• Title/Summary/Keyword: Beam equation

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A Study on the Correction of Beam Pattern for the Ultrasonic Attenuation Coefficient Estimation (초음파 감쇠계수 주정에 있어서 빔 형태의 보정에 관한 연구)

  • Kim, Gi-Uk;Choe, Heung-Ho;Hong, Seung-Hong
    • Journal of Biomedical Engineering Research
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    • v.8 no.1
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    • pp.41-48
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    • 1987
  • In estimating the freguency-dependent attenuation coefficient, we analyzed the range-dependent ultrasonic beam and proposed the method of calculating the experimental equation of beam pattern in order to reduce the error on the influence of beam pattern. These experimental equations are divided into the spectral centroid and the spec ural standard deviation slope according to axial propagation length. These are repnesented by the first-order equation in the near field of the beam and the second- order eqLlatlon In the far field. In order to prove the validity of this method, the attenuation coefficients of the non-corrected ease and the corrected case are compared. Using the reflected signal from acryle plate, the attenuation coefficients were estimated by the spectral shift method ann the spectral difference method. The result shows attenuation coeffi talents after correction are better than attenuation coefficients before correction. And this method can be applied In vivo measurement.

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Behavior and design of steel I-beams with inclined stiffeners

  • Yang, Yang;Lui, Eric M.
    • Steel and Composite Structures
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    • v.12 no.3
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    • pp.183-205
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    • 2012
  • This paper presents an investigation of the effect of inclined stiffeners on the load-carrying capacity of simply-supported hot-rolled steel I-beams under various load conditions. The study is carried out using finite element analysis. A series of beams modeled using 3-D solid finite elements with consideration of initial geometric imperfections, residual stresses, and material nonlinearity are analyzed with and without inclined stiffeners to show how the application of inclined stiffeners can offer a noticeable increase in their lateral-torsional buckling (LTB) capacity. The analysis results have shown that the amount of increase in LTB capacity is primarily dependent on the location of the inclined stiffeners and the lateral unsupported length of the beam. The width, thickness and inclination angle of the stiffeners do not have as much an effect on the beam's lateral-torsional buckling capacity when compared to the stiffeners' location and beam length. Once the optimal location for the stiffeners is determined, parametric studies are performed for different beam lengths and load cases and a design equation is developed for the design of such stiffeners. A design example is given to demonstrate how the proposed equation can be used for the design of inclined stiffeners not only to enhance the beam's bearing capacity but its lateral-torsional buckling strength.

Development of a neural network method for measuring the energy spectrum of a pulsed electron beam, based on Bremsstrahlung X-Ray

  • Sohrabi, Mohsen;Ayoobian, Navid;Shirani, Babak
    • Nuclear Engineering and Technology
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    • v.53 no.1
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    • pp.266-272
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    • 2021
  • In the pulsed electron beam generators, such as plasma focus devices and linear induction accelerators whose electron pulse width is in the range of nanosecond and less, as well as in cases where there is no direct access to electron beam, like runaway electrons in Tokamaks, measurement of the electron energy spectrum is a technical challenge. In such cases, the indirect measurement of the electron spectrum by using the bremsstrahlung radiation spectrum associated with it, is an appropriate solution. The problem with this method is that the matrix equation between the two spectrums is an ill-conditioned equation, which results in errors of the measured X-ray spectrum to be propagated with a large coefficient in the estimated electron spectrum. In this study, a method based on the neural network and the MCNP code is presented and evaluated to recover the electron spectrum from the X-ray generated by collision of the electron beam with a target. Multilayer perceptron network showed good accuracy in electron spectrum recovery, so that for the X-ray spectrum with errors of 3% and 10%, the network estimated the electron spectrum with an average standard error of 8% and 11%, on all of the energy intervals.

Crack detection method for step-changed non-uniform beams using natural frequencies

  • Lee, Jong-Won
    • Smart Structures and Systems
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    • v.30 no.2
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    • pp.173-181
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    • 2022
  • The current paper presents a technique to detect crack in non-uniform cantilever-type pipe beams, that have step changes in the properties of their cross sections, restrained by a translational and rotational spring with a tip mass at the free end. An equation for estimating the natural frequencies for the non-uniform beams is derived using the boundary and continuity conditions, and an equivalent bending stiffness for cracked beam is applied to calculate the natural frequencies of the cracked beam. An experimental study for a step-changed non-uniform cantilever-type pipe beam restrained by bolts with a tip mass is carried out to verify the proposed method. The translational and rotational spring constants are updated using the neural network technique to the results of the experiment for intact case in order to establish a baseline model for the subsequent crack detection. Then, several numerical simulations for the specimen are carried out using the derived equation for estimating the natural frequencies of the cracked beam to construct a set of training patterns of a neural network. The crack locations and sizes are identified using the trained neural network for the 5 damage cases. It is found that the crack locations and sizes are reasonably well estimated from a practical point of view. And it is considered that the usefulness of the proposed method for structural health monitoring of the step-changed non-uniform cantilever-type pipe beam-like structures elastically restrained in the ground and have a tip mass at the free end could be verified.

