Showing papers on "Inertia published in 1975"

Transfer of Particles in Nonisotropic Air Turbulence

Abstract: The inertia of particles is the basis of the present model of particle “dry deposition” from a turbulent fluid. The basic physical concepts of particle thermal motion as described by Einstein are herein extended to describe the particle motion in nonisotropic turbulence in terms of a “turbophoretic” velocity. The particle transfer from the turbulent fluid to a collecting black surface is therefore described in terms of a differential motion describing the chain of “inertial flights” undergone by the particle under the gradient of turbulence velocity component in the direction of the collecting surface. This model of dry deposition shows satisfactory agreement with experimental values of particle deposition velocity as a function of particle size.

Two-dimensional analysis of the split hopkinson pressure bar system☆

Abstract: T he split Hopkinson pressure bar is widely used to measure the dynamic properties of solid materials. This paper presents the results of the first comprehensive two-dimensional numerical analysis of the technique, and quantitatively describes the effects of realistic friction and of variations in both the specimen geometry and the imposed strain-rate on the validity of the assumptions used in analyzing experimental data. A two-dimensional axisymmetric numerical analysis is used to compute all components of the stress, strain and strain-rate tensors at each mesh point within the specimen and the elastic bars. The calculated response of the pressure bars is used to reconstruct the stress-strain behavior of the specimen and this is compared to both the input stress-strain curve and the actual calculated stress-strain states in the specimen. Thus, the validity of the assumptions and the corrections used in the analysis of the data is determined. Inertia and friction between the specimen and the elastic bars affect the response of the specimen differently for different length-to-diameter ratios. Inertia effects produce stress waves propagating radially and axially in the specimen and may result in an oscillating reconstructed stress-strain curve. If the ends of the specimen are well lubricated and care is taken to minimize the effects of inertia, the reconstructed stress-strain curve agrees with the input. However, serious stress and strain nonuniformity exists when the ends are not lubricated and this results in a reconstructed stress-strain curve where, for any given strain, the stress magnitude is larger than the correct value. A comparison of the calculations with experiment shows excellent agreement for various interface conditions. Finally, the inertia correction of E.D.H. Davies and S.C. Hunter (1963) is found to be reasonable.

A new method for the simultaneous measurement of the movement of inertia, the damping coefficient and the location of the centre of mass of a body segment in situ.

Abstract: A new method which permits, in a single measurement, the determination of the moment of inertia, the angular damping coefficient of the joint and the location of the centre of mass of a body segmentin situ is presented. The underlying principle is the theory of small, damped oscillations of a system about its equilibrium position. The fact that the oscillogram contains information about certain parameters of the oscillating system is used to find these parameters. The application of the method is simple and does not require highly sophisticated instrumentation. The results are very reproducable and immediately available.

Dynamic Stability of Cylindrical Shells Under Step Loading

Abstract: A study has been made to determine the dynamic stability of an imperfect circular cylindrical shell subject to a step loading in the axial direction. In the analysis, the radial displacement of the shell is approximated by a finite degree of freedom system. To assure that the created model is proper, its static buckling behavior was studied. It was found that the model gives the proper imperfection sensitivity behavior. The dynamic analysis includes not only the effect of the radial inertia, but also that due to the axial inertia in an approximate manner. The critical loads are determined by numerical integration of the equation of motion. In addition a study is carried out to consider the effects of wave number of the radial mode shape, mass on the loaded edge of the shell and damping of the axial motion. Compared with the static case, there is a significant reduction of the dynamic buckling load for the high wave numbers of the radial modes. Also, there is a critical clamping value, above which the dynamic buckling load is close to the static buckling load. The dynamic buckling load approaches half of the static buckling load with increasing mass on the loading edge. Through the parametric studies of the wave number, mass, and damping factor it is concluded that due to frequency coupling between axial and radial motions, the axial inertia plays an essential role in characterizing the dynamic instability of a finite length shell.

Wind power and flywheel apparatus

Abstract: A flywheel is provided having a plurality of radially extending spokes having axial bores. Mercury disposed in the axial bores moves toward the hub at low speeds to decrease the angular inertia of the wheel and toward the rim at higher speeds to increase the angular inertia. The flywheel may be used with the wind machine apparatus described or other rotating apparatus.

