Showing papers on "Inertia published in 1970"

Slender-body theory for particles of arbitrary cross-section in Stokes flow

Abstract: A rigid body whose length (2l) is large compared with its breadth (represented by R0) is straight but is otherwise of arbitrary shape. It is immersed in fluid whose undisturbed velocity, at the position of the body and relative to it, may be either uniform, corresponding to translational motion of the body, parallel or perpendicular to the body length, or a linear function of distance along the body length, corresponding to an ambient pure straining motion or to rotational motion of the body. Inertia forces are negligible. It is possible to represent the body approximately by a distribution of Stokeslets over a line enclosed by the body; and then the resultant force required to sustain translational motion, the net stresslet strength in a straining motion, and the resultant couple required to sustain rotational motion, can all be calculated. In the first approximation the Stokeslet strength density F(x) is independent of the body shape and is of order μUe, where U is a measure of the undisturbed velocity and e = (log 2l/R0)−1. In higher approximations, F(x) depends on both the body cross-section and the way in which it varies along the length. From an investigation of the ‘inner’ flow field near one section of the body, and the condition that it should join smoothly with the ‘outer’ flow which is determined by the body as a whole, it is found that a given shape and size of the local cross-section is equivalent, in all cases of longitudinal relative motion, to a circle of certain radius, and, in all cases of transverse relative motion, to an ellipse of certain dimensions and orientation. The equivalent circle and the equivalent ellipse may be found from certain boundary-value problems for the harmonic and biharmonic equations respectively. The perimeter usually provides a better measure of the magnitude of the effect of a non-circular shape of a cross-section than its area. Explicit expressions for the various integral force parameters correct to the order of e2 are presented, together with iterative relations which allow their determination to the order of any power of e. For a body which is ‘longitudinally elliptic’ and has uniform cross-sectional shape, the force parameters are given explicitly to the order of any power of e, and, for a cylindrical body, to the order of e3.

Simple shear flow round a rigid sphere: inertial effects and suspension rheology

Abstract: An analysis is presented of the flow field near a neutrally-buoyant rigid spherical particle immersed in an in compressible Newtonian fluid which, at large distances from the particle, is undergoing simple shear flow. Subject to conditions of continuity of stress at the particle surface and to conditions of zero net torque and zero net force on the sphere, the effect of fluid inertia on the velocity and pressure fields in the vicinity of the particle has been computed to for a dilute (non-interacting) suspension of spheres. In addition it is found that inertial effects give rise to a non-isotropic normal stress.

Vibrations of Timoshenko Beams and Frameworks

Abstract: A general matrix formulation suitable for a use of the digital computer is presented for dynamic analysis of frameworks composed of prismatic members. The dynamic stiffness coefficients are derived in the form of nondimensional parameters corresponding to the effects of rotatory inertia, shear deformation, and of bending deformation. The individual parameter may be dropped when the appropriate effect is not considered; hence, the stiffness coefficients can be applied to a problem with various considerations of Timoshenko theory, Rayleigh theory, bending and shear, and of Bernoulli-Euler theory. Input data for the computer include the configurations of the framework and the elastic properties of constituent members. The method may be applied to irregular frameworks composed of sloping members with and without sidesway. Numerical examples presented indicate that the effect of rotatory inertia and of shear deformation on the frequencies of frameworks without sidesway is more significant than that of swayed structures.

Nutation damping in a dual-spin spacecraft

Abstract: A dual-spin spacecraft having a momentum wheel spinning relative to a platform to provide bias momentum utilizes cross products of inertia (POI) existing in the platform between the spinning axis and the transverse axes to achieve nutation damping. When the platform is rotating or is displaced from a reference the cross products of inertia are also rotating or are displaced causing thereby degradation of the optimum nutation damping time constant. Two or more phase shifting networks are provided to be sequentially coupled into a control loop to shift nutation signals to effect optimum nutation damping at selected positions of the rotating or displaced platform without substantial nutation damping time constant degradation.

