Showing papers on "Deflection (engineering) published in 1989"

The constituent equations of piezoelectric bimorphs

Abstract: The constituent equations that describe the behavior of piezoelectric bimorphs for various mechanical boundary conditions are derived. The internal energy density of infinitesimally small volume elements in thermodynamic equilibrium is calculated in the presence of a voltage on the electrodes, a clamped cantilever condition on one side of the beam, and a set of three different classical boundary conditions on the other side of the beam: a mechanical moment M at the end of the beam, a force F perpendicular to the beam, applied at its tip, and a body force p. The total internal energy content is calculated by integrating over the entire volume of the beam. The canonical conjugate of the moment is calculated as the angular deflection at the tip of the beam, while that of the force at the tip is the local vertical deflection. The canonical conjugate of the uniform load on the beam proves to be the volume displacement V of the beam. The equations are given in the direct form, with internal parameters (M,V), (F,V), and (p,V) as independent variables. >

Experimental Study of Prestressed Composite Beams

Abstract: The concept of prestressing steel structures has only recently been widely considered, despite a long and successful history of prestressing concrete members. Several analytical studies of prestres...

Nonlinear vibrations of unsymmetrically laminated beams

Abstract: The purpose of this study was to develop a simple one-dimensional finite element for the nonlinear analysis of symmetrically and unsymmetrically laminated composite beams including shear deformation. The beam element has 10 degrees of freedom at each of the two nodes: the axial displacement, the transverse deflection and the slope due to bending and shear, the twisting angle, the in-plane shear rotation, and their derivatives. The formulation, the solution procedure, and the computer program have been evaluated by solving a series of examples on the static response, free vibration, and nonlinear vibrations of isotropic and laminated beams. For unsymmetrically laminated beams, the nonlinear vibrations were found to have a soft spring behavior for certain boundary conditions as opposed to a hard spring behavior observed in isotropic and symmetrically laminated beams. The in-plane boundary conditions were found to have a significant effect on nonlinear responses.

Analytical Study of Prestressed Composite Beams

Abstract: This paper analyzes the behavior of steel beams prestressed with highstrength steel tendon and compositely connected to a concrete deck. In particular, the deflection and the strains in the steel b...

Vibration analysis of composite turbopropellers using a nonlinear beam-type finite-element approach

Abstract: An analytical model for determining the free vibration characteristics of advanced composite turbopropellers (prop-fans) is presented. The blade is modeled using a number of straight beam-type finite elements, where the elastic axis of each element is a piecewise straight representation of the curved line of shear centers of the swept blade. The finite-element model is obtained from Hamilton's principle with allowances for: generally anisotropic material behavior, arbitrary cross-sectional properties, large pretwist angles, out-of-plane cross-section warping, and geometrically nonlinear behavior based upon moderate deflection theory. The natural frequencies and mode shapes of the rotating blade are calculated assuming linear perturbations about the nonlinear static equilibrium position of the blade. This model is sufficiently general to analyze other advanced composite aerospace structures. Numerical results are presented to illustrate the versatility of the method by applying it to 1) a conventional propeller (TRW-Hartzell 101/16) and 2) a highly swept and pretwisted isotropic turbopropeller (NASA SR-3). Excellent agreement with experimental test results is obtained for the lower modes of both the conventional propeller and the advanced turbopropeller.

A comparison of the stress transfer characteristics of a dental implant with a rigid or a resilient internal element

Abstract: It has been suggested that there is a unique set of problems associated with joining an implant and a natural tooth with a fixed partial denture. The manufacturer of the IMZ implant system claims that this procedure can be accomplished successfully because of the planned stress-distributing characteristics of their resin internal (intramobile) element. This study compared the difference in the stress patterns generated in photoelastic plastic by an IMZ implant with a resilient or a rigid internal element. Under a standardized cantilever load, the stress patterns were photographed in the field of a circular polariscope. The total stress areas were calculated and a statistical comparison performed. The static load conditions of the model demonstrated no statistical difference between the area of stress pattern generated by an IMZ implant with or without a resilient internal element. Moreover, a single load produced the same deflection of the cantilever beam regardless of which element was interposed.

