Showing papers on "Inertia published in 1976"

Flow of a Newtonian fluid between eccentric rotating cylinders: Inertial effects

Abstract: A detailed analysis is carried out of the flow of a Newtonian fluid in the annular region between two infinitely long circular cylinders with parallel axes, resulting from the uniform rotation of one, or both, of the cylinders about their axes. No restriction is placed on the geometry of the system and results are obtained both with the neglect of inertial effects and for the linearized inertial approximation. In both cases, the resultant of the forces exerted by the fluid on the cylinders and the distribution of their normal and tangential components over the cylinders are calculated, and the stream-line patterns are analyzed in some detail. A number of conditions, under which stagnation points, separation points and eddies can exist, are established.

Squeezing flows of Newtonian liquid films - An analysis including fluid inertia

Abstract: A theoretical study is made of the flow behavior of thin Newtonian liquid films being “squeezed” between two flat plates. Solutions to the problem are obtained by using a numerical method, which is found to be stable for all Reynolds numbers, aspect ratios, and grid sizes tested. Particular emphasis is placed on including in the analysis the inertial terms in the Navier-Stokes equations. Comparison of results from the numerical calculation with those from Ishizawa's perturbation solution is made. For the conditions considered here, it is found that the perturbation series is divergent, and that in general one must use a numerical technique to solve this problem.

Thermal inertia imaging: A new geologic mapping tool

Abstract: A thermal model of the earth's surface has been developed and used to determine the thermal inertia of a test site in the Mojave Desert, California. The model, which includes meteorological heating terms as well as radiation and conduction heating terms, is used with remotely sensed surface temperature and reflectance data to determine the thermal inertia of the surface materials at the test site. The thermal inertia is displayed in image form, and can aid in the differentiation of the various lithologic materials in the test site. Since this thermal property is representative of the upper several cm of the surface, it complements visible and reflected near-IR image data.

Perturbation Solution for the Flat Spin Recovery of a Dual-§pin Spacecraft

Abstract: Euler's differential equations for free-body attitude motion are solved for the constant bearing axis torque recovery maneuver of a spacecraft with a symmetric rotor and asymmetric platform. The rotor bearing axis coincides with the spacecraft's centroidal principal axis of least inertia. The recovery time and the residual nutation angle are algebraically related to the initial flat spin rate, the spacecraft inertia properties, and the bearing axis torque. The differential equations are solved by use of two asymptotic parameter expansions of the multiple time scale type, which are matched to a transition expansion with a limit process matching procedure.

The principle of inertia in the Middle Ages

Abstract: Perhaps the most significant change in the transition from Aristotelian or medieval science to classical or Newtonian mechanics is the change from the Aristotelian view of ’’Omne quod movetur ab alio movetur’’ (’’All that is moved is moved by something else’’) to Newton’s first law or the principle of inertia that ’’Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed on it’’ [I Newton, Principia (Univ of California Press, Berkeley, 1960), Motte’s translation revised by Cajori, p 13] In this paper we shall show that this is not a sudden change but rather that it has a long and detailed history in the medieval critiques of Aristotle’s physics The treatment of the problems of motion in a void, projectile motion, falling bodies, and the inclined plane by medieval scientists makes this transition quite understandable

Dynamic Stability of Timoshenko Beams by Finite Element Method

Abstract: A Finite Element model is developed for the stability analysis of Timoshenko beam subjected to periodic axial loads. The effect of the shear deformation on the static buckling loads is studied by finite element method. The results obtained show excellent agreement with those obtained by other analytical methods for the first three buckling loads. The effect of shear deformation and for the first time the effect of rotary inertia on the regions of dynamic instability are investigated. The elastic stiffness, geometric stiffness, and inertia matrices are developed and presented in this paper for a Timoshenko beam. The matrix equation for the dynamic stability analysis is derived and solved for hinged-hinged and cantilevered Timoshenko beams and the results are presented. Values of critical loads for beams with various shear parameters are presented in a graphical form. First four regions of dynamic instability for different values of rotary inertia parameters are presented. As the rotary inertia parameter increases the regions of instability get closer to each other and the width of the regions increases thus making the beam more sensitive to periodic forces.