A note on dipolar inertia

Abstract: With reference to the spatial form of the kinetic energy in the theory of simple dipolar continuum mechanics, a suitable expression is obtained for dipolar inertia. This includes the case in which the coefficient of the kinetic energy due to velocity gradient (in spatial form) may be constant. Using a system of generalized coordinates qa (a = 1, • • • , v) for generalized continuum mechanics, Green and Rivlin [1] adopted a kinetic energy per unit mass in the form v T = hY. aa»qaq& , (1) a = 1 where aa|3 is a function of qy (y = 1, • • • , v) and a superposed dot denotes differentiation with respect to time t. It was then shown that the material time derivative of T is given by t = E d_ §T_ (It \\dq0 dT~\\ . dqa\\qa ' (2) and that the inertia term corresponding to the velocity qa is A. _ dT dt \\dqaJ dqa Taking the reference frame to be rectangular Cartesian and using tensor notation, in the theory of simple dipolar continuum mechanics in which the basic generalized velocities are v< and viwi , a suitable form for the kinetic energy per unit mass is \\viVi + T, (4) where T = hmkiVi,kVi,i , (5) and ( ),,• denotes partial differentiation with respect to the spatial coordinate Xj holding t fixed. Also, mtl is a symmetric function of displacement gradients xinA where ( ),x denotes partial differentiation with respect to a reference position XA holding t fixed. If we assume that T is unaltered by a static rigid body rotation, then * Received September 8, 1969.

External and material damped three dimensional rotor system

Abstract: This paper extends and improves previous work by the authors on the motion of a whirling elastic shaft-disc system. Using an energy technique the effects of external damping, linear and non-linear internal damping, linear and non-linear elastic restoring forces and non-linear inertia forces are isolated and investigated. The results are summarized in the form of stability theorems. In addition, using techniques previously developed by the authors, solutions to the linear damped system, for both the homogeneous and non-homogeneous cases, are presented. Apart from being of interest in their own right use is made of them in the non-linear analysis.

Series type vibration damper

Abstract: A vibration damper for rotating members consisting of a hub member and at least two annular inertia members mounted upon the hub member by elastic elements. The hub and inertia members include cylindrical surfaces concentric to the axis of hub member rotation and the elastic elements cooperate with these surfaces for mounting one inertia member upon the hub member in a vibration absorbing relationship, and the second inertia member is mounted upon a cylindrical surface defined on the previously mentioned inertia member by an elastic element creating a ''''series'''' relationship between the inertia members and the hub member.

Kinematically consistent unsteady aerodynamic coefficients in supersonic flow

Abstract: A finite element method to determine unsteady aerodynamic influence coefficients, consistent with the stiffness and inertia properties of a lifting surface in supersonic flow, is described. This is basically a kinematic method, which reduces the dynamical equations of a non-conservative system to a simple and elegant form. It is illustrated by application to a delta wing using triangular elements to calculate steady and unsteady lift and moment coefficients. Throughout the calculations only a coarse grid system has been employed and the answers have been compared with available results.

Does a rod, pushed by a force, accelerate less than the same rod pulled by the same force?

Abstract: The answer is yes, if we consider the mean accelerations of the rod’s points. Namely, the acceleration of the application point of the external force only depends on the rod’s mass and the force’s magnitude. Consequently the other points of the rod accelerate differently according to their positions in order to set up Lorentz contraction. In Sect.1 the problem is solved kinematically, considering that the rod’s motion is rigid if the external force is constant and assuming that the motion of the application point of the external force is hyperbolic. In Sect.2 the above assumption then proves to be in agreement with the relativistic equations of motion for elastic continua. Moreover, by these equations, the acceleration of the application of the external force turns out to be given, in any instantaneous rest system of inertia, byF/m0, whereF is the force’s magnitude andm0 the rod’s proper mass. In Sect.3 the problem is studied also by the equations recently proposed by Cavalleri and Salgarelli in the context of a new formulation called « asynchronous », to distinguish it from the usual « synchronous » formulation of the relativistic dynamics for extended bodies. By the asynchronous equations, the hyperbolic motion for the rod can be immediately deduced. The problem studied can interest models of extended particles, « pushed or pulled » by exchanges of real and virtual photons, mesons, gravitons.

Inertia Effects in Hydromagnetic Inclined Slider Bearing

Abstract: A theoretical investigation of inertia effect in an inclined slider bearing with an electrically conducting lubricant in the presence of uniform transverse magnetic field is presented. It is found that for open-circuit case, load capacity increases due to inertia at small Hartmann number and decreases at large Hartmann number.

