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Showing papers on "Inertia published in 1999"


Book
29 Dec 1999
TL;DR: In this paper, a two-dimensional theory of Corners and junctions is proposed for growing cracks in three space dimensions, and two dimensions of the junction and junction are modeled with configurational forces.
Abstract: Configurational Forces within a Classical Context.- Kinematics.- Standard Forces. Working.- Migrating Control Volumes. Stationary and Time-Dependent Changes in Reference Configuration.- Configurational Forces.- Thermodynamics. Relation Between Bulk Tension and Energy. Eshelby Identity.- Inertia and Kinetic Energy. Alternative Versions of the Second Law.- Change in Reference Configuration.- Elastic and Thermoelastic Materials.- The Use of Configurational Forces to Characterize Coherent Phase Interfaces.- Interface Kinematics.- Interface Forces. Second Law.- Inertia. Basic Equations for the Interface.- An Equivalent Formulation of the Theory. Infinitesimal Deformations.- Formulation within a Classical Context.- Coherent Phase Interfaces.- Evolving Interfaces Neglecting Bulk Behavior.- Evolving Surfaces.- Configurational Force System. Working.- Second Law.- Constitutive Equations. Evolution Equation for the Interface.- Two-Dimensional Theory.- Coherent Phase Interfaces wtih Interfacial Energy and Deformation.- Theory Neglecting Standard Interfacial Stress.- General Theory with Standard and Configurational Stress within the Interface.- Two-Dimensional Theory with Standard and Configurational Stress within the Interface.- Solidification.- Solidification. The Stefan Condition as a Consequence of the Configurational Force Balance.- Solidification with Interfacial Energy and Entropy.- Fracture.- Cracked Bodies.- Motions.- Forces. Working.- The Second Law.- Basic Results for the Crack Tip.- Constitutive Theory for Growing Cracks.- Kinking and Curving of Cracks. Maximum Dissipation Criterion.- Fracture in Three Space Dimensions (Results).- Two-Dimensional Theory of Corners and Junctions Neglecting Inertia.- Preliminaries. Transport Theorems.- Thermomechanical Theory of Junctions and Corners.

628 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigate the origin of deviations from the classical Darcy law by numerical simulation of the Navier-Stokes equations in two-dimensional disordered porous media and find that such a transition can be understood and statistically characterized in terms of the spatial distribution of kinetic energy in the system.
Abstract: We investigate the origin of the deviations from the classical Darcy law by numerical simulation of the Navier-Stokes equations in two-dimensional disordered porous media. We apply the Forchheimer equation as a phenomenological model to correlate the variations of the friction factor for different porosities and flow conditions. At sufficiently high Reynolds numbers, when inertia becomes relevant, we observe a transition from linear to nonlinear behavior which is typical of experiments. We find that such a transition can be understood and statistically characterized in terms of the spatial distribution of kinetic energy in the system. [S0031-9007(99)09541-1]

244 citations


Journal ArticleDOI
TL;DR: In this paper, the natural frequency and vibration mode sensitivities to system parameters are rigorously investigated for both tuned (cyclically symmetric) and mistuned planetary gears, including support and mesh stiffnesses, component masses, and moments of inertia.

144 citations


Journal ArticleDOI
TL;DR: Experimental data and numerical/computational models concerning the internal inversion of metal tubes and the dynamic crushing of aluminium honeycombs are presented and discussed as illustrations of impact energy absorbers whose behaviour is strongly influenced by inertial effects.

134 citations


Proceedings ArticleDOI
27 Jul 1999
TL;DR: In this article, the authors developed systematic analysis and design methods for a two-inertia PI system with a torsional load and derived the damping characteristic of the system.
Abstract: Our purpose is to develop systematic analysis and design methods for a two-inertia system. A conventional PI speed control system with a torsional load is redesigned, and the damping characteristic of the system is derived and analyzed. It is shown that the dynamic characteristic of the system strongly depends on the inertia ratio of load to motor. Three kinds of typical pole assignments with identical radius/damping coefficient/real-part are applied and compared, and the merits of each pole assignment design are concluded. Furthermore, for small inertia ratio, we show how to improve the damping by a derivative feedback of motor speed.

