Showing papers on "Inertia published in 1969"

On the response of beams to an arbitrary number of concentrated moving masses

Abstract: A theory describing the response of a beam under an arbitrary number of moving masses is developed. The theory is based on the Fourier technique and shows that, for a simply supported beam, the resonance frequency is lower with no corresponding decrease in maximum amplitude when the inertia is considered.

Water Hammer Analysis

Abstract: Simplified methods of calculating hydraulic transients are set forth, with techniques for increasing the computing time interval over that permitted by the characteristics method. Lumping and interpolation methods are compared with mixed implicit and characteristics methods. Complex boundary conditions are treated, including a spring-mass system with coulomb friction, an accumulator with inertia and fluid friction, pump failures, and column separation.

Application of matrix displacement methods in the study of panel flutter.

Abstract: A finite element approach to panel flutter problem has been attempted in this analysis. A method to derive the aerodynamic influence coefficient matrices kinematically consistent with the stiffness and inertia matrices, has been suggested. These matrices have been employed in the formulation of the dynamic equations of motion and the system of equations solved for their complex eigen values and vectors by the usual methods. This approach is general and is applicable to any boundary conditions. Some examples have been worked out, on a computer, for simply supported panels in supersonic flow and the results found to be in good agreement with those from other conventional methods.

Detailed Analysis of a Two-Stage Four-Way Electrohydraulic Flow-Control Valve:

Abstract: A detailed analysis is given of a flow-compensated, two-stage, four-way, closed-ports electrohydraulic flow-control valve Factors considered in the analysis of the first stage include: the electromagnetic forces generated by the torque motor, impedance of the motor coil, inertia of the flapper, viscous damping forces, spring forces, pressure feedback forces, and leakage flow Factors considered in the analysis of the second stage include the acceleration force on the spool, viscous friction forces, restraining spring forces, flow reaction forces, leakage flow, and the compressibility of the oilExperimental verification of the analytical work is included

Dynamic Response of Frames with Nonrigid Connectors

Abstract: A computer oriented method is described for determining the dynamic response of rectangular plane frames with nonrigid beam-to-column connections. The dynamic loads may be either lateral forces applied directly to the frame or inertia forces due to lateral acceleration of the ground. The moment-rotation relationships for the nonrigid connections are assumed to be bilinear, and the effects of elasto-plastic behavior in the columns, finite joint sizes, and initial vertical loads are included in the analysis. The results of analyses of a 10-story frame show that both lateral displacements and member end-actions are influenced to a large extent by the stifnesses of the connections.

On the Balancing of the Fluctuating Input Torques Caused by Inertia Forces in the Crank-and-Rocker Mechanisms

Abstract: Some methods have been investigated both theoretically and experimentally to reduce the fluctuating torques in the driving shafts caused by the inertia forces in the crank-and-rocker mechanisms; the spatial four-bar mechanism having two revolute and two spheric pairs is cited as an example. The fluctuating torque has been actually reduced to 1/20–1/3 .

Free damped oscillations in viscoelastic materials

Abstract: In a recent paper Struik has shown how approximate values of the dynamic viscoelastic functions for a material subjected to undamped oscillatory shear may be correctly deduced from observations on the free damped oscillation of a system in which the restoring force is provided by that material. On the assumption that the material has a discrete positive spectrum of relaxation times and negligible inertia, he was able to obtain bounds to the errors in the values of the dynamic functions as calculated from certain simple formulae involving the frequency and logarithmic decrement of the damped oscillations. In the present paper the work is carried a stage further by the calculation of attainable limits to the errors, and these are appreciably narrower than Struik's bounds. Further, it is shown that the results apply equally to cases in which the internal inertia of the material is important, provided there is no other elastic member in the oscillating system. The justification for assuming a discrete positive spectrum of relaxation times is briefly discussed.

Method of inertia welding

Abstract: A method of inertia welding wherein a pair of relatively rotatable workpieces are axially engaged under pressure at a common interface with one of the workpieces then being associated for rotation with a rotatable inertia mass or flywheel for transfer of rotational energy from the flywheel to the workpieces to accomplish a bond at their interface and the one workpiece then being dissociated from rotation with the flywheel.