Effect of inertia on losses from a plasma in toroidal equilibrium

Abstract: We investigate theoreticall y the MHD equilibrium of a resistive, low-density plasma in a model stellarator field. Th e effect of inertia on plasma motion is treated exactly and its influence on plasma loss determined. The results are valid for arbitrary aspect ratio. For the existence of a stationary equilibrium we show that there are two unconnected regions of solution, described in terms of the mass fluxes the long and the short way within a magnetic surface. For the region containing the case of the well-known classical resistive diffusion we argue that the increase in plasma loss due to inertia is strongly limited and does not appreciably exceed the classical diffusion rate.

Servo compensation for inertia change

Abstract: An improvement in the servo drive system as used in a missile director during the elevation function to compensate for changes in inertia. The secant potentiomenter and its associated circuitry is amended to compensate for inertia change as well as changes in elevation angle.

Effect of Lubricant Inertia on Squeeze Film in Spherical Bearing

Abstract: A theoretical investigation of inertia effects on squeeze film in a spherical bearing is presented. It is shown that inertia forces make a significant contribution to the time of approach.

Centrifugal-balance gravity gradiometer

Abstract: An improved gradiometer for accurately measuring gravity gradients without the need for prior calibration. Since calibration is not required, the instrument operates independent of any external standards or references, except time. Further, one instrument in one orientation can provide all the components of the gravity gradient. The gradiometer comprises a suitably configured gradient sensor mass within a case which, in turn, is mounted within a cage such that its input axis is aligned with the axis of rotation of the cage. The entire assemblage is contained within a chamber which is preferably mounted on a stabilized base. Forces are induced on the sensor due to gravity gradients, causing the mass to move relative to its case. This motion is sensed and used to rotate the cage relative to the chamber. The angular rotation of the cage, in turn, causes the sensing device (specifically, its case) to rotate about an axis perpendicular to the inertia reaction forces on the sensor which are in an opposite sense to the forces induced on the sensor by the gravity gradients. The sensor is thus dynamically balanced. The angular velocity of the cage is indicative of the magnitude and direction of the gravity gradients being measured.

Instability of an Elastically Supported Beam under a Travelling Inertia Load

Abstract: It is shown that an unstable bending wave may be excited in an elastically supported beam by a travelling inertia load. Since the occurrence of this dynamic instability reduces the axial buckling load of the beam, the result is relevant to present studies of the temperature buckling of continuous welded railway track.

Inertial potentials in classical and quantum mechanics

Abstract: The study of wave equations in accelerated reference frames allows, in principle, a selection among theories of inertia based on the transformation properties of the corresponding potentials It is shown, in particular, that invariance of the classical equations of motion and of the Schrodinger equation under the same set of transformations leads to Sciama’s theory of inertia in the limitGM/c2R∼1 Tests which allow to distinguishing between this vector theory and general relativity are proposed and briefly discussed

Vehicle Trajectories After Intersection Collision Impact

Abstract: THE POSTCOLLISION MOTION STARTS IMMEDIATELY UPON COMPLETION OF A COLLISION IMPACT WHERE THE VEHICLES OBTAIN NEW SETS OF VELOCITIES THROUGH AN EXCHANGE OF MOMENTUM. SIMILITUDE WITH MODEL STUDY AND FULLSCALE AUTOMOBILE EXPERIMENTS INDICATE THAT THE POST-COLLISION TRAJECTORY IS ESSENTIALLY A PLANE MOTION, GOVERNED BY INERTIA AND TIRE FRICTION. TRAJECTORIES DEPEND ON MANY PARAMETERS (SUCH AS TIRE FRICTION COEFFICIENT, FRONT WHEEL STEERING ANGLE, VEHICLE GEOMETICS, AND WHETHER WHEELS ARE LOCKED OR FREE TO ROTATE) BUT NOT ON THE VEHICLE WEIGHT. THEORETICAL COMPUTATION OF TRAJECTORIES ARE COMPARED WITH EXPERIMENTS. /AUTHOR/