106 citations


Journal ArticleDOI
TL;DR: In this paper, a cubic weak inertia correction of Darcy's law which is valid for any matrix anisotropy was derived for porous media, and a description of flow by the weak inertia equation for low Reynolds numbers and a Forchheimer equation for high Reynolds number laminar flow was given.
Abstract: We consider two problems of nonlinear flow in porous media: 1) a derivation of a cubic weak inertia correction of Darcy's law which is valid for any matrix anisotropy, and 2) a description of flow by the weak inertia equation for low Reynolds numbers and a Forchheimer equation for high Reynolds number laminar flow Recent homogenization studies show that the weak inertia correction to Darcy's law is not a square term in velocity, as it is in the Forchheimer equation, but instead a cubic term in velocity By imposing that the pressure loss is invariant under flow reversion, it has been shown that the weak inertia equation is valid even for anisotropic media We show, by using the homogenization technique, that the weak inertia equation is valid for any anisotropic matrix symmetry without imposing a reversed flow symmetry For the second problem, we reexamine published data We find that the description 2) applies well A spline may be applied in the crossover regime

98 citations


Journal ArticleDOI
TL;DR: In this paper, the axial instability of the free-surface front of a viscous fluid in a horizontal cylinder rotating about its longitudinal axis was investigated and a simplified model equation for the evolution of free surface is derived and includes the effects of gravity, capillarity, inertia, and viscosity.
Abstract: We investigate the axial instability of the free-surface front of a viscous fluid in a horizontal cylinder rotating about its longitudinal axis. A simplified model equation for the evolution of the free surface is derived and includes the effects of gravity, capillarity, inertia, and viscosity. This equation is solved numerically to determine the base state with no axial variation, and a numerical linear stability analysis is carried out to examine the onset of unstable axial modes. Various computational results are presented for the wavelength of the axial instability. Inertia is found to play an important role in the onset of the instability and the wavelength of the instability λ satisfies the power law λ∼γ1/3, where γ is surface tension. Finally some numerical simulations of the simplified evolution equation are presented to show that they can capture the steady shark-teeth patterns observed in recent experiments [R. E. Johnson, in Engineering Science, Fluid Dynamics: A Symposium to Honor T. Y. Wu (Wo...

96 citations


Journal ArticleDOI
TL;DR: In this article, a theoretical analysis of a viscous liquid film flowing down a vertical one-dimensional periodic surface is performed based on both Navier-Stokes and integral equations and performed over a wide range of Reynolds number and surface geometry characteristics taking into account viscosity, inertia and surface tension.

92 citations


Journal ArticleDOI
01 Oct 1999
TL;DR: A novel yet simple approach for experimental determination of the link (mass and inertia-related) parameters and friction coefficients is developed and the identified model predicts the joint torques, in both static and dynamic conditions, with a very good accuracy.
Abstract: A novel yet simple approach for experimental determination of the link (mass and inertia-related) parameters and friction coefficients is developed for a typical excavator arm. The parameters are needed for indirect measurement of the external forces, compensation for the link weights in the operator's hand in a force-feedback teleoperation setup, impedance control of the arm, simulation of the manipulator dynamics, and model-based fault detection. Treating the machine arm as an open kinematic chain, its dynamic equations are presented symbolically. The static torque equations are derived from these equations and the gravitational parameters are defined accordingly. A new method for decoupled estimation of the gravitational parameters from static experiments is presented. Furthermore, the arm dynamics are expressed in a form which is linear in the inertia and friction-related parameters. The results obtained show that the identified model predicts the joint torques, in both static and dynamic conditions, with a very good accuracy.

88 citations


Journal ArticleDOI
TL;DR: This paper used a preferential looking method, a perceptual judgment method, and a predictive judgment method to investigate the development of sensitivity to the effects of gravity and inertia on inanimate object motion.
Abstract: Experiments using a preferential looking method, a perceptual judgment method, and a predictive judgment method investigated the development, from 7 months to 6 years of age, of sensitivity to the effects of gravity and inertia on inanimate object motion. The experiments focused on a situation in which a ball rolled off a flat surface and either continued in linear motion (contrary to gravity), turned abruptly and moved downward (contrary to inertia), or underwent natural, parabolic motion. When children viewed the three fully visible motions, both the preferential looking method and the perceptual judgment method provided evidence that sensitivity to inertia developed between 7 months and 2 years, and that sensitivity to gravity began to develop after 3 years. When children predicted the future location of the object without viewing the motions, the predictive judgment method provided evidence that sensitivity to gravity had developed by 2 years, whereas sensitivity to inertia began to develop only at 5‐6 years. These findings suggest that knowledge of object motion develops slowly over childhood, in a piecemeal fashion. Moreover, the same system of knowledge appears to be tapped both in preferential looking tasks and in judgment tasks when children view fully visible events, but a different system may underlie children’s inferences about unseen object motions.

