Showing papers on "Deflection (engineering) published in 1972"

Convergence of consistently derived Timoshenko beam finite elements

Abstract: The accuracy and convergence properties of two new Timoshenko beam finite elements are compared to those now widely used. Both of the new elements are consistently derived from a variational principle written in terms of the transverse beam deflection and normal rotation. The deflection is expanded as a cubic and the rotation as a quadratic in the axial co-ordinate of the beam, giving rise to a seven degrees of freedom element. The first element, called TIM7, includes all the degrees of freedom while the second, called TIM4, reduces this number to four through a constraint introduced by Egle. Both elements display monotonic covergence for beam natural frequencies as a function of the number of degrees of freedom and both will give the analyst some measure of confidence in response calculations for beams excited at high frequencies.

Gas generating device

Abstract: A gas generating device is disclosed which includes combined filtering and cooling means through which the gas stream in the device is directed. This means includes specially constructed deflection means for causing the gas stream to undergo a plurality of direction changes each of which is at least 90 degrees.

Nonlinear Panel Response from a Turbulent Boundary Layer

Abstract: The vibration of a flexible elastic plate is investigated by a Monte Carlo technique. The response analysis is performed in time domain by numerically simulating the resulting generalized forces. The nonlinear plate deflection and mutual interaction between the plate motion and external and/or internal airflow is included. The fluid perturbations due to the structural motion are described by linear aerodynamic theory. The boundary-layer pressure field is idealized as a homogeneous multidimensional Gaussian random process with mean zero. The plate differential equations of motion and boundary conditions are satisfied in a Galerkin sense by developing a modal solution. Illustrative examples are presented for subsonic and supersonic flow regions using shallow cavity and two plate mode approximations.

Axisymmetric Postbuckling and Nonsymmetric Buckling of a Spherical Shell Compressed Between Rigid Plates

Abstract: Presents an analysis of the stresses and deflections produced during axisymmetric postbuckling and determines the deformation states at which the shell may buckle into a nonsymmetric shape. The analysis accounts for finite deflections and rotations, but assumes that the material remains linearly elastic throughout the deformation. An experiment shows that both the primary axisymmetric bifurcation point and the secondary nonsymmetric bifurcation point are stable for a shell with R/h approximately equal to 40.

Vibration of circular and annular plates using finite elements

Abstract: The finite element method is applied to the free transverse vibration of circular and annular plates of varying thickness An annular element is derived which incorporates the number of diametral modes in the deflection function This results in an element having only four degrees of freedom, these being the deflection and slopes at the inner and outer radii of the element at an anti-node of the particular vibration mode Thickness variation in the radial direction is readily introduced, and stiffness and inertia matrices are presented for elements with linear and parabolic variations in thickness The method is checked with several numerical examples Calculations of free vibration of circular and annular plates of constant, linear and parabolic thickness variation are compared with available exact solutions

Colinear acousto-optic deflection in thin films

Abstract: We report the experimental demonstration of a colinear interaction between an optical film-guided wave and an acoustic surface wave producing a noncoplanar optical-beam output. With an interaction length of 4 mm and an acoustic-power input of 2.5 W at 86 MHz, 5% of the guided optical wave was scattered out of the film.

Large Deflection Buckling of Space Frames

Abstract: Buckling loads of space rigid frames based on large deflection theory were determined herein by a method referred to as the constant load method. In this method, the load is maintained at certain constant level and the deflected position which will provide the necessary internal forces to balance the external load is determined by iteration. The load is then increased to the next level and the process repeated until the process becomes divergent or the determinant of the stiffness matrix becomes zero. The advantages of the method are: (1) the direct application of stiffness coefficients developed for the small deflection buckling and (2) the possibility of starting iteration at any level. Verification of the method with various published examples was made. An illustration was made for the determination of large deflection buckling mode of a symmetrically loaded framed dome.

Large Deflection of Rectangular Orthotropic Plates

Abstract: A theoretical analysis is presented for the large deflection elastic behavior of clamped, uniformly loaded, rectangular, orthotropic plates. The governing differential equations including the nonlinear terms in the sense of von Karman are solved by the method of perturbation. This results in the predictions of the load deflection relations, and bending stresses are presented in the graphical form for glass-epoxy, boron-epoxy and graphite-epoxy plates having various aspect ratios. In the case of isotropic plates, the present solution reduces to two of the existing solutions.

Method of making a plastic optical element

Abstract: The invention relates to a transparent element for the deflection of incident electromagnetic radiation having an optical axis extending therethrough. The element includes a shaped polymeric matrix having an organic diluent therewithin, the diluent forming a continuous gradient in refractive index extending in a direction substantially perpendicular to the optical axis of the element. The element has lens-like properties.

