Showing papers on "Displacement (vector) published in 1981"

On the displacement height in the logarithmic velocity profile

Abstract: The displacement height appears in the logarithmic velocity profile for rough-wall boundary layers as a reference height for the vertical co-ordinate. It is shown that this height should be regarded as the level at which the mean drag on the surface appears to act. The equations of motion then show that this also coincides with the average displacement thickness for the shear stress.A simple analytical model, experimental results and dimensional analysis are all used to indicate how the displacement height depends upon the detailed geometry of the roughness elements.

Segregation of cognitive and motor aspects of visual function using induced motion

Abstract: Targets were displaced to cancel an apparent displacement induced by a step motion of a background or were held stationary while appearing to jump in an induced displacement. Target and background were then extinguished, and the subject pointed to the target’s last position. When the target had appeared to move but did not, background position did not significantly affect pointing; when the target had moved but appeared to remain stationary (displacement canceled by opposite induced displacement), pointing depended upon the target’s egocentric position. A similar result was obtained with sinusoidal motion. In terms of a two visual-systems hypothesis, the motor system uses more veridical spatial information and is less affected by relative changes in two retinal signals than is the cognitive system.

Global invertibility of Sobolev functions and the interpenetration of matter

Abstract: A global inverse function theorem is established for mappings u: Ω → ℝn, Ω ⊂ ℝn bounded and open, belonging to the Sobolev space W1.p(Ω), p > n. The theorem is applied to the pure displacement boundary value problem of nonlinear elastostatics, the conclusion being that there is no interpenetration of matter for the energy-minimizing displacement field.

Speckle Displacement and Decorrelation in the Diffraction and Image Fields for Small Object Deformation

Abstract: Laser-speckles show displacement accompanied by structure change when diffuse objects generating them undergo displacement and/or deformation. This behaviour is theoretically investigated by calculating the cross-correlation functions of speckle intensities before and after the deformation. The dependences of speckle displacement on geometries of object illumination and speckle observation as well as on deformation parameters are clarified. The relations derived are interpreted physically by introducing the shift in diffraction rays due to displacement and deformation of a grating. Distributions of speckle displacement are calculated numerically and shown graphically.

Free-Vibration Analysis of Rotating Beams by a Variable-Order Finite-Element Method

Abstract: The free vibration of rotating beams is analyzed by means of a finite-element method of variable order. This method entails displacement functions that are a complete power series of a variable number of terms. The terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and, additionally, displacements at certain points within the element. The displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series. Numerical results are presented for uniform beams with zero and nonzero hub radii, tapered beams, and a nonuniform beam with discontinuities. Since the present method reduces to a conventional beam finite-element method for a cubic displacement function, the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom. Indeed, essentially exact eigenvalues and eigenvectors are obtained with this technique, which is far more rapidly convergent than other approaches in the literature.

Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams

Abstract: Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.

Video signal interpolation using motion estimation

Abstract: Information defining elements of a picture is estimated by interpolation using information from related locations in preceding and succeeding versions of the picture. The related locations are determined by forming an estimate of the displacement of objects in the picture. Displacement estimates are advantageously formed recursively, with updates being formed only in moving areas of the picture. If desired, an adaptive technique can be used to permit motion compensated interpolation or fixed position interpolation, depending upon which produces better results.

Photo-displacement imaging

Abstract: A modulated laser beam, incident on a surface, gives rise to a time-varying surface displacement. This displacement can be detected by means of a laser interferometer, thereby forming the basis for a novel imaging system. Preliminary results to demonstrate the viability of such a technique are presented.

Controlled motion apparatus

Abstract: A controlled motion apparatus capable of at least three degrees of freedom, such as apparatus for vibration testing of equipment, comprises a support suspended from a reaction mass by three anti-rotation, linear motion displacement actuator devices each extending and movable along one axis of an XYZ coordinate system. Each actuator may be independently activated to cause the support to undergo simultaneously controlled motion along the three axes.

The determination of displacement fields from geodetic data along a strike slip fault

Abstract: Observations of angles or distances between stations of a geodetic network are commonly used to infer information about the movement of the surface of the earth. The absence of any observations external to the network leads to an ambiguous displacement field. Existing techniques for eliminating this ambiguity are all unsatisfactory in some respect. The best technique, an ‘inner coordinate’ solution, is not appropriate for networks located in a strike slip fault environment. The inner coordinate solution zeros the rotation of all stations about their center of mass. Along a strike slip fault like the San Andreas, however, motion normal to the fault is less likely than motion parallel to the fault. The solution presented here, an ‘outer coordinate’ solution, finds the rotation of the network that minimizes the components of displacement normal to the fault. Since motion along a strike slip fault is generally expected to be parallel to the fault, the displacements obtained with the outer coordinate solution are more reasonable than those obtained with other techniques. Examination of a trilateration network near San Francisco Bay demonstrates the large effect that the choice of adjustment technique can have on the inferred relative motion of the two sides of the fault. The inner coordinate solution gave a rate of about 1 mm/yr, whereas the preferred outer coordinate solution rate was 36 mm/yr.

