Showing papers on "Displacement (vector) published in 1973"

A note on tsunamis: their generation and propagation in an ocean of uniform depth

Abstract: The waves generated in a two-dimensional fluid domain of infinite lateral extent and uniform depth by a deformation of the bounding solid boundary are investigated both theoretically and experimentally. An integral solution is developed for an arbitrary bed displacement (in space and time) on the basis of a linear approximation of the complete (nonlinear) description of wave motion. Experimental and theoretical results are presented for two specific deformations of the bed; the spatial variation of each bed displacement consists of a block section of the bed moving vertically either up or down while the time-displacement history of the block section is varied. The presentation of results is divided into two sections based on two regions of the fluid domain: a generation region in which the bed deformation occurs and a downstream region where the bed position remains stationary for all time. The applicability of the linear approximation in the generation region is investigated both theoretically and experimentally; results are presented which enable certain gross features of the primary wave leaving this region to be determined when the magnitudes of parameters which characterize the bed displacement are known. The results indicate that the primary restriction on the applicability of the linear theory during the bed deformation is that the total amplitude of the bed displacement must remain small compared with the uniform water depth; even this restriction can be relaxed for one type of bed motion. Wave behaviour in the downstream region of the fluid domain is discussed with emphasis on the gradual growth of nonlinear effects relative to frequency dispersion during propagation and the subsequent breakdown of the linear theory. A method is presented for finding the wave behaviour in the far field of the downstream region, where the effects of nonlinearities and frequency dispersion have become about equal. This method is based on the use of a model equation in the far field (which includes both linear and nonlinear effects in an approximate manner) first used by Peregrine (1966) and more recently advocated by Benjamin, Bona & Mahony (1972) as a preferable model to the more commonly used equation of Korteweg & de Vries (1895). An input-output approach is illustrated for the numerical solution of this equation where the input is computed from the linear theory in its region of applicability. Computations are presented and compared with experiment for the case of a positive bed displacement where the net volume of the generated wave is finite and positive; the results demonstrate the evolution of a train of solitary waves (solitons) ordered by amplitude followed by a dispersive train of oscillatory waves. The case of a negative bed displacement in which the net wave volume is finite and negative (and the initial wave is negative almost everywhere) is also investigated; the results suggest that only a dispersive train of waves evolves (no solitons) for this case.

Analysis of errors in digitized strong-motion accelerograms

Abstract: To devise the optimum procedures for the processing of digitized strong-motion accelerograms, detailed error analysis is required. This paper summarizes some aspects of previous error analyses (Trifunac, 1970; Trifunac et al. , 1971) and adds the results of several recent investigations. The error analysis described here is divided into two main parts. The first part deals with particular sources of errors. Each major source of error is analyzed individually with the aim of developing methods of error correction at the source wherever feasible. The second part deals with the overall effects of all errors at high and low frequencies. The objective of this part is to find the optimum frequency band in which the digitized accelerograms are least affected by the errors in the recordings and in the data processing steps, and which can be used to derive accurate velocity and displacement curves. The digitized accelerograms were found to represent accurately the absolute ground acceleration in the frequency band between 0.07 and 25 cps. This frequency band is significantly wider than anticipated and indicates a wide range of new research possibilities in strong-motion seismology and earthquake engineering based on strong-motion accelerograms.

Linear displacement transducer utilizing an oscillator whose average period varies as a linear function of the displacement

Abstract: A measuring system comprises a transducer producing a time varying function, a digital counter, and a reference oscillator to produce a direct digital measurement of a displacement. Axial displacement of a movable component of a variable inductor causes the average period of a self-contained oscillator to vary as a linear function of the measured displacement. A single coaxial cable provides the necessary electrical connections to the transducer. Linear components used in the variable inductor produce a linear output function derived from a complex combination of square and square-root functions. Deviations from true linearity are compensated. The device is particularly useful where precise, high resolution, displacement measurements are made over a relatively short range, or where such measurements are multiplexed for computer data storage and analysis.

Feedback stabilized fabry-perot interferometer.

Abstract: A method of stabilizing a Fabry-Perot interferometer with respect to a reference wavelength, while simultaneously stabilizing the parallelism of the flats, is described. The method consists of creating correcting signals proportional to the displacement of the fringe maxima of three auxiliary spectral sources with respect to a fixed reference point and feeding these signals back to the interferometer piezoelectric drive so that the correcting signals become time invariant, and the interferometer is stabilized. The stability of the finished instrument with respect to the reference wavelength and parallelism is near lambda/1000, at 546 nm, for a 6-h period; however, the actual parallelism of the etalon is limited by the surface defects of the flats. The method, as described, allows simultaneous stabilization and data taking, since the instrument is continuously updating itself.

