Strip Beam Research Articles

Uniformization of a large beam spot using sextupole magnets for a compact multiple-energy electron accelerator

We have commissioned a multiple-energy electron accelerator that illuminates an 800 mm × 800 mm target. The energy of the beam ranges from 0.5 to 5 MeV. A beamline following the accelerator has horizontal and vertical sections that include an alpha dipole and a “focus sextupole”. In the horizontal section, the alpha magnet, having a bend angle of 270° and a field index of 0.8, provides both vertical collimation and energy selection. In the vertical section, a focus sextupole converts the initial Gaussian beam distribution to a uniform distribution in one dimension without beam loss. We used a scanning magnet just ahead of the target to expand the beam in the orthogonal dimension. Using the French code TraceWin, we simulate the beam dynamics in this beamline by integrating electron trajectories through field maps of the magnets. We have determined experimentally that the focus sextupole creates a horizontal strip beam on target having a current density uniformity of better than 90 %. By scanning this strip beam vertically, we have achieved a two-dimensional current density uniformity of better than 90 %.

A finite element based parametric study to assess the suitability of factors used in EJMA for estimation of the meridional stresses in bellows

Bellows are highly engineered components. In general, the design of bellows is carried out as per the standards of the expansion joints manufacturer’s association (EJMA). In EJMA, the basic form of the expressions for estimation of stresses was derived by considering the half convolution of the bellows as a strip beam. Since axisymmetric shell theory leads to a more realistic response of the bellows, EJMA had introduced factors Cp, Cd and Cf for estimation of the meridional stress in the bellows due to pressure and deflection. These factors in EJMA are plotted as a function of two parameters viz. QW and QDT, which are dependent on bellows geometry and ply thickness. This paper discusses the suitability of the above-mentioned factors considering various configurations of the bellows. A finite element based parametric study was carried out and meridional stresses in the bellows were calculated due to pressure and deflection loading for various values of the QW and QDT. Around 36 bellows geometries with different ranges of QW and QDT were analysed numerically. Based on FE analysis, the EJMA factors Cp, Cd and Cf values were estimated and compared with the corresponding values given in EJMA. It was observed that for both shallow (QW approaching 1) and deeper convolutions (QW approaching 0.2), the EJMA solutions lead to an under prediction of membrane stress due to deflection loading and over-prediction of meridional bending stress due to deflection and pressure loading. The effect of geometric nonlinearities on elastically calculated stresses bellows was quantified for various geometries.

Revealing deformation of segments and their supports in a hydrostatic segmental bearing

At present, there are theoretical and experimental studies of such bearings without taking into account the elastic deformation of the bearing segments. The rotor bearings of powerful turbines at nuclear power plants are subjected to loads as high as tens of tons. One of the important issues in designing segmental bearings operating under these conditions consists in taking into account elastic deformations of the segments. A schematic diagram of a segmental hydrostatic bearing was presented and the principle of its operation was described. When determining the deformation of spherical support, a formula of change in volume of a solid steel ball subjected to uniform pressure was applied. To determine the segment deformation in the axial direction, differential equation of bending of the strip beam as the initial one. The basic equation of deformation of rods with a curved axis acting in the plane of curvature was taken as a starting point of determining the segment deformation in the circumferential direction. It was found in the studies that the maximum deformation of the segment is 4.5 % of radial clearance at a feed pressure of 5 MPa and can affect the bearing characteristics. A substantially nonlinear character of deformations along the segment axis was revealed. It was found that the pressure of the working fluid significantly affects the segment thickness. With an increase in feeding pressure from 1 MPa to 10 MPa, the thickness of the steel segment increased more than 2 times and the thickness of the bronze segment increased more than 3 times. It was established that the pressure of the working fluid exceeding 10 MPa substantially affects the deformation of the spherical support and the bearing clearance. The study results will make it possible to determine more accurately the main characteristics of the segmental bearing and design it more efficiently.

Pure Bending of Strip (BEAM) with Crack in Strip of Tensile Stress with Allowance for Plastic Strips Near Crack Tips

Abstract In the article, the pure bending problem for strip (beam) with straight, perpendicular to its axis crack located in the zone of tensile stresses is investigated on the assumption of narrow plastic strips near crack tips. Using methods of the theory of functions of a complex variable and complex potentials, the problem is reduced to the several linear conjunction problems. The solutions of latter problems are obtained in the class of functions confined in the edges of plastic strips. Formulas for the calculation of their lengths are derived. Expressions for the determination of crack tip opening values are written. Numerical analysis of the problem is performed.

