the particle, and the initial conditions. A large oblate spheroid may approach asymptotically a steady, stable configuration, at which it is located close to the tube centreline, with its major axis slightly tilted from the undisturbed flow direction. The motion of non-axisymmetric ellipsoids is also illustrated and discussed with emphasis on the effect of the particle shape and size.

Exteroception and exproprioception by dynamic touch are different functions of the inertia tensor

Abstract: When an object is held and wielded, a time-invariant quantity of the wielding dynamics is the inertia tensor Iij. The 3 x 3 quantity Iij is composed of moments of inertia (on the diagonal) and products of inertia (off the diagonal). Examination of Iij as a function of different locations at which a cylindrical object is grasped revealed that the products related systematically to grip position (a direction), and both the products and moments taken together related systematically to the extent of the rod to one side of the hand (a magnitude in a direction). In two experiments, observers wielded an occluded rod that was held at an intermediate point along its length and reproduced both the felt grip position and partial rod length. In both experiments, perceived grip position was a function of the rod's products of inertia and perceived partial rod length was a function of the moments and products. Discussion focuses on the specificity of exteroception and exproprioception to Iij.

A novel inertia identification method for speed control of electric machine

Abstract: In most servomotor drive applications, a precise speed control is required irrespective of load variations and frequent speed changes. To achieve high performance speed control with better transient characteristics. It is necessary to consider the moment of inertia of the system in determining the controller gains. This paper presents a new technique of the inertia identification using an extended Kalman filter which is an optimal full order estimator of a nonlinear system. An inertia term of the disturbance observer and controller gains are readjusted by this identification technique. The validity and effectiveness of this method are confirmed by experimental results on a PM synchronous motor.

Material forces in thermoelastic ferromagnets

Abstract: A systematic construction of the canonical balance of momentum (“pseudomomentum” on the material manifold) and energy is presented for materially inhomogeneous thermoelastic hard ferromagnets in which both exchange forces and magnetic-spin inertia are taken into account. The latter is of the gyroscopic type and endows the sources of quasi-inhomogeneities in the balance of pseudomomentum with special properties. The equations obtained will prove useful in further studies of the fracture of hard ferromagnets and of the propagation of phase-transition fronts in such materials.

Vibration Control of Tall Buildings under Seismic and Wind Loads

Abstract: A procedure for the design of a second-order dynamic controller is presented. The proposed method is applied to the control of structures under earthquake and wind excitations. The controller gains are determined by minimizing the root-mean-square value of the response parameter of interest for the structure, assuming that the excitation is Gaussian white noise. Three examples of structures (of which two are assumed to be subjected to the N-S component of the 1940 El Centro earthquake and one is assumed to be excited by wind loads) are considered to illustrate the design technique. In the first of the earthquake engineering applications, the controller is used for active base isolation of a building modeled as a shear frame, while in the second, it is used to develop an active mass damper for a three-dimensional building with eccentric axes of inertia and rotation (and consequently coupled longitudinal, lateral, and torsional motions). The wind engineering application is the design of an active mass damper for a high-rise building modeled as a planar frame subjected to wind loads. Numerical results for the examples reveal that the actively controlled base-isolation system with velocity feedback has better performance than that with either acceleration or displacement feedback. Complete feedback (i.e. feedback using position, velocity, and acceleration) was used for the active mass damper designs, and the controller was seen to be quite effective in reducing displacement and acceleration levels for both the three-dimensional building (with various eccentric locations of the axes of rotation and inertia) and for the planar frame. For all examples studied the active control systems were observed to perform better than their passive counterparts. Comments on the performance and control effectiveness of these designs and closed-loop-system behavior are made.

Nonsmoothness, indeterminacy, and friction in two-dimensional arrays of rigid particles.

Abstract: An algorithm is proposed to simulate regular arrays of perfectly rigid particles with exact Coulomb's law of friction. Relying on this approach, we explore the problems of indeterminacy and dissipation in granular systems. When driven by a basal plane moving at a constant acceleration, a ``steady state'' is achieved where contact forces and angular accelerations of all particles stay constant in time. This state shows a well-defined organization of particle rotations and contact forces. When the driving speed is kept constant, the dissipation rate decreases dynamically to reach its minimum in the steady state. The global frictional behavior of the system can be described in terms of an effective coefficient of friction and an effective inertia. \textcopyright{} 1996 The American Physical Society.