Design of laterally loaded driven piles using the flat dilatometer

Abstract: The nonlinear subgrade reaction method (P-y curves) is widely used for the design of laterally loaded piles. This method replaces the soil reaction with a series of independent nonlinear Winkler springs. A preliminary semi-empirical approach for the determination of P-y curves using data obtained from a flat dilatometer test (DMT) is presented and evaluated. A brief description of the equipment, testing procedures, and the theory that enables the family of P-y curves to be determined are presented. The P-y curves are used as input for an existing finite-difference program, which calculates pile deflection versus depth at various lateral loads. An evaluation of the proposed method is presented using data from three full-scale laterally loaded test piles. A comparison and discussion are provided between the predicted and measured behavior of the piles during lateral loading.

Simulation of circular silicon pressure sensors with a center boss for very low pressure measurement

Abstract: A characteristics simulation method of circular silicon-diaphragm piezoresistive pressure sensors was developed to obtain accurate sensors for very-low-pressure measurement. The anisotropic stress-strain relationship of a silicon single-crystal plate and the nonlinear characteristics of silicon piezoresistive gauges were considered. Nonlinear deflection and strain formulas of circular silicon diaphragm sensors with a center boss and sensors with a center boss and ribs were derived by taking the effects of the large deflection and the support stiffness of the diaphragms into account. Based on these considerations, the characteristics of the sensors were simulated. The simulated results show good agreement with the observed results and indicate that output voltage can be greatly increased while maintaining low nonlinearity even in the low-pressure range by narrowing the rib width and thinning the diaphragm thickness of sensors with a center boss and ribs. This is because the rib strain that produces output voltage is increased while maintaining small deflection by using this type of sensor. >

Deflection Reading Accuracy and Layer Thickness Accuracy in Backcalculation of Pavement Layer Moduli

Abstract: Accurate deflection readings must be obtained when using nondestructive testing (NDT) devices in order to obtain correct backcalculated layer moduli. This paper provides an analysis of the sources of deflection errors and illustrates through a series of examples how random deflection errors and random pavement thickness errors affect backcalculated moduli. The consequence of these errors is most pronounced in the backcalculated modulus of the surface course. The moduli of the base and subbase layers are also affected, and the subgrade moduli are only slightly affected by these errors. To some degree this outcome may be due to the bottom-to-top approach used by the backcalculation program MODCOMP2. The consequence of the variability of the backcalculated moduli on the required pavement overlay thickness was found to be minimal. This was due to the fact that, generally speaking, data errors which cause an overestimate of the base course modulus also cause an approximately equally significant, but opposite, underestimation of the surface course modulus. Thus, the needed overlay requirement remains nearly the same. The paper shows how certain falling weight deflectometer (FWD) calibration and testing procedures can be used to minimize deflection measurement errors. The accuracy of backcalculated moduli is shown to be determinable from the RMS error of the deflection fit. The examples provide an impression of the extent to which random layer thickness errors and deflection measurement errors will influence the ability to discern point-to-point variability of layer moduli for the specific pavement structure considered in this investigation. This provides a perspective from which the practical accuracy of the backcalculation approach can be judged.