Angular acceleration sensor with piezoelectric element

Abstract: A rotary accelerometer using a piezoxide (prepolarized ceramic piezoelectric element) A shaft drives a rotating mass in the form of a cylindrical sleeve through a resilient connection in one embodiment During angular deceleration, the rotating mass tends to lead because of inertia and the resulting force is applied to a cam device which converts that force into a compressive stress applied to the piezoxide to generate a voltage analog of deceleration In another embodiment a block mass is attached to a piezoxide block directly, so that inertial forces during deceleration are directly applied to the piezoxide The combination is then mounted so as to respond to tangential forces about a decelerating shaft

Variable inertia flywheel apparatus

Abstract: Variable inertia flywheel apparatus for use with a chassis dynamometer, during vehicle engine exhaust gas emission measurements. The apparatus simulates the effect of vehicle roadway-inertia loads on the engine during acceleration and deceleration, while the vehicle is being operated on the dynamometer. A wide range of inertia loads are simulated by three flywheels, each having a different mass; two of the flywheels are each driven from a main shaft, connected with a dynamometer roll, at two different speed ratios, and the third flywheel is driven from the same main shaft at three different speed ratios. More specifically, the flywheels are driven by sheaves and separate sets of belts that can be independently and selectively tensioned to drive one or more of the flywheels at a speed ratio relative to the speed of the dynamometer rolls so as to simulate the corresponding inertia loads. The third flywheel, which normally is in use at all times during a test, is designed to compensate for the inertia load of the particular power absorption unit, dynamometer rolls, drive belts, etc., with which the apparatus is used. Inertia load increments of 250 pounds can be simulated for testing vehicles weighing between about 1,500 pounds through 3,000 pounds, and 500 pound inertia load increments can be simulated for vehicles weighing between about 3,000 and 5,500 pounds. The flywheels are driven by sets of belts tensioned by idlers carried by shift plates operated by control levers that can be individually and selectively shifted to provide the 1,500 to 5,500 pound vehicle weight range of inertia loads, as well as a no-inertia load condition.

Hydraulic vibration damper

Abstract: An hydraulic vibration damper arrests vibration of a boring bar, lathe chuck, or other support. It comprises an inertia member adapted to be mounted on the support for vibration-induced movement. A case is mounted for relative movement on one end of the inertia member with its walls spaced from the walls of the latter. Seal means divide the space between the walls into two chambers. Both chambers are filled with mercury or viscous oil. Upon vibration of the support, the liquid is driven from one side to the other, providing an hydraulic vibration damping effect which supplements the inertia damping effect of the inertia member. In addition, frictional engagement of the end of the inertia member with the case provides a frictional damping effect.

Inertia systems for dynamometers

Abstract: An inertia system for supplying a predetermined amount of energy through a rotating shaft to a dynamometer or like apparatus to permit testing various devices such as brakes. The system includes rotatably supported inertia elements on preferably two shafts connected together by a gear train to permit a substantially infinite variation of inertia and at the same time reduce the required strength of the torque transmitting gearing by employing a connecting gear train.

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.

Inertia, relativity, and cosmology.

Abstract: Starting with the idea that the inertia of bodies is a general property of all kinds of their potential energy, the author arrives at the two fundamental “megaphysical” equations (I, II)0Π+c2=0,0ϕ=0 where0Π is the scalar gravitational potential due to the smoothed-out universe,0ϕ is its electrostatic potential andc denotes the light velocity in vacuo.

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.

Inertia Effect in Hydromagnetic Slider Bearing

Abstract: A theoretical investigation of inertia effects in an inclined slider bearing with an electrically conducting lubricant in the presence of azimuthal magnetic field is presented. It is shown that the load supporting capacity of bearing is increased for short circuit case if the lubricant inertia effects are taken into account. However, the inertia effect becomes smaller when the strength of magnetic field increases. In open circuit case for Hartmann number M≤4 the load capacity increases due to inertia and for M≥5 the load capacity decreases due to inertia. Further it is seen that the effect of inertia is rather small at Hartmann numbers 4.1, 4.2, 4.2 and 4.4 for Reynolds numbers .01, .1715, .25 and 1.39 respectively.

A Study of the Performance of Inertia Air Filters

Abstract: This paper presents an experimental and theoretical study of the design and performance of inertia air filters, with particular reference to rail traction duty. Using a specially constructed test rig, performance testing of commercially available filters was carried out over a wide range of operating conditions. Subsequently, a more fundamental study of some design variables was carried out in a small-scale test rig. The testing was supported by a theoretical approach using a digital computer model of the inertia filtration process. The results of the work indicate that the inertia filter is suited to high-volume, low pressure drop applications. However, operational difficulties, owing to dust build-up occurring within the filter and variations of bleed ratio, may be encountered.The theoretical model was shown to reproduce all the major operating characteristics of the filters measured in the test programme, and to respond to design changes in a similar way to that indicated by earlier published work. A h...