The hydrodynamic stability of channel flow with compliant boundaries

Abstract: An asymptotic theory is developed for the hydrodynamic stability of an incompressible fluid flowing in a channel in which one wall is rigid and the other is compliant. We exploit the multideck structure of the flow to investigate theoretically the development of disturbances to the flow in the limit of large Reynolds numbers. A simple spring-plate model is used to describe the motion of the compliant wall, and this study considers the effect of the various wall parameters, such as tension, inertia, and damping, on the stability properties. An amplitude equation for a modulated wavetrain is derived and the properties of this equation are studied for a number of cases including linear and nonlinear theory. It is shown that in general the effect of viscoelastic damping is destabilizing. In particular, for large damping, the analysis points to a fast travelling wave, short-scale instability, which may be related to a flutter instability observed in some experiments. This work also demonstrates that the conclusions obtained by previous investigators in which the effect of tension, inertia, and other parameters is neglected, may be misleading. Finally it is shown that a set of compliant-wall parameters exists for which the Haberman type of critical layer analysis leads to stable equilibrium amplitudes, in contrast to many other stability problems where such equilibrium amplitudes are unstable.

Strain Rate and Inertial Effects in Free External Inversion of Tubes

Abstract: The free inversion process of a metal tube is analysed considering a rigid linear strain hardening material and taking into account the changes in the thickness of the tube during plastic deformation. The effects of strain rate and inertia during dynamic inversion are examined. The predictions are compared with experiments and the agreement is seen to be good. While strain rate effects are seen to increase the resistance of the tube to inversion, the effect of inertial forces differ during deformation. In the initial stages inertia increases the inversion force by a considerable extent but reduces the same, by a lesser extent, during the inversion process. Language: en

Haptically Perceiving the Length of One Rod by Means of Another

Abstract: Two experiments examined perception of the extent of a target rod that is contacted and wielded by a second probe rod. The equations that define the dynamics of the probe-target system suggest a higher order moment of inertia as the relevant perceptual variable. The particular inertial term implicates parameters of both the target and probe rod. Experiment 1 manipulated the inertia of the target rod and Experiment 2 manipulated the inertia of the probe rod. In both experiments, perceived length was a function of the complex inertial term. Results were discussed in terms of haptic perception at a distance, the equivalence of inert and neural appendages, and the scaling of perceived to actual variables.

Nonlinear Convective Stability in a Porous Medium with Temperature-Dependent Viscosity and Inertial Drag

Abstract: A nonlinear stability analysis of convection in a fluid-saturated porous medium with temperature-dependent viscosity and inertia drag is presented. It is shown that the quadratic drag term is mathematically important and physically significant in ensuring conditional stability.

Dual-mode, viscous crankshaft vibration damper

Abstract: A viscous torsional vibration damper having an annular chamber surrounding a central hub and first and second annular inertia masses located within the annular chamber. The innermost first inertia mass is closely coupled with an inner surface of the working chamber, and has a Teflon bearing arranged between the first inertia mass and the inner surface. The second annular inertia mass is closely mechanically coupled with the first inertia mass by lateral damping units, such as by elastomeric O-rings, such that the combination of the first and second inertia masses and the damping units are substantially freely rotatable within the working chamber due to the Teflon bearing but are arranged to absorb lateral vibrations by the lateral dampers. A viscous fluid is disposed within the working chamber surrounding the inertia masses.

Releasing manipulation

Abstract: In this paper, first we propose a new kind of manipulation-releasing manipulation, that is, by some means, the manipulator gives the object initial translational and rotational velocities to make the object slide on a surface by its inertia under the action of friction. Second, we give the basic equations and analyze the motion of the object. Third, based on numerical calculation, we summarize the motion characteristics, especially for a rectangle. Finally, we perform experiments to verify the validity of this manipulation.

Discrete-time sliding mode based feedback compensation for motion control

Abstract: The main contribution of this paper to examine, via experimental investigations of a type 2 servomechanism, the engineering feasibility of a sliding mode based control design, in which a discontinuous estimator is used in feedback compensation of uncertainties and exogenous disturbances. Experimental results of a transputer controlled single-degree-of-freedom motion control system are presented. The experimental system consists of a conventional DC servo gear motor with encoder feedback and variable inertia load coupled by a relatively rigid shaft.