Showing papers on "Inertia published in 1971"

The Dynamics of a Current Collection System for an Electric Locomotive

Abstract: The motion of an overhead trolley wire, suspended at equal intervals by stiff springs, in response to a pantograph moving with constant speed is analysed. The pantograph is modelled by two discrete masses connected by springs and dampers. Away from the supports the inertia and elasticity of the pantograph can be neglected and a simple solution for the wire and pantograph displacement is obtained. Near a support this solution is not valid as it predicts discontinuities in the vertical pantograph velocity. A different first approximation is then required in which the support elasticity and the pantograph inertia and elasticity must be included. This problem is reduced to that of solving a system of four linear differential equations containing one term with a stretched argument. The numerical and asymptotic solution of such a system is discussed and results are obtained for the contact force and pantograph displacement near a support in typical operating conditions. This disturbance at the support is propagated with the wire wave speed and reflected at the subsequent support, thus interacting with the pantograph again. This interaction is analysed and a uniformly valid solution obtained for the contact force over a complete span. Some conclusions are made about possible operating conditions in which loss of contact between the pantograph and the wire may occur.

Axisymmetric Vibrations of Isotropic Composite Circular Plates

Abstract: A Kirchhoff‐type theory is established for axisymmetric motions of heterogeneous isotropic circular plates. It is shown that a coupled extensional‐flexural inertia term exists, in addition to the classical extensional and rotatory inertia terms. An analogy is found between the composite plate problem and the vibrations of homogeneous shallow spherical shells. The obtained sixth‐order system of equations is solved in closed form in terms of Bessel functions, with an argument determined from a characteristic cubic equation. A transcendental frequency equation is then derived for a circular composite plate with clamped edge conditions. Numerous examples are studied, showing the significant effect of plate heterogeneity on its vibrational response. Possibility of composite systems to transcend the frequencies of the individual constituents is clearly indicated by the theoretical results and checked experimentally.

On the Parametric Resonance of a Cylindrical Shell Subjected to a Periodic Axial Load

Abstract: The dynamic stability of thin‐walled circular cylindrical shell is studied for the case of periodic axial load. In computing the internal membrane stress induced by the axial pressures, the cylinder is assumed to act as a longitudinal bar. The internal membrane stress is computed by considering the shell to be a longitudinal rod with axial inertia terms included. Hence, the internal axial coordinate as well as with time and to include the resonances of the cylinder acting as a longitudinal rod. The problem under study is to determine the stability of the flexural motions of the shell oscillating about this inextensional mode. The shell motion is represented by Donnell's equations. A study of the solutions of these equations reveals parametric resonance of the well‐known type and a second parametric resonance which appears to be new. The latter includes the combination resonance between two modes having the same modal pattern, and also between two modes having different modal patterns. In particular, this includes combination resonance between two transverse modes having a different number of axial half waves. This result is believed to be new and is considered the principal result of the study being described. It is only obtained when axial inertia is included in computing the axial membrane stress. It is found that combination resonance does not exist between modes having a different number of circumferential waves. The two modes must have the same number of axial waves. An estimate is given for the width of the unstable regions, and numerical results are presented. The extension to a shell having the effects of rotatory inertia and shear deformation is briefly discussed.

Stable Member Equations of Motion for a Three-Axis Gyro Stabilized Platform

Abstract: This paper presents a detailed development of the equations of motion for the stable member of a three-axis platform. Kinematic relations are presented for an x, z, y Euler sequence. This development includes the effects of friction, inertia, and torque motors. A set of six first-order differential equations of state are presented representing the equations of motion of the system members. These equations may be integrated and the resulting Euler angles and rates used to describe the stable member motions. When combined with the servo loops, the motion of the stable member represents the angular motion environment of the stable member mounted instruments.