Effect of Lubricant Inertia in Bearings

Abstract: The inertia effects in squeeze film between two curved surfaces and externally pressurized bearing with a converging lubricant film are considered. It is shown that lubricant inertia for squeeze film bearing increases the load supporting capacity and decreases the squeeze. For externally pressurized bearing it is found that there is a negative contribution to the load supporting capacity by inertia forces.

Stability of Motions Involving Fluid Interfaces in Porous Media

Abstract: A theory of stability is developed which accounts for the effects of fluid inertia. The inertial effects are found to stabilize certain otherwise unstable situations in a manner analogous to that discovered by Taylor.

Effect of angular inertia of lubricant in MHD hydrostatic thrust bearings

Abstract: Circumferential motion of a conducting lubricant in a hydrostatic thrust bearing is caused either by the angular motion of a rotating disk or by the interaction of a radial electric field and an axial magnetic field. Under the assumption that the fluid inertia due to radial motion is negligibly small in comparison with that due to angular motion, it is found analytically that the rotor causes an increase in flow rate and a decrease in load capacity, while both are increased by the application of an electric field in the presence of an axial magnetic field. The critical angular speed of the rotor at which the bearing can no longer support any load is obtained, and the possibility of flow separation in the lubricant is discussed.

Testing apparatus for determining the mass inertia moment of a specimen

Abstract: A RECEIVER IN OPERATIVE PROXIMITY WITH A SUPPORT ROTATABLY SUPPORTING A SPECIMEN PRODUCES AN OUTPUT SIGNAL PROPORTIONAL TO THE ANGULAR VELOSITY OF THE SUPPORT AND SPECIMEN. A SIGNAL PROPORTIONAL TO THE OUTPUT SIGNAL IS SUPPLIED TO A DRIVE FOR THE SUPPORT TO APPLY TO THE SUPPORT A TORQUE CORRESPONDING TO THE ANGULAR VELOCITY OF THE SUP- PORT AND SPECIMEN. A CONTROL CIRCUIT CONNECTED BETWEEN THE RECEIVER AND THE DRIVE MAINTAINS THE ANGLE OF OSCILLATION OF THE SUPPORT AND SPECIMEN.

Vibrational and Stability Characteristics of Circular Membranes Subjected to Gyroscopically Induced Inertia Loads

Abstract: An analytical study is presented for the response of circular membranes subjected to a simultaneous state of constant spin and precessional motions at a fixed angle of nutation. The equations of motion are formulated for a random orientation of the membrane relative to the spin axis, from which a Hill equation may be obtained for the amplitude coefficients of the motion. A considerable reduction in mathematical difficulties occurs for two special, but frequently occurring, orientations of the membranes: (a) membranes perpendicular to the spin axis and (b) membranes parallel to the spin axis. These equations of motion contain distributed harmonic inertial forces that excite certain modes and whose amplitude and frequency depend on the spin and precessional motions. For Case (a), the natural frequencies of the membrane are reduced by the precessional angular velocity and angle of nutation, while for Case (b), it is necessary to solve a Mathieu equation with the associated stability characteristics for the amplitude coefficients of the motion.

On gas ingestion and fluid inertia effects in viscoseals.

Abstract: Turbulent viscoseals gas ingestion and fluid inertia analysis using stability of dynamic gas-liquid interface between rotating cylinders

Gyroscopically induced vibrations of circular plates

Abstract: An analytical study is presented for the vibrational response of simply supported and clamped circular plates subjected to gyroscopically induced, inertia loads. The plates are considered to be spinning at a constant rate while simultaneously undergoing a constant precession at a fixed angle of nutation. The equations of motion are formulated for members mounted either parallel or perpendicular to the spin axis and it is found that these equations contain distributed harmonic inertia forces whose amplitudes and frequencies are dependent on spin and precession. The solutions of these equations, obtained by Fourier-Bessel series expansions, show that the natural frequencies are reduced by the effects of spin and precession and that this effect may become appreciable for appropriate combinations of material properties and geometry. It is also shown that only certain modes of vibration respond to the gyroscopically induced inertia loading and that for members mounted parallel to the spin axis the motion is governed by a set of Mathieu equations along with the associated stability characteristics.