Multidomain multiphase fluid mechanics

Abstract: A set of multiphase field equations—conservation of mass, momentum and energy-based on multiphase mechanics is developed. Multiphase mechanics applies to mixtures of phases which are separated by interfaces and are mutually exclusive. This is in contrast to the field equations of mixtures based on continuum mechanics which directly applies to molecular mixtures where the phases coexist at the same points in space. Based on the multiphase mechanics formulation, additional terms appear in the field equations when the physical size of the dispersed phase (bubble or droplet) is many times larger than the inter-molecular spacing:These terms are the' inertial coupling due to virtual mass and the additional viscous coupling due to unsteadiness of the flow field. These physical effects as well as the continuum inertia! coupling terms were neglected in many other two-phase calculations. By including this inertial coupling term, the onedimensional multiphase equations are found to give real characteristics. Furthermore, the sum of momentum equations of all phases reduces to the momentum equations of the mixture as should be expected.

Aeroelastic analysis for helicopter rotor blades with time-variable, non-linear structural twist and multiple structural redundancy: Mathematical derivation and program user's manual

Abstract: The differential equations of motion for the lateral and torsional deformations of a nonlinearly twisted rotor blade in steady flight conditions together with those additional aeroelastic features germane to composite bearingless rotors are derived. The differential equations are formulated in terms of uncoupled (zero pitch and twist) vibratory modes with exact coupling effects due to finite, time variable blade pitch and, to second order, twist. Also presented are derivations of the fully coupled inertia and aerodynamic load distributions, automatic pitch change coupling effects, structural redundancy characteristics of the composite bearingless rotor flexbeam - torque tube system in bending and torsion, and a description of the linearized equations appropriate for eigensolution analyses. Three appendixes are included presenting material appropriate to the digital computer program implementation of the analysis, program G400.

Damping device for a stepper motor

Abstract: A device for damping the natural oscillations of the rotor of a stepper motor. A permanent magnet is fixed to the rotor and magnetically coupled with an inertia mass constructed of material with distinct hysteresis. The rotor is damped by conversion of mechanical momentum to hysteresis loss.

Acceleration sensitive motion snubber

Abstract: Relative axial movement of telescopically mounted support members is converted to rotation of an inertia mass by means of a ball-screw arrangement and a capstan spring loosely surrounding a portion of one of the support members. Slow acceleration of the inertia mass is accommodated, but rapid acceleration causes the inertia mass to lag which winds the capstan spring enough to grip one of the support members, which are rotationally fixed, and thereby snub movement until acceleration forces decrease. A spring band clutch positioned within the inertia mass and linked to the capstan spring ends enables the mass to slip in the event high velocity movement of the support members occurs and is then interrupted.

Development of the Equations of Motion and Transfer Functions for Underwater Vehicles.

Abstract: : Derivation of the linear, small-perturbation equations of motion for underwater vehicles is presented These equations include the inertial, hydrodynamic, and gravity-buoyancy forces and moments Necessary assumptions are introduced to linearize the equations and decouple the longitudinal from the lateral motions Solutions to the equations are obtained by Laplace transform techniques Complete expressions for the transfer functions are given in terms of the hydrodynamic coefficients An example problem is presented to provide typical values for the characteristic vehicle motions (Author)

Computation of geometrical and inertial properties for general areas and volumes of revolution

Abstract: Methods are developed to compute geometrical and inertial properties for regions of general shape. Formulae are deduced which show the changes occurring in plane or axisymmetric inertia properties when reference axes are subjected to a linear transformation. Various two-dimensional integrals are transformed into line integrals convenient for numerical evaluation. An 1100 statement FORTRAN program determining area and volume properties for regions bounded by contiguous circular :arcs and straight line segments is discussed. More concise exact results applicable in the case of straight line boundaries are obtained. Several numerical examples are presented which illustrate the versatility of the program.

Hydrodynamic forces and moments acting on a body emerging from an infinite plane

Abstract: An iteration procedure has been developed for calculating the time‐dependent velocity potential on the wetted surface of a prescribed body emerging into a fluid from an infinite, moving plane at an arbitrary angle of attack. The mathematical singularities encountered in the velocity‐potential computations are removed by exact, analytical means. The classic motion equations of Kelvin–Kirchhoff have been extended for the present case to include the effects of the time‐varying inertia terms. A simple illustrative example, that of a half‐emerged sphere, is given. Numerical values obtained are compared with those of the pressure integration method, and of an exact analytically derived solution. Numerical solutions for a spheroid of fineness ratio 2 with linear and angular velocities emerging from an infinite, moving plane at two different angles, are presented.