Servo system for reading from a disc-shaped record carrier containing signals coded in optical form

Abstract: Apparatus for reading a disc-shaped record carrier in which video and/or audio information is recorded in a preferably spiral track. This information is optically read by means of a beam of radiation which via a reflecting element transmits the information present in the scanned point of the record carrier to a read detector. The radial position of the scanning point is controlled by controlling the angular position of the reflecting element which for this purpose is included in a control loop. In order to reproduce the information at a speed different from the recording speed, for example to display slow-motion pictures or still pictures, the reflecting element may be subjected by means of a control signal to an abrupt change in angular position so that the scanning point undergoes an abrupt radial displacement. This displacement preferably takes place during the frame flyback periods of the video information.

New Ferroelastic-Ferroelectric Compound: Tanane

Abstract: We report here evidence for the first paraferroelectric transition observed in a pure molecular solid (without H bonds); we present results from x-ray diffraction, calorimetric and dielectric measurements, and direct optical observation of domain-wall displacement under an applied electric field.

Accurate analytic expectation values for an anharmonic oscillator using the hypervirial theorem

Abstract: An analytic recursion relation for the calculation of expectation values of any power of the internuclear displacement from equilibrium in an arbitrary vibration‐rotation level of 1Σ‐state diatomic molecules is derived via an iterative solution of the hypervirial theorem. Explicit results, more accurate than those previously published, are given for the first six powers of the displacement along with numerical results for H2 and HCl to illustrate the accuracy obtained.

Finite-Difference Energy Models versus Finite-Element Models: Two Variational Approaches in One Computer Program

Abstract: Publisher Summary This chapter demonstrates the similarity of the finite-difference energy method and the finite-element method by the application of both methods to problems involving shells of revolution. Curved finite elements are introduced into the BOSOR3 computer program and rates of convergence and computer times are established for stress, buckling, and vibration analyses of an elastic hemisphere. In both the finite-element and finite-difference energy methods, the unknowns of the problem are certain generalized displacement components located at discrete nodes in the domain. Integration can then be performed analytically or numerically. In the finite-difference calculations the “element” properties corresponding to the centroid of each element were provided as input. No interpolation is required because the energy is evaluated at only one point within each element. The eigenvalues and modes are determined by the inverse power iteration method with spectral shifts.

Interferometer apparatus for measuring the roughness of a surface

Abstract: An apparatus for measuring the roughness of a surface is described which includes an optical system by means of which two images of the surface which have a mutual phase difference and displacement are superposed on one another. It is disserted that for this purpose the phase difference is produced between two sub-beams polarized in directions at right angles to one another by means of an electro-optical modulator, the displacement being effected in an interferometer which discriminates in respect of direction of polarisation. It is set forth that the interferometer may include the series arrangement of the two Wollaston prisms which produce opposite angle splittings between cross-polarized beams of radiation which enter the series arrangement.

Analysis of the Nonlinear Dynamics of a Railway Vehicle Wheelset

Abstract: The nonlinear equations of motion for a railway vehicle wheelset having curved wheel profiles and wheel-flange/rail contact are presented. The dependence of axle roll and vertical displacement on lateral displacement and yaw is formulated by two holonomic constraint equations. The method of Krylov-Bogoliubov is used to derive expressions for the amplitudes of stationary oscillations. A perturbation analysis is then used to derive conditions for the stability characteristics of the stationary oscillations. The expressions for the amplitude and the stability conditions are shown to have a simple geometrical interpretation which facilitates the evaluation of the effects of design parameters on the motion. It is shown that flange clearance and the nonlinear variation of axle roll with lateral displacement significantly influence the motion of the wheelset. Stationary oscillations may occur at forward speeds both below and above the critical speed at which a linear analysis predicts the onset of instability.

Measuring characteristics of the displacement cardiograph

Abstract: The displacement cardiograph (d.c.g.) is a noncontacting electromagnetic transducer that can be used to measure movement of tissue. In normal operation a sensing probe is placed near the moving tissue, and this produces an output voltage. The d.c.g. detects movement by means of the electromagnetic field it generates. Since this field penetrates into tissue, two sources of output exist: changes in the air-gap distance between the tissue surface and the probe, and movements occurring within the tissue itself. The dominant source of signal proved to be movement of the tissue surface. A quantitative relationship exists between instrument output and surface movement only when the movement is primarily one-dimensional. Where surface movement is small or absent, instrument response is due to movements within the tissue. The significance of these results is discussed in relation to measurement of heart movements in the closed and open chest.

Analysis of the displacement vectors of antiphase domain boundaries in anorthites (CaAl2Si2O8)

Abstract: As part of an electron microscopic study of plagioclase, displacement vectors for b- and c-domains have been determined from contrast experiments and calculations. In lunar anorthite from breccia 15459 (An 94.9), b-domains could be imaged in dark field with b-reflections and c-domains with c-reflections. The vector corresponding to these contrast conditions is 1/2[110] for b-domains and 1/2[111] for c-domains. The face centering vector 1/2 [110] relates two domains with a reverse Al/Si arrangement. The body-centering vector 1/2[111] relates domains of identical Al/Si distribution but different atomic coordinates. Fringe patterns for c-domains have been obtained for Pasmeda anorthite. Calculated intensity profiles applying multi-beam dynamic theory and a 1/2[111] displacement vector are in agreement with the observations.