New Method for Analyzing the Flutter Stability of Hingeless Blades with Advanced Geometric Configurations in Hovering

A new method used to analyze the aeroelastic stability of a helicopter hingeless blade in hovering has been developed, which is especially suitable for a blade with advanced geometric configuration. This method uses a modified doublet-lattice method (MDLM) and a 3-D finite element (FE) model for building the aeroelastic equation of a blade in hovering. Thereafter, the flutter solution of the equation is calculated by the V-g method, assuming blade motions to be small perturbations about the steady equilibrium deflection. The MDLM, which is suitable to calculate the unsteady aerodynamic force of nonplanar rotor blade in hovering, is developed from the doublet-lattice method (DLM). The structural analysis tool is the commercial software ANSYS. The comparisons of the obtained results against those in the literatures show the capabilities of the MDLM and the method of structural analysis. The flutter stabilities of swept tip blades with different aspect ratios are analyzed using the new method developed in this work and the usual method on the basis of the unsteady strip theory and beam model. It shows that considerable differences appear in the flutter rotational velocities with the decrease of the aspect ratio. The flutter rotational velocities obtained by the present method are evidently lower than those obtained by the usual method.

Structural behavior of SCC continuous deep beam strengthening and retrofitting with carbon fiber reinforced polymer strips

This study presents an experimental work to investigate the structural behavior of continuous self-compacting concrete (SCC) deep beams strengthened and retrofitted with woven carbon fiber reinforced polymer (CFRP) strips and evaluate their shear capacity. The work includes casting and testing fourteen beams specimens. All tested beams have the same dimensions, the same flexural reinforcement and concrete compressive strength with two continuous span and have been subjected to two-point loads. The test specimens were divided into three groups. The first group including eight beams with minimum ratio of shear reinforcement (ρv= ρh=0.25%) and two parameters considered, shear span to overall depth ratio (a/h) and three different schemes of CFRP strip. The second group including four beams without interior vertical and horizontal shear reinforcement (ρv=ρh=0%) with three different schemes of CFRP strip and control beam. The third group consists of two beams with minimum ratio (ρv= ρh=0.25%) were firstly loaded to 65% of the ultimate load of control beams, after that the loads were released and then retrofitted by CFRP strip by two different schemes. The experimental results show that the specimens with vertical CFRP strips an increase in ultimate strength load by 32.6% and 20% compared to the control beams.

Чистий згин полоси (балки) з довільно орієнтованою наскрізною тріщиною

The problem of pure bending of strip (beam) with transverse rectilinear crack, edges of which are free from acuter load, is investigated in this paper. Under bending moment its edges may not contact or smoothly contact throughout its area length or part. Dependently on where it is located.Using methods of theory of functions of complex variable and complex potentials the problem at issue has been reduced to the problems of linear conjugation, their analytical solution is found. Explicit expressions on complex potentials is written. Based on the energy criterion of destruction stress intensity factors are determined. Limit value of moment when the crack begins to propagate is found. For the case when crack edges partially contact, area length of contact of her edges is determined. Numerical analysis of critical moment of failure of strip (beams) is performed under various parameters of the problem, which are related to the mechanical state of crack. The corresponding graphic dependencies are constructed.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ НАПРЯЖЕННО-ДЕФОРМИРОВАННОГО СОСТОЯНИЯ В ПОВЕРХНОСТНО УПРОЧНЕННЫХ ВТУЛКАХ С УЧЕТОМ ОСТАТОЧНЫХ КАСАТЕЛЬНЫХ НАПРЯЖЕНИЙ