Diurnal variations in the thermosphere 1. Theoretical formulation

Abstract: A nonlinear perturbation theory is formulated for the solution of the multicomponent equations of energy, mass, and momentum conservation in the atmosphere. The theory is three-dimensional and includes the effects of heat conduction and advection, viscosity, ion drag, and diffusion. The theory is described as a superposition of mathematical modes obtained by expanding the physical quantities into vector and spherical harmonics. The coupling between the various modes, both linear and nonlinear, is included. The theory provides a basis for the treatment of the thermosphere and its interaction with the lower atmosphere, where 'mode coupling' is most important. As an example, a comparison is presented between one-dimensional and three-dimensional calculations of the fundamental mode of the diurnal component in the thermosphere. Coupling between the lowest modes is considered to describe the physical conditions of the lower thermosphere where inertia and Coriolis forces become dominant over the ion-drag and viscous forces. In this region, the latitude structures of the temperature, wind field, and diffusively controlled oxygen are shown to change significantly.

An axially stressed railroad track on an elastic continuum subjected to a moving load

Abstract: The recent introduction of the welded railroad track raises the possibility that high axial compressive forces may occur in the rails due to constrained thermal expansions. This in turn may reduce the critical velocity of the track to within the operational velocities of present day trains. Recently the effect of axial forces upon the critical velocities of the track was analyzed byA. D. Kerr using the Winkler model for the base response. In this study, the effect of the axial compressive force on the critical velocity of the track is studied assuming for the base an elastic half space with inertia.

Earthquake induced pressures on a rigid wall structure

Abstract: This paper describes the application of linear elastic theory to estimate the earthquake-induced soil pressures on a wall forming part of the structure of a power station founded on rock. Analyses showed that the Mononobe-Okabe assumptions would not be applicable for this relatively rigid wall structure and it was found that elasticity theory gave greater forces and moments than would be obtained by using the Mononobe-Okabe method. The extent to which deformations of the structure and its foundations influence the wall pressures was investigated. It was found that even for this relatively rigid structure and foundation, the displacements resulting from the inertia of the wall structure can produce a significant increase in the total forces acting on the wall.

Dynamic Response of Cantilevers with Attached Masses

Abstract: Using generalized functions, the frequency equation for free vibrations of a cantilever beam-column having rotational and translational springs at its support, and carrying concentrated masses, is established in matrix form and is evaluated numerically. The effect of rotatory inertia of the concentrated masses is also included. Moreover, a procedure for establishing the mode shapes is presented. Finally, the differential equation for the modal amplitudes of forced motion is established.

Equation of motion of a solid particle suspended in a fluid

Abstract: Consistent approximation calls for taking into consideration the effect of inertia of the fluid in a pressure gradient thus canceling out the term due to static pressure alone. Inconsistency may lead to ill−posed formulations.

Forceless machian dynamics

Abstract: A model is proposed in which the inertial and gravitational forces of Newtonian mechanics (together with small Machian corrections) are derived from a single simple concept—mass in relative motion The model provides an example of the forceless dynamics, or dynamics of pure motion, mooted by Hertz If a velocity that occurs in the model is identified with the velocity of light, the correct order of magnitude of the gravitational constant is predicted

Bending and vibration of transversely isotropic two-layer plates

Abstract: T use of composite materials in various aerospace and industrial applications has prompted a considerable amount of research on the static and dynamic response of multilayer plates. During the past decade, several authors' have formulated plate theories by a direct extension of Mindlin's theory for homogeneous plates. Sun and Whitney have shown that laminated plate theories which are based on Kirchhoff's hypothesis, or a simple extension of Mindlin's theory, yield grossly inaccurate natural-frequency predictions for twoand three-layer plates whose layers have widely differing shear rigidities. In a recent paper, the principle of virtual work was used to derive the equations of motion in an invariant form for an arbitrary three-layered plate. No restrictions were placed on the relative thicknesses, densities, elastic moduli, or symmetries of the layers. The formulation accounts for the shear deformation of each layer as well as the translational and rotational inertia of the composite. Continuity of displacements and stresses was imposed in accordance with a perfect interface bond assumption. In the current analysis, the previously derived equations will be used to analyze a transversely isotropic two-layer plate by deleting the terms associated with the third layer and neglecting the transverse contraction of the composite. The theory then becomes the two-dimensional analog of Theory II as presented by Sun and Whitney. If we assume that each layer is transversely isotropic, the equations of motion are written in vector notation and can be uncoupled to yield a sixth-order equation in the transverse displacement. By neglecting certain in-plane and rotatory inertia terms, we can obtain a somewhat simpler fourth-order equation, which is very similar to Mindlin's dynamic plate equation with modified stiffness, mass, and inertia coefficients. This equation reduces to Mindlin's formulation if either of the layers is assumed to vanish or the properties of both layers are identical. From virtual work, the natural boundary conditions