83 citations


Journal ArticleDOI
TL;DR: In this article, the influence of inertia in the particle dynamics for the noise induced, directed current was investigated by means of two approximation schemes: a unified colored noise approximation and a pathintegral approach.
Abstract: The colored ~Ornstein-Uhlenbeck! noise-driven nonequilibrium dynamics of massive damped Brownian particles in a periodic but asymmetric potential ~ratchet! is investigated Our special focus is on the influence of inertia in the particle dynamics for the noise induced, directed current By means of two approximation schemes ~a unified colored noise approximation and a path-integral approach! and by numerical matrixcontinued-fraction evaluations of the inherent, three-dimensional Fokker-Planck dynamics as well as by direct simulations of the stochastic differential equations we examine the dynamics at various inertial strengths For the case of a large mass we find current reversal with respect to both a variation of the mass and of the noise-correlation time Possibilities for efficient mass-sensitive scenarios for separation of particles are discussed @S1063-651X~99!00802-8#

Proceedings ArticleDOI
02 Jun 1999
TL;DR: In this paper, an adaptive attitude control law is presented that realizes linear closed-loop dynamics in the attitude error vector, where the modified Rodrigues parameters (MRPs) are used as the kinematic variables since they are nonsingular for all possible rotations.
Abstract: An adaptive attitude control law is presented that realizes linear closed-loop dynamics in the attitude error vector. The modified Rodrigues parameters (MRPs) are used as the kinematic variables since they are nonsingular for all possible rotations. The desired linear closed-loop dynamics can be of either PD or PID form. Only a crude estimate of the moment of inertia matrix is assumed to be known. An open-loop nonlinear control law is presented which yields linear closed-loop dynamics in terms of the MRPs. An adaptive control law is developed which asymptotically enforces these desired linear closed-loop dynamics in the presence of large inertia and external disturbance model errors. Since the unforced closed-loop dynamics are nominally linear, standard linear control methodologies can be employed to satisfy design requirements. The adaptive control law is shown to track the desired linear performance asymptotically without requiring a priori knowledge of either the inertia matrix or external disturbance.

Journal ArticleDOI
TL;DR: In this paper, the authors consider the free boundary problem for the evolution of a nearly straight slender fiber of viscous fluid and show that the shape of the cross-section can be described by means of a conformal map which depends on time and distance along the fibre axis.
Abstract: We consider the free boundary problem for the evolution of a nearly straight slender fibre of viscous fluid. The motion is driven by prescribing the velocity of the ends of the fibre, and the free surface evolves under the action of surface tension, inertia and gravity. The three-dimensional Navier-Stokes equations and free-surface boundary conditions are analysed asymptotically, using the fact that the inverse aspect ratio, defined to be the ratio between a typical fibre radius and the initial fibre length, is small. This first part of the paper follows earlier work on the stretching of a slender viscous fibre with negligible surface tension effects. The inclusion of surface tension seriously complicates the problem for the evolution of the shape of the cross-section. We adapt ideas applied previously to two-dimensional Stokes flow to show that the shape of the cross-section can be described by means of a conformal map which depends on time and distance along the fibre axis. We give some examples of suitable relevant maps and present numerical solutions of the resulting equations. We also use analytic methods to examine the coupling between stretching and the evolution of the cross-section shape.

Journal ArticleDOI
TL;DR: In this article, a control law based on cubic velocity feedback is proposed to suppress the vibrations of the first mode of a cantilever beam when subjected to a principal parametric resonance.

Journal ArticleDOI
TL;DR: In this article, the authors present a formulation for the analysis of impact problems with friction in open-loop multibody mechanical systems, which recognizes the correct mode of impact; i.e., sliding, sticking, and reverse sliding.
Abstract: Analysis of impact problems in the presence of any tangential component of impact velocity requires a friction model capable of correct detection of the impact modes. This paper presents a formulation for the analysis of impact problems with friction in open-loop multibody mechanical systems. The formulation recognizes the correct mode of impact; i.e., sliding, sticking, and reverse sliding. Poisson’s hypothesis is used for the definition of the coefficient of restitution, and thus the energy gains inherent with the use of the Newton’s hypothesis are avoided. The formulation is developed by using a canonical form of the system equations of motion using joint coordinates and joint momenta. The canonical momentum-balance equations are solved for the change in joint momenta using Routh’s graphical method. The velocity jumps are calculated balancing the accumulated momenta of the system during the impact process. The impact cases are classified based on the pre-impact positions and velocities, and inertia properties of the impacting systems, and expressions for the normal and tangential impulse are derived for each impact case. The classical problem of impact of a falling rod with the ground (a single object impact) is solved with the developed formulation and verified. Another classical problem of a double pendulum striking the ground (a multibody system impact) is also presented. The results obtained for the double pendulum problem confirms that the energy gain in impact analysis can be avoided by considering the correct mode of impact and using the Poisson’s instead of the Newton’s hypothesis.