Extrusion of a beam from a rotating base

Abstract: This paper deals with a new method for simulating motions of a beam that is being extruded from, or retracted into, a rigid body rotating in a general manner. In essence, the method consists of modeling the beam as a series of elastically connected rigid links and then working with equations of motion linearized in the modal coordinates for the links outside the rigid body at a given time. The theory is applied to a problem of current interest, the extrusion/retraction of the WISP antenna from the Shuttle. Simulation results show that beam tip deflections are highly sensitive to the total time devoted to extrusion /retraction, with retraction the less stable process of the two; and the nature of the angular velocity of the rigid body from /into which the beam is being extruded/retracted is found to affect beam behavior significantly. I. Introduction C URRENT interest in dynamics of extrusion of a beam from a rotating base stems from project WISP (Waves In Space Plasma), which involves extending two booms from the Shuttle, each to a final length of 150 m and having a tubular cross section with a 0.0635-m diam and a 0.00254-m wall thickness, while the Shuttle is rotating at a rate of 1 deg/s. Clearly, it is helpful in a project of this kind to be able to perform simulations leading to results such as those shown in Figs. 1 and 2, the first of which contains time plots of the tip deflection, the root bending moment, and the length of each boom during an extrusion operation, whereas the second deals with the same quantities during retraction. It is the purpose of this paper to provide an algorithm for the performance of such simulations. In previous attacks1"5 on the problem under consideration, beams were modeled as continua, and deflections were described by linear combinations of modal functions weighted by time-dependen t "generalized coordinates," an approach familiar from the classical vibrations literature. However, whereas the arguments of the classical modal functions are independent, purely spatial variables, those of the modal functions used in Refs. 1-5 are treated as time-dependen t spatial variables. The deployment of tethers, 6 plates,7 and other structures8 has been treated similarly. Regarding the soundness of this approach as questionable, we adopt a new technique, one that can be applied not only to the title problem but also to the simulation of motions of continua other than beams undergoing extrusion from, or retraction into, moving bases. In what follows, a simulation algorithm is described in sufficient detail to permit a reader to construct a simulation program; numerical results in addition to those plotted in Figs. 1 and 2 are reported and discussed, and the rationale underlying the algorithm is explained.

Solid-state image pickup device

Abstract: PURPOSE:To make a charge accumulation time longer as a rotary optical system is rotated and to improve sensitivity by composing the locus of luminous flux image-formed on an image pickup device out of a large loop and a small loop and forming the small loop on a detector. CONSTITUTION:Parallel plates 14 and 15 as first and second deflection optical elements rotate around an optical axis OX by a driving system 50. In this case, the driving system 50 is constituted so as to rotate the plates 14 and 15 in directions opposite to each other and rotate the plate 14 of which deflection quantity is large at lower speed than the plate 15 of which deflection quantity is small. While the plate 14 of which deflection quantity is large makes one rotation, the locus of the luminous flux on a solid image pickup element 11 draws the large loop to pass through the neighborhood of the central point of a detector 11i on the element 11 and draws the small loop in the neighborhood of the central point. That is, by setting the deflection quantities and the rotation speeds of the plates 14 and 15 so that the holdup time of the luminous flux may be long on the detector 11i, even when the plates 14 and 15 are revolved continuously, the charge accumulation time becomes longer than it used to be and the sensitivity can be improved.

A finite element formulation for the large deflection random response of thermally buckled beams

Abstract: The effects of temperature and acoustic loading are included in a theoretical finite element large deflection formulation for thin, isotropic beams. Thermal loads are applied as steady-state temperature distributions, and acoustic loads are taken to be ergodic and Gaussian with zero mean and uniform magnitude and phase along the length of the beam. Material properties are considered presently to be independent of temperature. Also, inplane and rotary inertia terms are assumed to be negligible, and all inplane edge conditions are taken to be immovable. For the random response analysis, both auto- and cross-correlation terms are included. The nature of the loads leads to the solution of two separate problems. First, the problem of thermal postbuckling is solved to determine the deflections and stresses due to the thermal load only. These deflections and stresses are then used as initial deflections and stresses for the random vibration analysis. Root-mean-square (RMS) maximum deflections and strains are obtained and compared with previous classical equivalent linearization results.