Engine with an annular chamber

Abstract: An engine comprises an annular chamber, a plurality of runners disposed in the annular chamber in a manner to be moved in the same direction by gas pressure through the annular chamber, the runners being divided into two equal groups each having at least two units, two rotor members respectively coupled with each group of runners, inertia imparting blocks attached to the respective rotor members so as to apply the momentum of the runners of one group to those of the other group by collision between the block associated with one rotor member and that coupled with the other rotor member, a power take off shaft journaled in bearings in a manner to be aligned with the rotating axis of the rotor members, two power transmitting members fixed to the power take off shaft so as to cooperate with each rotor member in the advancing direction of the runner, and means for preventing the rotor members from being moved backwards.

Axisymmetric Stress Wave Propagation in Sand

Abstract: Experiments were conducted in which a rigid cylindrical weight was dropped onto the surface of a bed of sand. Soil stress gages and soil strain gages embedded in the sand were employed to measure the soil response to the impacting weight. These measurements were analyzed to determine the effects of inertia on the soil behavior. Experimental results indicated, due to soil inertia during the intial phases of the impulse loading, the displacements were elastic with plastic behavior being evident in the stress measurements. Beyond the initial phase the inertia effects decreased and plastic behavior was noted in the strain and displacement measurements as well as the stresses. The results further indicated the response of a footing to an impulsive load may be divided into different inertial regimes depending on the rise time of the transient load.

On Fluid Inertia Effects in Infinitely Wide Foil Bearings

Abstract: : Equations for a foil over a lubricating film in which the effects of fluid inertia are taken into account are derived. Approximate solutions showing the effect of inertia and fluid compressibility are obtained. The effect of inertia is to increase the fluid film thickness. (Author)

Active Damping of Free-Rotor Gyroscopes during Initial Spin-Up

Abstract: The free-rotor gyro is so named because the nearly spherical gyrorotor is not mechanically constrained to rotate about a particular axis. Therefore, it may be initially spun up about any rotor fixed axis. As seen in the rotor, the subsequent motion of the angular velocity vector after spin-up is the well-known classical polhode motion about either the maximum or the minimum principal axes of inertia. The maximum axis of inertia is the desired spin axis direction because it is the only stable free-rotor spin direction in the presence of minute energy losses during flexures of the rotor. Consequently, the rotor-fixed markings used for spin axis readout of many of these gyros are referenced to the maximum axis of inertia. The principle delays in activating typical gyros are 1) waiting for a passive d.c. field to damp the gyro spin axis into the maximum axis of inertia of the rotor after it has been spun up (this requires typically five times the spin-up time) and 2) waiting for the thermal transient (of spin-up and damping) to subside. This paper describes a method of actively controlling the spin axis in the rotor, while leaving it unchanged with respect to a case-fixed reference. A control algorithm, called "Hemispheric Torquing" is used to actively damp the spin axis to the proper rotor fixed direction. It offers the advantage of being able to reduce damping times to less than is required for initial spin-up.

Deceleration-responsive sensors

Abstract: The invention is a deceleration-responsive sensor particularly adaptable for use with vehicle safety devices of the type comprising an inflatable air bag which inflates at the moment of impact to protect passengers. The sensor comprises a movable inertia mass responsive to deceleration forces acting over a wide range of direction. The inertia mass is biased to an initial position to avoid undesired continued small motion activation. The inertia mass and its mounting is constructed to have a natural frequency such that an activating deceleration force of predetermined magnitude and duration is required for the device to respond and trigger the safety mechanism.

Optimal control of nonlinear systems

Abstract: Conditions on the nature of nonlinearities in higher order systems which permit determination of analytical solutions for the Hamilton-Jacobi equations arising in the classical optimal control problem of quadratic cost function minimization are presented. The possible applications of the study are illustrated with an example from the field of aerospace systems, namely, optimum stabilization of a rigid body with variable inertia.

Classical and relativistic forces of inertia

Abstract: It is shown that — in contrast to the classical physics and special relativity — the self-consistency of general relativity requires that the forces of inertia follow unambiguously from the field equations as inductive gravitational effects of the cosmic matter and that this requirement is perfectly satisfied, without supplementary hypotheses, for the Einstein universe, in full agreement with Mach's principle.