Journal Article
TL;DR: In this paper, a new closed-form analytical solution to the equations governing the wave-induced seabed response, including inertia items, was presented, and the numerical results showed that the inertia forces cannot always be ignored in a softer seafloor and that the relative difference between the present solution and the previous solution may reach 5% of po under certain combinations of wave and soil conditions.
Abstract: The analysis of wave-induced seabed response is an important factor in the design of offshore installations. However, to simplify the complicated problem, most previous investigations have ignored the effects of inertia forces. This paper presents a newly closed-form analytical solution to the equations governing the wave-induced seabed response, including inertia items. The numerical results show that the inertia forces cannot always be ignored in a softer seabed. The relative difference between the present solution (with inertia items) and the previous solution (without inertia items) may reach 5% of po under certain combinations of wave and soil conditions. *ISOPE Member. Received February 9, 1999; revised manuscript received by the editors September 9, 1999. The original was submitted directly to the Journal.

Journal ArticleDOI
TL;DR: A brief overview of matrix stability and inertia theory can be found in this paper, where a nonspectral implicit matrix equation method is used to determine the stability of a nonhermitian matrix.


Journal ArticleDOI
TL;DR: In this paper, the influence of both viscous dissipation and fluid inertia on the property measurements in oscillatory sliding plate rheometry is investigated, and a unified criterion for avoiding measurement errors is provided.
Abstract: For liquids with high viscosity and low thermal conductivity, viscous dissipation can cause appreciable errors in rheological property measurements. Here, the influences of both viscous dissipation and fluid inertia on the property measurements in oscillatory sliding plate rheometry are investigated. For Newtonian fluids, Bird (1965) solved the combined problem analytically, but only for high frequencies. Here his solution is extended to any frequencies. Also, the equations of motion and energy are solved for linear viscoelastic fluids, and new analytical solutions for the velocity and temperature profiles are given. In both Newtonian and linear viscoelastic fluids, the temperature rise in the gap increases with frequency. The location of the maximum temperature shifts from the mid-plane at low frequency towards the moving wall at high frequency. The fluid inertia increases the viscous dissipation in both fluids. By solving the combined problem, this paper simplifies rheometer design by providing one unified criterion for avoiding measurement errors. Operating limits are presented graphically for minimizing the effects of both fluid inertia and viscous dissipation in oscillatory sliding plate rheometry.

Journal ArticleDOI
TL;DR: In this paper, the effects of rotatory inertia, shear deformation and axial deformation of non-circular arches are derived and solved numerically to obtain frequencies and mode shapes.

Journal ArticleDOI
TL;DR: In this paper, the authors compared results from experiments that were carried out on a ball and disk apparatus with results obtained with the EHL contact model, and a qualitatively close agreement has been found.
Abstract: In elastohydrodynamic lubrication (EHL), one generally imposes force balance, i.e., the contact force resulting from the pressure in the contact is equal to the applied load. When studying the effect of structural vibrations, this force balance equation obviously does not hold and the more general equation of motion is required. In Wijnant and Venner (1996), an EHL contact model was introduced that incorporates both squeeze and entraining motion as well as the equation of motion. It was shown numerically that due to a small initial deviation or initial velocity, the rolling element starts an oscillatory motion around the equilibrium position. This motion is slightly damped because of the viscous losses in the lubricant. Moreover, it was shown that these oscillations cause film thickness modulations with a wavelength, directly related to the dimensionless frequency Ω. This paper compares results from experiments that were carried out on a ball and disk apparatus with results obtained with the EHL contact model. In this experiment, the applied load was rapidly increased by impacting a wedge between the base and the ball holder. This results in an increase of the contact area and, as a result of inertia forces of the ball, disk and supports, and oscillatory motion of the contacting bodies. Modulations in the film thickness which result from these oscillations, are clearly visible. The contact model was tailored to this experiment and a qualitatively close agreement has been found.

Journal ArticleDOI
TL;DR: In this article, an adaptive non-linear friction compensation scheme for a friction model is presented, which captures problematic friction effects such as Stribeck effect, hysteresis, stick-slip limit cycling, pre-sliding displacement and rising static friction.
Abstract: Non-linear frictional dynamics reduce the tracking performance of machine control systems involving high-precision, low-velocity tasks. We present an adaptive non-linear friction compensation scheme for a friction model, which captures problematic friction effects such as Stribeck effect, hysteresis, stick-slip limit cycling, pre-sliding displacement and rising static friction. We show that without robust adaptation, frictional dynamics and other modelling uncertainties can cause an adaptive friction compensation scheme to become unstable. We extend robust adaptive theory to include a new type of error model with a non-linear regression vector and Lipschitz disturbances. By using persistent excitation in the desired trajectory, our controller achieves stable adaptation for friction force effects due to static, Coulomb and viscous components, as well as for inertia and the Stribeck effects, while remaining robust to perturbations in friction force due to frictional lag and frictional memory. Although the S...