Analysis of Displacements and Stresses in Oil Storage Tanks Caused by Differential Settlement

Abstract: Differential vertical settlement around the circumference of the foundations of large open-topped oil storage tanks can produce deformation of the tank including radial deflection of the tank shell. Excessive radial deflections may result in jamming of the floating roof.The results of an analysis by Malik et al. (1), based on the assumption that the behaviour of the shell is inextensional, are outlined.Two further analyses of the tank shell and the primary wind girder are presented. Both of these are simple, but use less restrictive assumptions than in reference (1). In the first analysis the shell is considered to act as a membrane. The second analysis makes use of a simplified version of the modified Donnell equation. The results of these analyses are compared with those of the analysis based on the inextensional behaviour of the shell. The limits of validity of the three different analyses are identified.It is proposed that the membrane solution is valid for all practical applications, and the results ...

General procedure for backcalculating layer moduli

Abstract: An efficient microcomputer program for back calculating moduli from nondestructive testing results is described. Its use is illustrated by analyzing a typical section where several deflection bowls were measured at the same location. sources of errors in the testing and backcalculating are presented and discussed. The error source is taken into consideration in the formulation of the objective function, the relative squared error between measured and computed deflections. The Hooke-Jeeves pattern search algorithm was selected for minimizing the objective function. The direct computation of the deflection at each move of the pattern search was replaced by the three-point Lagrange interpolation, using a data base generated ahead of time. The pattern search and interpolation were included in a microcomputer program named MODULUS, capable of performing and back calculation in 1 to 2 min per deflection bowl. It is highly efficient where several deflection bowls are measured along the pavement section or at the same location. The analysis of the typical section shows clearly that the measurement errors can be quite large. Averaging deflection measurements at each sensor cancels out some of the random errors and generally leads to acceptable values of the backcalculated moduli. The program MODULUS is especially suited toward these cases where multiple deflection bases are available for the same pavement geometry.

Resilient Railpads: Their Dynamic Behaviour in the Laboratory and on Track

Abstract: Resilient railpads in a variety of materials and with different surface profiling have been tested in the laboratory and in track. A laboratory impact test based on that initially developed at the Battelle Columbus Laboratories provides a reliable ranking of the extent to which railpads attenuate dynamic strain in concrete sleepers in track. The test is also a good indication of the average attenuation provided by a pad in track. If dynamic loads in track are particularly severe the fractional attenuation provided by a pad is greater than that indicated by the laboratory impact test.Laboratory resonance apparatus, in which the pad is the principal resilient element in a simple dynamic system, has been made to find the railpad's effective dynamic stiffness. There is good correlation between the stiffness measured in track and that measured in this apparatus.A pad's dynamic stiffness is consistently at least as great as its tangent stiffness found from the static load/deflection curve. The load/deflection b...

Antenna apparatus and attitude control method

Abstract: Attitude control is implemented by detecting the phase difference between signals received by at least two antennas and detecting the angle of deflection between the direction of arrival of radio signals and the antenna beams. By using antennas that are separately driven, within the plane of rotation in which the deflection angle is to be detected, the phase of the received signals can be shifted equivalently to when the antennas are driven as a consolidated unit. Also, when at least three antennas are used in an orthogonal arrangement for detecting the deflection angle in two directions, the antennas are divided into two groups which are individually driven. This reduces the inertia of the moving parts and enables the size and weight of the drive mechanisms to be reduced. In addition, two orthogonal functions are used to represent the phase of the deflection angle of the direction of arrival of the radio wave and the antenna beam as a multiplicity of quadrants, and by storing these, when there is a change in the deflection angle, the sequence of change can be traced back and the control effected accordingly. This enables pointing error to be eliminated.

Effect of tire pressure and type on response of flexible pavement

Abstract: Radial, bias, and wide-base radial single tires were tested in the laboratory under three levels of inflation pressures and axle loads. The measured characteristics of the tires were gross contact area, net contact area, tire deflection, and contact pressures. Distributions of the contact pressures were used in a mechanistic solution to predict various flexible pavement response parameters. A modified version of the BISAR computer program, which takes concentric circles of various pressures, was used to predict the response parameters. The response of various flexible pavement structures was investigated in terms of the tensile strains at the bottom of the asphalt layer, the compressive stress at the asphalt layer interface, and the surface deflection. The effects of tire inflation pressures and axle loads on the response parameters were evaluated for all tires and asphalt thickness combinations. The three tire types were also compared for underloaded, loaded, and overloaded cases.