The displacement and stress fields of a general dislocation close to a free surface of an isotropic solid

Abstract: The displacement and stress fields of a dislocation with any Burgers vector which meets the surface of a semi-infinite isotropic solid at any angle are given in an explicit form.

Quasi-static displacements due to faulting in a layered half-space with an intervenient viscoelastic layer.

Abstract: This paper presents a method for the computation of quasi-static surface displacements caused by the sudden appearance of a dislocation in a stratified elastic half-space with an intervenient, Maxwellian viscoelastic layer. Integral representations of the displacements are derived from those in the associated elastic case by applying the correspondence principle of linear viscoelasticity. Evaluation of the integral is carried out by using a method of approximating a part of the integrand by an analytical function. The surface motion consists of an instantaneous elastic rebound at the time of faulting and a transient viscoelastic movement after the event. Time dependent properties of the viscoelastic movement are formally prescribed by a certain number of time constants, those are functions of a wave number determined by the rheological structure of the medium. General features of the viscoelastic movement are investigated from various aspects. First, changes in the displacement profiles with dip-angle are examined for the point dislocation sources located in the elastic surface layer of a three-layered model at different depths. Second, variations of the displacement profiles with time are examined for various structure models with different thicknesses of the viscoelastic layer. Finally, the vertical and horizontal displacement fields due to a finite-dimensional fault are calculated for a three-layered model, and compared with those for different types of structure models, such as a viscoelastic half-space model and a two-layered model which consists of an elastic layer overlying a viscoelastic half-space.

Sea ice displacement from Seasat synthetic aperture radar

Abstract: Images obtained by a synthetic aperture radar on SEASAT have been used to measure sea ice displacements over a three day interval in October 1978. The position of a natural ice feature was measured on 5 October and again on October 8; the difference in these two positions is a displacement. The displacement of many features was measured. The tracked features lie roughly along a line and are quite dense—about 2 km apart—over a distance of 865 km. The displacements are about 20 km. Displacement errors grow with distance from shore becoming as large as 3 km. The graph of displacement versus distance has occasional discontinuities of several kilometers. Displacement discontinuities are accurate to ±0.07 km along track and 3% of their magnitude across track.

Ink jet printing using electrostatic deflection

Abstract: Electrostatic deflection is used in an oscillating bar drop-on-demand ink jet printer to compensate for about one half of the droplet displacement caused by bar velocity. The disclosed system provides a method for printing that is not sensitive to variations in ink droplet ejection velocity.

Algorithms based on optimality criteria to design minimum weight structures

Abstract: The paper deals with the minimum weight design of structures with stress and displacement constraints. The various algorithms based on an optimality criterion are derived with different degrees of ...

Periodic displacement and stress fields near a phase boundary in the isotropic elasticity theory

Abstract: The elastic stress and displacement fields near a periodic boundary separating two different media are derived in the frame of the classical isotropic elasticity theory by using a Fourier series analysis. The coefficients of the trigonometric terms are found from the solution of a linear system of twelve equations with twelve unknowns for any planar boundary structure which has a one-or a two-dimensional periodicity. Analytical solutions of this system are given for a structure having a one-dimensional periodicity only, or for two media having the same Poisson's ratio. Applications to extrinsic and intrinsic (or misfit) dislocation networks emphasize the close connection between the two corresponding displacement fields. For cases where the dislocations are parallel, coplanar and without any related long-range stresses, calculation gives estimates of the elastic energy contribution to the phase-boundary free energy.

Self-positioning welding or cutting torch

Abstract: A sensor for detecting the relative position of a workpiece with respect to the tip of a welding or cutting torch, which is movable in optional directions by positioning devices, is provided with a sensing body in annular form which surrounds the tip and is adapted to make contact with the workpiece on any side of the central opening of the sensing body. An arm is attached to the sensing body and is displaced in a direction and to a degree corresponding to the displacement of the sensing body. The displacement of the arm is detected and a signal corresponding to that displacement is generated to reposition the welding head in response to the signal.