Drive line vibration absorber

Abstract: A drive line vibration absorber, for a mass elastic system having an engine operatively connected to a gear train through an elongated drive shaft, includes an inertia mass disposed in parallel relation to such mass elastic system and a resilient ring secured to the mass elastic system in axially driving cooperation with the inertia mass and permitting limited torsional movement thereof for effectively reducing the amplitude of the relatively low natural frequency torsional vibrations of the mass elastic system.

Rubber torsional vibration damper with cooling means

Abstract: A vibration damper for rotating members consists of a hub member joined to an inertia member by a plurality of elastic elements Cooling fins on the inertia member and between the elastic element provide for dissipation of heat from the inertia member and the elastic elements The cooling fins are parallel to the side surfaces of the insertia member In an alternate embodiment, the cooling fins are angled to the side surfaces of the inertia member to augment the cooling effect of integral fins therein In further alternate embodiments the hub member is bifurcated and the cooling fins and elastic member are oriented at angles to the axis of rotation of the hub

Inertia power system

Abstract: An inertia power system in which the rotational energy stored in a rotating inertia wheel is translated into useful work. The system includes an inertia wheel which is electrically driven. A magnetic clutch is provided for engaging and disengaging the rotating inertia wheel into and out of driving relationships with a transmission assembly through which the rotation of energy of the inertia wheel is translated into useful work, e.g.; to drive a vehicle.

Elastomer and liquid torsional vibration damper

Abstract: A torsional vibration damper having two inertia members. A first inertia member is coupled to a hub by elastomer. A second inertia member is positioned within an annular cavity and is surrounded by a liquid of high viscosity. Under the influence of torsional vibrations relative movement arises between the hub and first inertia member, the hub and the second inertia member, and the first and second inertia members. The latter relative motion inhibits the attainment of resonance by either of the two inertia members.

Ball actuated inertia device

Abstract: A belt winder with a quick-locking vehicle inertia sensitive action including a ball and tipping member which can be brought into operative position in any mounting position in space.

Hydrodynamic modeling of fishing nets

Abstract: Design of efficient fish nets by means of small scale hydrodynamic models is of fairly recent origin in the United States. While investigators have developed basic equations for modeling flow around fish nets by considering the inertia and gravity forces as primary forces, they assume that the elastic deformations of twines and ropes in the net are negligible. However, the shape of the fish net and therefore the forces acting on it are affected by the elongation of twines and ropes under load. In order to allow the correct numerical transfer of model observations to the prototype, it is necessary to establish special hydrodynamic model laws which take the stress-strain characteristics of the model and prototype net materials into consideration. This paper outlines the establishment of such laws and their verification by full scale ocean tests and by laboratory tests. It is also shown how distortion of mesh and twine size prevents a relatively too high influence of viscous forces in the models.

On local inertia in Cosserat continua

Abstract: A new equation governing local rotational inertia is obtained here for all theories employing the Cosserat continuum with deformable director triad. This equation represents a condition necessary to insure the invariance of the rotational kinetic energy under superposed rigid body motions.

Wave Forces on Bottom-Mounted Large-Diameter Cylinder

Abstract: A systematic set of experimental results for the wave force acting on a large horizontal bottom-mounted circular cylinder is presented and compared with a simple theory based on an unseparated flow model. The horizontal force is represented as an inertial component while the uplift force is represented by a lift force arising from the flow velocity plus a Froude-Krilov component. The test results show agreement with the theory.