Journal ArticleDOI
TL;DR: In this paper, the effects of inertia on hydrodynamics in the microscopic vicinity of moving contact lines were investigated at low capillary number (Ca<01) and negligible (10−4) to moderate (Re∼1) Reynolds number.
Abstract: We investigate the effects of inertia on the hydrodynamics in the microscopic vicinity of moving contact lines These hydrodynamics control the macroscopic shape and spreading of fluid bodies across solid surfaces We perform experiments at low capillary number (Ca<01) and negligible (10−4) to moderate (Re∼1) Reynolds number On a microscopic scale, inertia decreases the dynamic curvature of the free surface near the contact line compared to the case with Re=0 at the same Ca On a macroscopic scale, inertia lowers the apparent contact angle of the static-like macroscopic interface compared to the situations with the same Ca but negligible Re

Journal ArticleDOI
TL;DR: In this paper, the results of singular perturbation calculations of the lift on a sphere in a linear shear flow were presented, and the results provided some physical understanding of the effects of unsteadiness and the frequency regime in which one may assume quasisteady conditions.

Journal ArticleDOI
TL;DR: In this article, a frequency domain spectral analysis is presented for the seismic analysis of cable-stayed bridges for the multi-component stationary random ground motion incident at an angle with the longitudinal axis of the bridge.

Journal ArticleDOI
TL;DR: In this paper, the journal equation of motion and the complete Reynolds equation of compressible fluid film are numerically solved and a computer program is developed to obtain journal center trajectories and effects of fluid inertia.
Abstract: The journal equation of motion and the complete Reynolds equation of compressible fluid film are numerically solved and a computer program is developed. The formulas are for externally pressurized bearings, but results are shown only for self-acting bearings. For certain cases, the validity of the theoretical results is verified by comparison with the experimental data available from the literature. Through intensive use of the program, journal center trajectories are obtained and effects of fluid inertia are investigated. New stability parameters are presented and stability diagrams are established for bearings with L/D = 0.25, 0.5, 1, 1.5, and 2. The rotor unbalance effects on bearing stability limits are illustrated for several cases.

Journal ArticleDOI
TL;DR: In this paper, a statistical analysis of errors generated through the process of inertia property identification is performed, and the major factors influencing their accuracy are derived, such as length, area, and volume.

Journal ArticleDOI
TL;DR: In this paper, the synchronization phenomena in a set of globally coupled oscillators under external periodic driving, with emphasis on the effects of small inertia, were analyzed analytically, and it was found that the inertia induces discontinuous transitions between the coherent and incoherent states.
Abstract: We study analytically the synchronization phenomena in a set of globally coupled oscillators under external periodic driving, with emphasis on the effects of small inertia. We examine in detail both the integer and fractional mode locking present in the system with inertia, and derive the self-consistency equation for the order parameter, which reveals variation of the magnitude of the order parameter according to the external periodic driving. In particular, it is found that the inertia induces discontinuous transitions between the coherent and incoherent states.

Journal ArticleDOI
TL;DR: In this paper, a scaling theory is proposed to predict the dependence of a steady state domain size on shear rate, but assumes low Reynolds number (inertia is neglected).
Abstract: Symmetric binary fluids, quenched into a regime of immiscibility, undergo phase separation by spinodal decomposition. In the late stages, the fluids are separated by sharply defined, but curved, interfaces: the resulting Laplace pressure drives fluid flow. Scaling ideas (of Siggia and of Furukawa) predict that, ultimately, this flow should become turbulent as inertial effects dominate over viscous ones. The physics here is complex: mesoscale simulation methods (such as lattice Boltzmann and dissipative particle dynamics) can play an essential role in its elucidation, as we describe. Likewise, it is a matter of experience that immiscible fluids will mix, on some lengthscale at least, if stirred vigorously enough. A scaling theory (of Doi and Ohta) predicts the dependence of a steady state domain size on shear rate, but assumes low Reynolds number (inertia is neglected). Our preliminary simulation results (three-dimensional, so far only on small systems) show little sign of the kind of steady state envisaged by Doi and Ohta; they raise instead the possibility of an oriented domain texture which can continue to coarsen until either inertial effects, or (in our simulations) finite size effects, come into play.