Lateral Structure Interaction With Seismic Waves

Abstract: The interaction of lateral structural inertia forces with horizontal seismic motion is formulated in terms of an integral equation of the Volterra type. By means of normal mode theory the inertia force at the base of the structure is expressed as a function of the foundation motion. After the motion of the two-dimensional elastic half space resulting from a uniform horizontal foundation force varying arbitrarily with time over a specified interval on the boundary of the half space has been determined, the interaction equation is derived. Numerical studies for two free-field acceleration inputs are made for different ground stiffnesses and structural characteristics. The first of these free-field inputs is a ramp sine function and the second is the east-west ground acceleration recorded at Golden Gate Park during the 1957 San Francisco earthquake. The interaction effects for structures similar to nuclear power plants prove to be significant.

Static means for generating inertia compensation signals in reel drives

Abstract: Static circuit means is provided for generating an inertia compensation signal in response to a first input signal proportional to the diameter of strip material on a reel and a second signal proportional to the linear acceleration, or deceleration, of the strip material. The inertia compensation signal is utilized in the control for the reel drive motor to maintain strip tension substantially independent of changes in line velocity of the strip.

Effects of Wall Inertia on Cylindrical Magnetic Domains

Abstract: The effects of wall inertia on cylindrical magnetic domains are considered, with attention to internal motion and to motion of a domain as a whole. Criteria are given for determining the importance of inertial effects in different materials and under various conditions. The range of validity of the concept of domain‐wall mass is discussed.

Librations of Gravity-Oriented Satellites in Elliptic Orbits through Atmosphere

Abstract: The coupled librational dynamics of gravity-orien ted, axisymmetric satellites in elliptic orbits is investigated. An approximate closed form solution is obtained using variation of parameter approach to study the effect of eccentricity and inertia on the response. The plots for stability in the large, generated numerically, show the transverse motion to be relatively more stable. Since in the presence of atmosphere the static equilibrium configuration varies continuously with the satellite's orbital position, the response becomes relatively complex and the stability region diminishes rapidly. However, with a suitable choice of a velocity-sensitive, semipassive controller, the normally destabilizing aerodynamic moment can be used to advantage in damping the librational motion.

Effects of products of inertia on re-entry vehicle roll behavior

Abstract: Ballistic re-entry vehicles having lateral center-of-gravity offsets (mass asymmetries) exhibit anomalous roll behavior as a result of trim-angle-generated lateral aerodynamic forces. The trim angles caused by mass and aerodynamic asymmetries have been thoroughly investigated. However, inertia asymmetries, which result when the principal axes of the vehicle become inclined with respect to the body reference axes, are a source of trim angle which has not been considered in detail. This paper presents a linear quasi-steady theory which demonstrates that inertia asymmetries are 1) more effective than equivalent mass and aerodynamic asymmetries in generating trim angles over the super-resonant region of re-entry flight; 2) equally as effective at resonance; and 3) less effective over the subresonant region. The predictions of the theory are verified by numerical integrations of the complete equations of motion and by the the results of three angular degree-of-freedom wind-tunnel experiments.

Low inertia motor for fluid operated tool

Abstract: A rotary vane expansible chamber fluid motor having a rotor member constructed with relatively large axially extending grooves formed between the radially extending vanes. The moment of inertia of the rotor member is substantially less than a comparable cylindrical rotor and the expansible chamber volume is greater than a conventional rotary vane motor. The motor is advantageously used in fluid operated tools for tightening threaded fasteners.

Lyapunov methods applied to multimachine transient stability with variable inertia coefficients

Abstract: The paper is a contribution to the transient-stability study of multimachine power systems by Lyapunov's direct method. The mathematical model used is more rigorous than those already taken into account in that the machines' inertia coefficients are no longer considered as constant but varying with angular speed. This constitutes a more accurate approach to the transient-stability problem. A 9-machine realistic power system illustrates the proposed method, and permits comparisons and conclusions to be made.

The Effect of Fluid Inertia on a Porous Thrust Plate—An Analytical Solution

Abstract: A theoretical analysis was made to study the effect of fluid inertia on a porous thrust plate. The most elementary configuration was chosen as an analytic model to investigate this effect with a minimum of mathematical complexities. Numerical data were obtained for an incompressible film. The results reveal that the effect of fluid inertia can be important, depending on the film thickness H and a parameter Ω . For small value of H the inertia effect is essentially confined to a very narrow region near the edge of the bearing while for large values of H this effect spreads throughout the fluid film. This pressure boundary layer at low H is similar to that in a self-acting gas bearing. In general it was found that inertia effects tend to influence favorably the flow and load capacity of porous thrust plates.