Danish experiments with the french falling weight deflectometer

Abstract: The falling weight deflectometer is a portable apparatus used for measuring the deflection of a road surface under the influence of a load pulse of very short time duration. This pulse simulates a fast moving wheel load, and it can be adjusted to correspond to any desired wheel load of 5 tons (5000 kp.) or less. The unit is built into a trailer frame, which is easily pulled by a passenger automobile. To date, about 20 falling weight deflectometers have been produced in Denmark. The validity of comparing the effect of the falling weight to the effect of a moving wheel load has been investigated by two means, both of which showed good correlation between the two effects. One set of measurements was undertaken in Holland, where photo-electric equipment was used to measure the deflection due to a passing wheel load. Another set of measurements was undertaken in Denmark, using an accelerometer. The acceleration signal was integrated twice with an analog integrator to obtain the deflection in question. Static and dynamic surface deflection tests have shown poor correlation to each other, especially for roads with thick asphalt concrete layers. Investigations undertaken on a Danish experimental road, on the other hand, showed good correlation between dynamic deflection measurements and the corresponding theoretical elastic deflection values. The asphalt concrete moduli used in these theoretical calculations were the results of dynamic three-point bending tests. The moduli of the unbound layers were found by low frequency sound wave measurements taken on-site. Curves are shown which allow conversion of measured deflections from an arbitrary temperature between 5 C and 30 C to the corresponding deflections at 20 C (standard temperature). The 20 C curve can then be used to analyse certain limiting criteria. The limiting criteria are the strain in the bottom of the asphalt concrete layer and the verticle stress on the subgrade. These can be set to whatever values are deemed reasonable at the 20 C standard temperature. Finally, the diagrams can be used to help find the necessary thickness of a possible additional asphalt concrete reinforcement layer. /AUTHOR/

Measurements of plasma velocity distributions in free-burning DC arcs up to 2160 A

Abstract: An experimental technique is described from which plasma velocity distributions have been determined. The technique consists of dropping a line of ball bearings of 3, 4 or 5 mm through a horizontal arc and recording the horizontal deflection of the balls by allowing them to strike a carbon paper. Multiple drops through repeated arcs enabled a deflection curve to be compiled. This curve was then subjected to an Abel inversion so that the radial variation of aerodynamic drag on the balls could be determined. By iterative techniques it was then possible to calculate a plasma velocity distribution compatible both with the Reynold's number and the radial deflection profile. A comparison with Wienecke's results obtained using photographic techniques on a 200 A arc showed good agreement, although the maximum deflection recorded was less than 3 mm with balls of 3 mm diameter. It was not possible to increase the deflection resolution by using smaller balls, since the scatter in striking position even in the absence of an arc increased unacceptably for balls of 2 mm diameter. An examination of the validity of the assumptions involved and associated errors is included. In particular the disturbing influence of the ball within the plasma is considered to be small. A more serious difficulty, pointed out by Kimura and Kanzawa concerns the difficulty of assigning the effective temperature and Reynold's number which determines the drag coefficient, since the ball and plasma boundary layer are necessarily at different temperatures. It is argued that the error involved in assigning the undisturbed plasma temperature is small. The overall error in the velocity distributions, which reach to 1500 m s−1 for the 2160 A arc, is considered to be about ±11%.

Non-linear response of a beam to periodic loading

Abstract: The steady state response of a non-linear beam under periodic excitation is investigated The non-linearity is attributed to the membrane tension effect which is induced in the beam when the deflection is not small in comparison to its thickness The effects of multimode participation are investigated for simply supported and clamped boundary conditions The finite element technique is used to formulate the non-linear differential equations of the straight beam and the method of averaging is used to obtain an approximate solution to the non-linear equations under harmonic loading An analog computer was used to simulate the non-linear beam equation which was subjected to harmonic excitation The agreement between theoretical and experimental values is reasonably good

Adaptive numerically controlled machine tool responsive to deflection forces on the tool normal to the cutting path

Abstract: A data processing system supplies numerical control data to a controller for a machine tool connected in a system for adaptively controlling the machine tool feedrate in response to data measured by sensors connected to the machine tool The deflection forces on a tool operating upon a workpiece are measured and the data processing system program determines the tool deflection force transverse to the path of the tool relative to the workpiece The program computes the change in deflection required to meet a dimensional tolerance based upon data previously obtained relative to tool deflection characteristics of the tool Then the program calculates a new control value to change the feed rate to a value intended to provide the desired degree of deflection The data processing system then supplies the control value to apparatus to modify the feed rate and bite size, accordingly

Deflection Due to Contact between Gear Teeth with Finite Width

Abstract: In this paper, the experimental studies for the basic problem of the contact between gear teeth are presented. When a concentrated load acts on an infinite elastic solid, Sneddon's solutions are applied to the contact between gear teeth on the hypothesis that the effect of gear profile can be neglected in discussing local deformation on "line of contact". Correct functions are suggested. These correct functions contain the effect for the deformations with the distance from the free edge to the posiitons where a concentrated load acts on and where deformations are measured. There were applied to the contact between a finite width roller and a same width flat surface. The deflections and the load distribution were evaluated to make use of Sneddon's equation and the correct functions. The evaluatd results with these equations coincided with experimental results. And it becomes clear that the width of a gear tooth should be taken into consideration on the deflection when the width is narrow.

Large deflection elastic-plastic dynamic response of stiffened shells of revolution.