We suggest the phenomenological mathematical model of the stress-strain state reconstruction in the surface hardened thin-walled tube with an inner diameter 45 mm and outer diameter 51.5 mm made of steel EI961 and treated by diamond smoothing of the outer surface. It is shown that if all stress components depend on radius only, then the components are in the cylindrical coordinate system. The experimental research is made for the samples which were softened under two load modes (radial force) of the diamond ball attachment of 200 and 300 N value. The experimental values of residual stresses , , and in the surface layer are obtained by the ring and strip method using the layer-by-layer electrochemical pickling of the hardened layer. The experimentally measured values of the strip beam deflection, split ring angular opening and axial displacement of cut edges relative to each other are used for this purpose. The hardening anisotropy parameter which relates the axial and circumferential components of plastic strain is included in the mathematical model. To solve the formulated problems we use the hypotheses of plastic incompressibility of the material, the absence of secondary plastic deformations of the material in the surface layer compression area and the hypotheses of flat sections and straight radii. We present the method for solving the stress-strain state reconstruction boundary value problems, which allows obtaining the missing component and all residual plastic strain components. The validation of the computational data obtained by mathematical modelling for adequacy to the experimental data for the two modes of hardening is made. There is a close agreement between the computational and experimental data. The numerical values for the hardening anisotropy parameter are given. By using this parameter we are able to theoretically describe the observable experimental layering of axial and circumferential stresses in depth of the hardened layer. It is theoretically and experimentally established that the absolute values of maximum shear stresses is an order of magnitude smaller than the absolute values of maximum normal stresses. We also discuss the questions of the effect of shear stresses on high-cycle fatigue and creep of the hardened thin-walled tubes. The main results of the research are illustrated by the tabular data and corresponding diagrams of the residual stresses distribution in depth of the hardened layer.

Study of the scattered light with the strip beam incident to the LiNbO3:Fe crystal

In this paper, we systematically studied the scattered light when the stripe beam of ordinary polarized light and extraordinary polarized light are incident to the LiNbO3:Fe crystal, respectively. First, we observed the variation of scattered light with the different angle between the stripe beam and the c-axis. And find the scattered light is growing with time along the c-axis direction of the crystal when the e-light is incident; while the scattered light is growing along a special direction which is not the c-axis direction or the stripe direction, when o-light is incident to the crystal. Then we analyzed the causes of these phenomena. In addition, we also studied the diffraction efficiency of o-light and e-light, and the raster image in the crystal.

Pedestrians’ perception and response towards vehicles during road-crossing at nighttime

Pedestrian being involved in road traffic accidents (RTA) is about 22% of all road traffic related deaths. In this study, we have estimated the pedestrian’s response towards an approaching vehicle and the time taken to correctly recognize it while they crossed the road in dim-light nighttime conditions. This is also extendable to cycles and other low powered vehicles. Thirty volunteers participated in this study. A collection of six videos, which comprised of different vehicle scenarios were shown to each of the participants. It was observed that correct identification and time to recognize the vehicle was fastest when light emitting diode (LED) strip was fixed between headlights of a four–wheeler. Average time to recognize a low beam car and a high beam car with an LED strip was 7.62±2.39s and 11.23±2.94s respectively, whereas correct identification rates of the said low beam and high beam cars with LED strips were 93.33% and 86.67% respectively. Earlier when no LED was used, time to recognize low beam car and high beam car without LED strip were 20.55±3.50s and 25.57±4.14s respectively whereas correct identification of low beam car without LED strip and high beam car without LED strip were 90.00% and 56.67% respectively. Pedestrians are therefore less confused and can take right decision while crossing the road – particularly in a poor lighting environment – when there is a demarcating illumination between headlights of vehicle.

On the use of spring models to analyse the lateral-torsional buckling behaviour of cracked beams

This paper is focused on the lateral-torsional buckling of cracked or weakened elastic beams. The crack is modelled with a generalised elastic connection law, whose equivalent stiffness parameters can be derived from fracture mechanics considerations. The same type of generalised spring model can be used for beams with semi-rigid connections, typically in the fields of steel and timber engineering. As the basis for the present investigation, we consider a strip beam with fork end supports and exhibiting a single vertical edge crack, subjected to uniform bending in the plane of greatest flexural rigidity. We adopt both direct and variational approaches. In the former, conducted within the framework of the Kirchhoff–Clebsch theory, the effect of prebuckling curvature is taken into consideration. This effect is subsequently neglected in the variationally based analyses. First, the three-dimensional elastic connection law adopted is a direct extension of the planar case, which leads to a paradoxical conclusion: the critical moment is not affected by the presence of the crack, regardless of its location. It is shown that the above paradox is due to the non-conservative nature of the connection model adopted (in the sense that the connection law cannot be derived from a potential). Simple alternatives to this cracked-section constitutive law are proposed, based on conservative moment-rotation laws (quasi-tangential and semi-tangential) and consistent variational arguments. Only one of the proposed alternatives leads to a critical moment that depends on both the torsional and flexural stiffnesses of the spring modelling the cracked cross-section. The analyses are always conducted analytically, yielding closed-form characteristic equations for the buckling moments.