Inertia balancing means for power presses

Abstract: In power presses such as are used for stamping sheet metal and the like, the inertia forces of the reciprocating slide of the press and its attached parts set up very heavy and objectionable vibrations, particularly in high speed presses. The present invention provides primary and secondary counterweights. The primary counterweights rotate with the crankshaft or eccentric shaft of the press but with the center of gravity of the counterweight moving in a direction opposite to the direction of movement of the slide to neutralize at least a portion of the inertia forces of the slide and its connected parts. The secondary counterweight rotates opposite to the first counterweight but with its center of gravity moving in the same direction with respect to the vertical, so that the second counterweight has a cumulative effect with respect to the primary counterweight in neutralizing vertical inertia forces but has a subtractive effect with respect to lateral inertia forces produced by rotation of the primary counterweight.

Calculations on the steered motion of a ship under the action of external forces (part 1) coursekeeping and turning of a ship in uniform wind and flow

Abstract: Considering the possibilities of solving the non-linear equations of motion numerically on a digital computer, the author contrived a method for numerical calculation of the steered motion of ships in uniform wind and flow. The aerodynamic forces and moments and the longitudinal hydrodynamic force were taken in as the intermittent functions of relative wind direction and the Froude number respectively, and were interpolated at need. The so-called rotary derivatives were decided by a least-squares method, up to the third order of transverse velocity, turning rate and rudder angle, from the tested points at various values of the parameters. The equations of motion were described on the absolute motion of ship, and the external and inertia forces and moments caused by the relative motions were calculated at every small time interval and integrated. As an example, calculations were carried out on a mammoth tanker regarding the required lowest speed and the course stability in a straight course and the turning behaviour in wind and flow. Results of the calculation on the turning characteristics in calm sea were compared with the tested results on a free-running model and on the actual ship. The following conclusions were obtained concerning the method of the calculation and the calculated results on the steered motions of a ship in wind and flow. (1) The non-linear equations of the un-steady motion of a ship can be calculated numerically on a digital computor. (2) The required minimum speed and the course stability in a straight course within the limits of definite rudder and drift angles can be calculated. (3) In some cases the course stability index has a periodic solution. (4) At the above-mentioned minimum speed, the ship tends to be course-unstable mainly in case of following wind, though the stability is improved by the higher ship speed. (5) The effect of wind and flow change remarkably according to the loading condition of ship. (6) The average direction of the macroscopic "drift" of the steadily turning ship does not necessarily coincide with that of the uniform wind or flow, and the average speed of the "drift" is smaller than that of wind.

Athletic false starts detector

Abstract: The present device is constructed for detecting false starts in athletic events. For this purpose inertia switching means are rigidly but nevertheless removably attachable to the starting plate so that any athlete may use his own individual starting plate. The inertia switching means comprise an insulating block and a conducting inertia body movably supported in said insulating block which also has supported therein two contact wires with exposed ends to be directly connected to each other when the entire insulating block moves in a given direction in response to a start while the electrically conducting inertia body remains briefly in position due to its inertia. A slope in the insulating block assures that the inertia body goes back to its non-contacting position.

Electrical switch acting with the force of inertia

Abstract: An inertia switch for the closing of an electrical circuit. Said switch comprises an electrically conductive cup-shaped inertia body supported on and resiliently urged toward an electrically non-conductive support means. Said support means has a recess receiving said inertia body and said recess is provided with angular sides. The inertia mass is surrounded by an electrically conducted casing spaced slightly therefrom. The inertia mass is normally held against the support means and away from contact with said casing but a disturbance thereof either axially or radially will move the support means against such resilient urging either axially or radially to effect contact between said inertia mass and the casing whereby to complete the electrical circuit.