Wheel or endless track

Abstract: A ground engaging tire assembly in the form of a wheel for a vehicle, comprising a rim (11) and a plurality of ground engaging elements (13) mounted on the rim. Each ground engaging element (13) comprises a hollow body (31) having an inner face (32) in engagement against the rim and an outer face (33) for contacting the ground. The hollow body (31) also has side faces (34) extending between the inner and outer faces. The side faces (34) are constructed to be resiliently flexible for deflection under normal load conditions thereby to provide cushioning for the vehicle. The ground engaging elements are so positioned on the rim that confronting side faces of neighboring elements provide lateral support for each other when deflecting under load.

Calibration of scanning tunneling microscope transducers using optical beam deflection

Abstract: An accurate, sensitive, easily implemented method of calibration of the elastic displacement of piezoelectric transducers used in scanning tunneling microscopes has been developed. The axial displacement for both static and harmonic excitation has been measured using laser beam deflection amplified by an optical magnification system. For harmonic excitation where lock‐in amplifier detection can be utilized, displacements as small as 0.03 A have been measured. Measurements on PZT‐5H and PZT‐8 transducers over a range of five orders of magnitude in applied voltage demonstrate the power of the method in calibration of displacements from the subangstrom to the nonlinear region with an uncertainty of about 4%.

Three-dimensional Elasto–Plastic and Creep Analysis of Bulging in Continuously Cast Slabs

Abstract: The bulging behavior of the solidified shell in continuously cast slabs have been numerically analyzed using the elasto-plastic and creep Finite Element Method. Three-dimensional model has been applied in order to investigate the effect of the narrow face shell on restraining the bulging deflection. Three-dimensional shell profile and temperature distribution in it have been determined using the segregation considered solidification analysis method. In this way, strains occurring at the solidification front near the narrow face of the slab, as well as those occurring in the broad face have been computed. The computed bulging deflection have been in good agreement with measurements, and the relationship between the strain caused by the bulging and the internal cracks have been investigated. In addition, the effect of the slab width on the bulging are discussed.

Segmental Box Girder: Deflection Probability and Bayesian Updating

Abstract: Probabilistis prediction of the confidence limits on long-time deflection and internal forces of prestressed concrete segmental box-girder bridges is developed. The uncertainty of the predictions based on the existing models for concrete creep (the prior) is very large, but it can be greatly reduced by Bayesian updating on the basis of short-time measurements of the deflections during construction or of short-time creep and shrinkage strains of specimens made from the same concrete as the bridge. The updated (posterior) probabilities can be obtained by latin hypercube sampling, which reduces the problem to a series of deterministic creep structural analyses for randomly generated samples of random parameters of the creep and shrinkage prediction model. The method does not require linearization of the problem with regard to the random parameters, and a large number of the random parameters can be taken into account. Application to a typical box-girder bridge with age differences between its segments and with a change of structural system from statistically indeterminate to determinate is illustrated numerically. The results prove that design for extreme, rather than mean, long-time deflections and internal forces is feasible. Adoption of such a design approach would improve long-term serviceability of box-girder bridges.

Large-angle beam deflection of a laser-cooled sodium beam

Abstract: A sodium atomic beam has been decelerated and laser cooled to a longitudinal beam temperature of less than 30 mK. Subsequently these slow atoms with a typical velocity of 100 m/sec were selectively deflected by laser-light forces. The deflection angle was typically 30°. The deflection scheme permits a stabilization of the transverse velocities in the deflected atomic beam down to the quantum-limit temperature for one dimension (0.7 × 240 μK). The experimentally achieved temperatures are of the order of 1 mK.