Response of Nonlinear Beam to Random Excitation

Abstract: The technique of equivalent linearization is used, in conjunction with the finite element method, to investigate the effect of the membrane force on the mean-squared displacement of a simply supported and clamped beam undergoing moderately larger random vibrations. Cases for white and nonwhite excitation are presented. Computations show that for sufficiently large deflections the effect of higher modes must be considered when computing the mean-squared displacement of the fundamental mode.

The measurement of planar displacements of sand grains

Abstract: The note explores the application of stereo-photogrammetry to the measurement of planar displacement fields. A research program at Southampton University has extended the basic theory of the method to include determination of strain fields and velocity holographs from the displacements, detailed measurement of complex patterns of water surface velocities and the use of anaglyph slides. The note examines the possibility of detecting displacements of individual sand particles in a plane to at least 5 micrometer sensitivity. The angular rotation of individual sand grains during displacement is studied and the detailed information obtained by stereo-photogrammetry is compared with that provided by an embedded grid of discrete markers in the soil model. The investigation establishes that planar displacement of individual sand grains in a deforming model can be measured to within 5 micrometers using a photogrammetric technique. /TRRL/

Method and apparatus for the no-contact measurement of velocities, changes in relative position, or displacement paths

Abstract: Light diffracting or dispersing properties of an object dividing a wave front in angular differently oriented wave fronts are used for no-contact optical velocity-, acceleration-, change in relative position- or displacement path measurements of said object movable relative to a measuring head. No systematic markings affecting light phase or amplitude on the measuring surface are disposed in the depth of field of imaging system. Measurements are made respectively to one coordinate associated to one of the six possible spatial degrees of freedom of motion. The object under test and an optical component yielding sharply defined angular relationship among different but combined wave fronts are conjugatedly disposed in the imaging system. Light modulations produced upon changing the relative position are photoelectrically converted into signals exhibiting a frequency change proportional to linear or angular velocity variation. The measurement is improved by using components having negligible light absorption, and determining angular relationship among the wave fronts. Light fluxes from interaction among partial wave fronts containing information concerning the object movement, derived from solid angle areas of equal modulation phase are converted separately into photoelectrical signals having sinusoidally varying modulation characteristics with the respective measuring coordinate. The modulation period cycles are half as long as the statistical spatial frequency components of the object under test. The light energy proportions are split off from and outside the solid angle area of the illumination aperture. The electric signals produced are evaluated as direct or carrier-frequency signals with respect to the measured qualities desired.

Quantitative theory for predicting fringe pattern formation in holographic interferometry.

Abstract: The effectiveness of holographic interferometry for displacement studies was investigated and profiles of the fringe patterns characteristic of the basic displacement modes were developed. In addition, techniques were established for determining displacement directions and measuring displacement magnitudes. Procedures were also established for extending these studies to evaluate complex displacements. A quantitative theory for predicting fringe pattern formation was developed.

Improved Finite Elements for Vibration Analysis of Tapered Beams

Abstract: This paper gives two improved tapered elements for vibration analysis derived using quintic polynomial displacement functions. The elements employ different nodal continuity conditions. Results are compared with those given by the basic cubic approximations and analytical solutions for various end conditions. The advantages of the new elements over the basic element are discussed.

Method and apparatus for ultrasonic examination

Abstract: Method and apparatus are disclosed in which it is possible by means of ultrasonic examination according to the pulse echo method to obtain an indication, or a recording of images, of internal inhomogeneities in otherwise homogeneous bodies, corresponding substantially to the images obtained by producing a normal radiographic film of the body. To obtain this an ultrasonic angle probe is moved across the surface of the body and the echo signals are used to produce punctiform markings on a recording surface in such a way that (a) the markings are effected along a moving axis of indication, (b) the displacement of a reference point on the axis of indication follows the displacement of the sound emission point of the probe, (c) the direction of the axis of indication follows the direction of the projection of the sound path on the surface of the body, and (d) the distance from the reference point to each marking is proportional to the echo time of the corresponding ultrasonic pulse. Various methods of recording, including remote recording, are described.

Large Displacement Analysis of Thin Plates

Abstract: A finite element procedure for large deflection analysis of thin plates that exhibits monotonic convergence to results obtained using the von Karman plate equation is presented. A simplified method of solution is also developed that yields acceptable results with a significant reduction in computational effort. The Kirchoff thin plate assumptions are used, together with the appropriate nonlinear terms in the strain displacement equations to express the potential energy functional in terms of the displacement fields. The functional is discretized according to the usual finite element techniques and two sets of equations that essentially uncouple the in-plane and bending effects are obtained. Thus, the storage requirements of the computer program are based on a 3-degree-of-freedom per nodal point system although 5-degree-of-freedom are available to define the deformation of the idealized structure. This results in a significant reduction in storage requirements.