Capacitive transducer for accurate displacement control

Abstract: The underlying theory, design, and operation are presented for an interdigitated capacitive displacement transducer supported on an air-bearing stage. This device provides a purely electrical means of displacement measurement and offers the possibility of being closely matched to the substrate against thermal perturbations. Tests on a prototype system show the basic capacitive transducer to have a sensitivity of 2.6 mV/μm and a position uncertainty of 4 nm set by thermal noise.

Dispersion curves for waves in a cubic micropolar medium with reference to estimations of the material constants for diamond

Abstract: The authors start with an analytical study on the propagation of plane harmonic waves in an infinitely extended, cubi-anisotropic, elastic, and micropolar medium. It is possible to have six fundamental waves. Of these, a longitudinal uncoupled displacement wave and two coupled transverse waves of displacement and microrotation which become uncoupled with become uncoupled displacement waves at the limit of long wavelength are compared with the acoustical waves in the classical theory. The micropolar elastic constants of diamond, as well as its local moment of inertia, are estimated under the requirement that the theoretical dispersion curves for these waves fit the experimental data. Numerical computations are carried out and the results are made into a table.

An axisymmetric infinite element

Abstract: A parametric infinite element is presented for solving axisymmetric problems under non-axisymmetric forcing functions where the considered domain is assumed infinite. The element accuracy is compared against the exact solution for two classical problems: Boussinesq's and Cerruti's. Boussinesq's problem for a rigid circular plate is also presented. For these problems, using relatively simple displacement functions, the element provides a reasonable infinite domain representation.

Device for determining the real or the virtual distance of a source of light from a measuring plane

Abstract: The invention relates to a device for determining the real or the virtual distance of a source of light from a measuring plane. Such devices are preferably employed in position detectors in which light produced by a light source is caused to impinge on the surface of the object to be measured, said light being reflected from said surface towards a photodetector. The light emitted by the light source is imaged at different points on said detector, this depending on the position of the surface of the object to be measured, it thus being possible to draw a conclusion as regards the position of said object. According to the invention, the imaging system and the position-sensitive detector form a rotationally symmetrical arrangement. This renders the function of the device independent of any lateral displacement of the light source, of a displacement of the "center of gravity of illumination" as caused by different degrees of reflexion or scattering produced by the surface of the object to be investigated, and of the shape of the surface of the object to be investigated.

Continuously variable ratio power transmission

Abstract: A power transmission is provided characterized by smoothly and continuously variable gear ratios between the input and output shaft by incorporating a no-load restraint means for the ring gear of a ring, planetary and sun gear transmission system, the restraint comprising a wobble plate pump operative in a closed liquid circuit and driven by said ring gear to impose a restraint on same which varies according to an external control of the angle of the wobble plate and also including a second wobble plate pump in the same closed line or loop as the first pump and which is driven by the output shaft and whose liquid displacement capabilities per cycle is determined as a function of the wobble plate angle which may be controlled either manually or by the pressure at the liquid output line from the first pump.

Auxiliary drive system for combines

Abstract: A self propelled combine having forward main drive wheels and rear steerable wheels. A hydrostatic drive including a variable displacement motor is arranged to drive the main drive wheels. An electronic-hydraulic control system is automatically operable to drive the rear steerable wheels in response to sensing preselected pressure and combine attitude values while automatically varying the displacement of the hydrostatic drive motor to minimize combine speed changes and to provide torque as required under varying loads imposed by hilly terrain or increasing amounts of grain collected in the grain tank of the combine.

Web aligning process and apparatus

Abstract: An apparatus is disclosed for aligning at least two running webs with each other. It is characterized in that any lateral displacement is corrected at a position at a predetermined distance upstream of the displacement detection point or where excessive tension is not applied to the web to be corrected. Further, correction is made taking into consideration the time for the displacement detectors to follow the web movement and the time for the web to come back to a stable condition after splicing.

The determination of mode shapes for dynamically loaded rigid-plastic structures

Abstract: Mode solutions in rigid-plastic structures subjected to fixed external loads are dynamic solutions which are products of separate functions of space and time. If the small displacement assumptions are adopted, there will exist at least one mode shape for any structure subjected to given fixed external load, and possibly a multiplicity of modes. The time function is a simple linear function, and is easily determined once the mode shape is known. The paper puts forward, a simple in physical terms, algorithm for the determination of mode shapes. An iterative procedure is established in which each iteration is equivalent to the solution of a static limit analysis problem. Convergence is proved.