Out-of-Plane Buckling of Microstructured Beams: Gradient Elasticity Approach

AbstractThis paper deals with the lateral-torsional buckling of elastic microstructured beams. A linear gradient elasticity approach is presented. The elastic constitutive law is linear for the generalized beam model, expressed with first- and second-order moment variables in a sixth-order dimensional stress-strain space. The boundary conditions (including the higher-order boundary conditions) are derived from application of the variational principle applied to second-grade elastic models. The effect of prebuckling deformation is taken into consideration based on the Kirchhoff-Clebsch theory. Some analytical solutions are presented for a hinged-hinged strip beam. The lateral-torsional buckling moment is sensitive to small length terms inherent in the microstructured constitutive law. It is shown that the gradient parameter tends to increase the critical lateral-torsional buckling moment, a conclusion different from the one obtained with an Eringen-based nonlocal model. This tendency is consistent with tha...

One-dimensional models of a beam made of an anisotropic material with oblique anisotropy

One-dimensional equations of the statics and free vibration of a strip beam made of an anisotropic material of general form (oblique anisotropy) are derived. It is shown that neither the Kirchhoff-Love hypotheses nor the classical Timoshenko-Reissner hypotheses lead to well-posed one-dimensional equations. A variant of the generalized Timoshenko-Reissner model is proposed that permits one to satisfy the boundary conditions on the beam surface exactly and leads to an asymptotically correct one-dimensional model. The solutions of the one- and two-dimensional equations of the statics and free vibration problems are compared and the dispersion equation is analyzed.

On Lateral-Torsional Buckling of Non-Local Beams

Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with microor nanostructures. This paper deals with the lateral-torsional buckling of elastic nonlocal small-scale beams. Eringen's model is chosen for the nonlocal constitutive bendingcurvature relationship. The effect of prebuckling deformation is taken into consideration on the basis of the Kirchhoff-Clebsch theory. It is shown that the application of Eringen's model produces small-length scale terms in the nonlocal elastic lateraltorsional buckling moment of a hinged-hinged strip beam. Clearly, the non-local parameter has the effect of reducing the critical lateral-torsional buckling moment. This tendency is consistent with the one observed for the in-plane stability analysis, for the lateral buckling of a hinged-hinged axially loaded column. The lateral buckling solution can be derived from a physically motivated variational principle.

Investigation of an expanding copper plasma across a transverse magnetic field generated by strip-type electron-beam

The electron beam assisted thermal processes are well-established technique for various applications such melting, evaporation, isotope purification, ion-implantation etc. The processes are time average, wherein process is carried out over a larger duration so that real time dependent variations gets averaged out. During electron beam evaporation and atomic beam generation, ions also get generated inherently due to interaction of primary and back-scattered electrons with the atomic vapour along with other routes like Saha ionization, secondary electron ionization etc. The presence of ions has a bearing in the quality of deposited films and influence the ion implantation process. It also has strong effect on dilution factor in isotope purification. Thus the knowledge of ion content, its distribution and evolution in the freely expanding atomic beam in vacuum is important for any process optimisation in electron beam evaporation applications. The thermal ion content in atomic vapour for a given element as a function of aspect ratio (height/length) and source Knudsen number can be used as most inexpensive technique to characterized the evaporation on time average as well as teal time processes. With this intension, a series of experiments were carried out in a 100 kW strip beam evaporator with 130mm strip electron gun with copper as target material. A wedge shaped copper atomic beam is generated from a two dimensional evaporating source (120mm × 6mm) by impingement of the electron beam up to 90kW power. Disk type Langmuir probe is used for measuring I-V characteristic plots for deriving the thermal ion flux. The measurements are carried out as a function source Knudsen number (depends on incident electron beam power), and the probe distance from source that defines the aspect ratio. Along with probe data, the atom flux is also simultaneously measured using quartz crystal thickness monitor. The evolution of ions and atoms with distance from source is compared.