Abstract: The formulation and check out porblems for a computer code DYNAPLAS, which analyzes the large deflection elastic-plastic dynamic response of stiffened shells of revolution, are presented. The formulation for special discretization is by the finite element method with finite differences being used for the evaluation of the pseudo forces due to material and geometric nonlinearities. Time integration is by the Houbolt method. The stiffeners may be due to concentrated or distributed eccentric rings and spring supports at arbitrary angles around the circumference of the elements. Check out porblems include the comparison of solutions from DYNAPLAS with experimental and other computer solutions for rings, conical and cylindrical shells and a curved panel. A hypothetical submarine including stiffeners and missile tube is studied under a combination of hydrostatic and dynamically applied asymmetrical pressure loadings.

A new type of traveling-wave deflection system

Abstract: The analysis of the meander-line type of traveling-wave deflection system shows that the deficiency in the dispersion characteristics is due to the interaction of the electromagnetic field on a section of a finger with that on other fingers. Insertion of a shielding plate between two neighboring sections of the fingers reduces mutual interactions. The meander line with the shielding plate is called the trough-type traveling-wave deflection system. The analysis shows that uniform characteristics of the dispersion and the admittance with respect to the frequency are expected in the trough-type traveling-wave deflection system. Loading by the dielectric material of the space among electrodes serves to decrease the phase velocity and to increase the deflection sensitivity. In the experimental CRT in which the trough-type traveling-wave deflection system is used, a uniform sensitivity is confirmed experimentally in the frequency range from dc to above 4 GHz and the deflection of 6 mm by 10-mW input is measured.

Lateral vibration and stability relationship of elastically restrained circular plates.

Abstract: = radius of the plate = £/i/[12(l — v)], flexural rigidity of the plate = Young's modulus of material = thickness of plate = rotational spring constant = radial load per unit length of circumference = buckling load per unit length of circumference = [_ppha/D']' characteristic value of frequency = characteristic value of frequency without radial load = deflection of plate = polar coordinates = nondimensional coordinate defined by r/a = mass density of plate material = frequency of oscillation, rad/sec = Poisson's ratio = nondimensional boundary restraint factor defined by ka/D = nondimensional radial load defined by Ra/D

Ion beam deflection system

Abstract: The accel electrode in a Kaufman-type of electron bombardment ion thrustor is created by interengaging panels of insulative material. These panels are angularly related to each other to define the openings of the accel electrode. Conductive blades are installed in each opening for electrostatic deflection of the beamlet issuing therethrough.

Structural analysis of bituminous concrete pavements

Abstract: A COMPUTER PROGRAM THAT PERMITS ANALYSIS OF ELASTIC, MULTILAYERED PAVEMENT SYSTEMS WAS USED TO DETERMINE THE PATTERNS OF STRESSES, STRAINS, AND DEFLECTIONS IN A PAVEMENT SYSTEM. THE STUDY ALSO SOUGHT TO USE THE FATIGUE CONCEPT (EQUIVALENT AXLE LOADS) TO SHOW THE RELATION BETWEEN THESE STRESSES, STRAINS, AND DEFLECTIONS ON THE ONE HAND AND CURRENT AND PROPOSED DESIGN CURVES ON THE OTHER. THICKNESS DESIGN CRITERIA CANNOT BE BASED DIRECTLY ON DEFLECTION SPECTRA, AS SURFACE DEFLECTION IS NOT A DISCRETE, LIMITING PARAMETER: STRESSES AND STRAINS IN THE SUBGRADE SOIL AND IN THE EXTREME FIBERS OF THE AC LAYER MAY CONSTITUTE OVERRIDING, FUNDAMENTAL LIMITS. ACCORDINGLY, STRAIN DIAGRAMS ARE PRESENTED FOR BOTH SUBGRADE AND ASPHALTIC CONCRETE AS A FUNCTION OF CBR, TRAFFIC CHARACTERISTICS, LOAD CYCLES, ETC.. NOMOGRAPHS ARE DERIVED FOR ANALYSIS OF COMPRESSIVE AND TENSILE STRAINS. THE RESULTS ARE EVALUATED AND COMPARED WITH EXISTING DESIGN GUIDES.

Extensible load lifting frame

Abstract: A telescopic lifting frame or spreader for enaging, lifting and transporting freight containers by means of van carriers, lift trucks, and the like, having a longitudinal coaxial telescopic beam structure extensible the distance of about twice its collapsed length and having freight container corner casting engaging hooks which engage from the sides of the container. Opposed spreader beams are telescopical coaxially in and out of each other and are supported from and telescoped in a fixed center beam. When associated with a van carrier machine frames are provided for connecting the spreader to the side frames of the carrier for guided elevation relative thereto, as well as for guiding, skewing and side shifting of the spreader in the bay of the carrier and means compensating for carrier side frame deflection. In addition, positive locking means engages beam structure at various selectable lengths thereof, and an interior beam extension structure is connected to the opposed beam ends in a manner to provide a minimum collapsed length of the lifting frame or spreader for the maximum available extended length thereof.