Is gravity getting weaker

Abstract: Dirac's large-numbers hypothesis and Mach's principle of inertia which both predict that the strength of gravity decreases with time are discussed. Experiments to test this hypothesis such as observations of lunar occultations, lunar laser-ranging measurements and precise radar-ranging measurements are being carried out. Preliminary data indicate that the value of G is decreasing. One implication according to the large-numbers hypothesis is that the number of nucleons in the universe must be increasing at a rate proportional to the passage of time squared. A theory is proposed to account for this phenomena based on the hypothetical existence of a shield against gravity found only in very dense matter. Implications for the theories of special and general relativity are discussed. (BJG)

Latch structure for vehicle seats

Abstract: The disclosure relates to an inertia operated latch structure for preventing forward movement of a pivoted vehicle seat back upon impact or sudden deceleration. The latch structure comprises a primary inertia member supported for pivotal movement between a normal released position and an inertia induced locked position. The primary inertia member includes a track in which a secondary inertia member is positioned. The primary inertia member is movable from a normal position to an inertia induced position upon sudden deceleration and is maintained in this latter condition by the secondary inertia member.

Dynamic analyses of suspension bridge structures

Abstract: A method of dynamic analysis for vertical, torsional and lateral free vibrations of suspension bridges has been developed that is based on linearized theory and the finite-element approach. The method involves two distinct steps: (1) specification of the potential and kinetic energies of the vibrating members of the continuous structure, leading to derivation of the equations of motion by Hamilton's Principle, (2) use of the finite-element technique to: (a) discretize the structure into equivalent systems of finite elements, (b) select the displacement model most closely approximating the real case, (c) derive element and assemblage stiffness and inertia properties, and finally (d) form the matrix equations of motion and the resulting eigenvalue problems. The stiffness and inertia properties are evaluated by expressing the potential and kinetic energies of the element (or the assemblage) in terms of nodal displacements. Detailed numerical examples are presented to illustrate the applicability and effectiveness of the analysis and to investigate the dynamic characteristics of suspension bridges with widely different properties. This method eliminates the need to solve transcendental frequency equations, simplifies the determination of the energy stored in different members of the bridge, and represents a simple, fast and accurate tool for calculating the natural frequencies and modes of vibration by means of a digital computer. The method is illustrated by calculating the modes and frequencies of a bridge and comparing them with the measured frequencies.

Inertia of energy and the liberated photon

Abstract: We follow through the different variants of Einstein’s intuitive photon‐in‐a‐box derivation of the inertia of energy, and end with the very simple ’’radiating atom’’ derivation.

Rolling motion of a sphere on a plane boundary in oscillatory flow

Abstract: The rolling motion of a sphere on a smooth plane boundary in a simple-harmonic water motion has been analytically and experimentally investigated. For spheres having specific gravities ranging from 0·09 to 15·18 the sphere motion was found to be sinusoidal for both low and high values of the period parameter defined by Keulegan & Carpenter. The knowledge of the sphere motion, and hence the resultant force, allowed the determination of inertia and drag coefficients from Fourier-averaging techniques. Experiments in the inertial range yielded an added-mass coefficient of 1·2, compared with 0·67 from inviscid theory for translating spheres. For values of the period parameter greater than 30 the drag coefficient is reported to be approximately 0·74.

Torsional vibration damper measuring

Abstract: An apparatus and method for determining the response and performance of a torsional vibration damper. Normally aligned optical patterns are placed on an axial face of the hub and on an axial face of the inertia member. Light is projected on and reflected from both the pattern on the hub and the pattern on the inertia member. Displacement of the hub and inertia member and the phase relationship between the displacements is sensed during rotation by reflected light passed to two photocells. The performance of the damper, including its dynamic response, is computed by comparing the outputs of the two photocells and may be read by meters.

Device for automatic signalling of an automotive vehicle damaged by collision

Abstract: An inertial sensor device for automatically operating warning means in an automotive vehicle is provided which comprises an inertia block slidably mounted in tubular guide means and sensitive to acceleration and deceleration of the vehicle in two opposite predetermined directions relative to the axis of the vehicle, the inertia block being normally biased by two springs oppositely acting on said block to prevent a striker from moving into a striking position until inertial forces in one or the other of said directions are developed sufficiently to move the inertia block, against the action of said springs, a sufficient distance to release the striker for operating a utilization device.

Physical Principles of Locomotion

Abstract: Locomotion is the act of moving from place to place. Since motion is involved, Newton’s laws governing the motion of a particle, as used in mechanics and in particular in dynamics, are recalled and used as a starting point. It is obvious that the application of a force to a stationary body produces motion by overcoming inertia and by overcoming such restraining forces as friction and viscosity of the surrounding environment. Without the application of a force or forces no voluntary movement, in this case locomotion, can take place.