Measurement & simulation of backscattered electrons from a strip electron beam source

During electron beam processing, a fraction of the incident power gets backscattered from the target surface, which can be as high as 40% of the incident beam power depending on the beam energy and atomic number of the target material. In the case of a strip electron gun, a uniform magnetic field is used for focusing and deflection of electron beam through 270°. With the strip beam (78 mm×5 mm, 36 kW), experimental results of the 2-D distribution of the backscattered electron current from copper target in its plane, parallel and perpendicular to the focal strip are presented. These results are compared with calculated data using reported energy distribution of backscattered electrons (E.H.Darlington, J. Phys. 8 (1975) 85). The integrated heat flux associated with backscattered electron is experimentally measured and compared with calculated values for incident power of 86 kW. With 12.25 kW/cm 2 of incident strip beam power, the back reflected electron peak power density was observed to be 59W/cm 2. This power density will be higher for high incident power densities and for targets of high atomic numbers and can be used in pre-coating treatments of substrate such as outgassing and cleaning, keeping it at elevated temperature during continuous coating process, and also for outgassing, cleaning and sharing heat load required for pre-melting of the feeder material during melting and casting.

00/00520 Environmental assessment and characterization of residues from coal processing and steel industry activities

A new method is presented to eliminate the undesirable end-effect appearing in the formation of a strip beam of charged particles according to the Pierce theory, without any additional device. By this method, a beam with finite length can be formed, regarding the cross section of the beam reasonably as a thin ellipse.An analytical solution is given for a rectilinear elliptic beam formation. It is troublesome, however, to perform the complete evaluation of the solution, but an approximation is also presented with sufficient accuracy.

Modulational instability of a strip beam in a bulk type I quadratic medium

The evolution of a strip (one-dimensional) fundamental beam with propagation distance owing to spatial modulational instabilities was analyzed in a quadratic medium near type I phase matching. We obtained the gain coefficient for the modulational instability and showed that the wave evolves into a clean periodic sequence of solitary waves and does not reproduce the incident beam.

Entrance Window Design Parameters for High-Pressure Gas X-Ray Imaging Detectors

Gas ionization x-ray detectors operating at pressures up to 100 atm offer inherently high spatial and contrast resolution. However, incorporating the detector x-ray entrance window in a conventional pressure vessel designed for such pressures can result in high primary beam loss in the window and a much reduced overall detective quantum efficiency. The design of a gas chamber cover plate for a strip beam detector which mechanically isolates the x-ray entrance window from the lateral tensile stresses in the chamber body is described. A number of test windows of this design, varying in three geometric parameters-thickness, window curvature, and fillet radius-were fabricated from wrought aluminum [6061-T651 ] and subjected to pressures of up to 400 atm for the purpose of selecting an optimum window for a prototype digital x-ray imaging detector. The experimental data indicate that windows can be designed for a detector admitting a 1.0 cm wide x-ray beam that have rupture pressures exceeding 500 atm while maintaining x-ray transmittances of as much as 93.4% for a 120 kVp tungsten anode spectrum.

Entrance window design parameters for high-pressure gas x-ray imaging detectors

Gas ionization x-ray detectors operating at pressures up to 100 atm offer inherently high spatial and contrast resolution. However, incorporating the detector x-ray entrance window in a conventional pressure vessel designed for such pressures can result in high primary beam loss in the window and a much reduced overall detective quantum efficiency. The design of a gas chamber cover plate for a strip beam detector which mechanically isolates the x-ray entrance window from the lateral tensile stresses in the chamber body is described. A number of test windows of this design, varying in three geometric parameters—thickness, window curvature, and fillet radius—were fabricated from wrought aluminum [6061-T651] and subjected to pressures of up to 400 atm for the purpose of selecting an optimum window for a prototype digital x-ray imaging detector. The experimental data indicate that windows can be designed for a detector admitting a 1.0 cm wide x-ray beam that have rupture pressures exceeding 500 atm while maintaining x-ray transmittances of as much as 93.4% for a 120 kVp tungsten anode spectrum.