Defect Length Measurement using Underwater Camera and A Laser Slit Beam

  • Kim, Young-Hwan;Yoon, Ji-Sup
    • 제어로봇시스템학회:학술대회논문집
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    • 2003.10a
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    • pp.746-751
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    • 2003
  • A method of measuring the length of defects on the wall of the spent nuclear fuel pool using the image processing and a laser slit beam is proposed. Since the defect monitoring camera is suspended by a crane and hinged to the crane hook, the camera viewing direction can not be adjusted to the orientation that is exactly perpendicular to the wall. Thus, the image taken by the camera, which is horizontally rotated along the axis of the camera supporting beam, is distorted and thus, the precise length can not be measured. In this paper, by using the LASER slit beam generator, the horizontally rotated angle of the camera is estimated. Once the angle is obtained, the distorted image can be easily reconstructed to the image normal to the wall. The estimation algorithm adopts a 3-dimensional coordinate transformation of the image plane where both the laser slit beam and the original image of the defects exist. The estimation equation is obtained by using the information of the beam projected on the wall and the parameters of this equation are experimentally obtained. With this algorithm, the original image of the defect taken at arbitrary rotated angle can be reconstructed to an image normal to the wall. From the result of a series of experiments, the accuracy of the defect is measured within 0.6 and 1.3 % error bound of real defect size in the air and underwater, respectively under 30 degree of the inclined angle of the laser slit beam generator. Also, the error increases as the inclined angle increases upto 60 degree. Over this angle, the defect length can not be measured since the defect image disappears. The proposed algorithm enables the accurate measurement of the defect length only by using a single camera and a laser slit beam.

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Free Vibrations and Buckling Loads of Axially Loaded Cross-Ply Laminated Composite Beam-Columns with Multiple Delaminations (다층간분리된 직교 적층 보-기둥의 자유진동과 좌굴하중)

  • 이성희;김형열;박기태;박대효
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.15 no.3
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    • pp.523-534
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    • 2002
  • Free vibration and buckling analysis of multi-delaminated composite beam-columns subjected to axial compressive load is performed in the present study In order to investigate the effects of multi-delaminations on the natural frequency and the elastic buckling load of multi-delaminated beam-columns, the general kinematic continuity conditions are derived from the assumption of constant slope and curvature at the multi-dclamination tip. The characteristic equation of multi-delaminated beam-column is obtained by dividing the global multi-delauunated beam-columns into segments and by imposing recurrence relation from the continuity conditions on each sub-beam-column. The natural frequency and the elastic buck)ing load of multi-delaminated beam-columns according to the incremental load of axial compression, which is limited to the maximum elastic buckling load of sound laminated beam-column, are obtained. It is found that the sizes, locations and numbers of multi-delaminations have significant effect on natural frequency and elastic buckling load, especially the latter ones.

Particle Simulation Modelling of a Beam Forming Structure in Negative-Ion-Based Neutral Beam Injector (중성빔 입사장치에서 빔형성 구조의 입자모사 모형)

  • Park, Byoung-Lyong;Hong, Sang-Hee
    • Nuclear Engineering and Technology
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    • v.21 no.1
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    • pp.40-47
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    • 1989
  • For the effective design of a beam forming structure of the negative-ion-based neutral beam injector, a computer program based on a particle simulation model is developed for the calculation of charged particle motions in the electrostatic fields. The motions of negative ions inside the acceleration tube of a multiple-aperture triode are computed at finite time steps. The electrostatic potentials are obtained from the Poisson's equation by the finite difference method. The successive overrelaxation method is used to solve the matrix equation. The particle and force weighting methods are used on a cloud-in-cell model. The optimum design of the beam forming structure has been studied by using this computer code for the various conditions of elctrodes. The effects of the acceleration-deceleration gap distance, the thickness of the deceleration electrode and the shape of the acceleration electrode on beam trajectories are exmined to find the minimum beam divergence. Some numerical illustrations are presented for the particle movements at finite time steps in the beam forming tubes. It is found in this particle simulation modelling that the shape of the acceleration electrode is the most significant factor of beam divergence.

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Nonlinear analysis of finite beam resting on Winkler foundation with consideration of beam-soil interface resistance effect

  • Zhang, L.;Zhao, M.H.;Xiao, Y.;Ma, B.H.
    • Structural Engineering and Mechanics
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    • v.38 no.5
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    • pp.573-592
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    • 2011
  • Comprehensive and accurate analysis of a finite foundation beam is a challenging engineering problem and an important subject in foundation design. One of the limitation of the traditional Winkler elastic foundation model is that the model neglects the effect of the interface resistance between the beam and the underneath foundation soil. By taking the beam-soil interface resistance into account, a deformation governing differential equation for a finite beam resting on the Winkler elastic foundation is developed. The coupling effect between vertical and horizontal displacements is also considered in the presented method. Using Galerkin method, semi-analytical solutions for vertical and horizontal displacements, axial force, shear force and bending moment of the beam under symmetric loads are presented. The influences of the interface resistance on the behavior of foundation beam are also investigated.

A Characteristic Study on Shear Strength of Reinforced Concrete Beams according to Shear Reinforcement Ratio and Beam Section Size (전단철근비와 보의 단면크기에 따른 철근콘크리트 보의 전단강도 특성 연구)

  • Noh, Hyung-Jin;Yu, In-Geun;Lee, Ho-Kyung;Baek, Seung-Min;Kim, Woo-Suk;Kwak, Yoon-Keun
    • Journal of the Architectural Institute of Korea Structure & Construction
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    • v.35 no.6
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    • pp.111-119
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    • 2019
  • The purpose of this study is to investigate the shear strength of reinforced concrete beam according to beam section size and shear reinforcement ratio. A total of nine specimens were tested and designed concrete compressive strength is 24 MPa. The main variables are shear reinforcement ratio and beam section size fixed with shear span to depth ratio (a/d = 2.5), the tensile reinforcement ratio (${\rho}=0.013$) and width to depth ratio (h/b = 1.5). The test specimens were divided into three series of S1 ($225{\times}338mm$), S2 ($270{\times}405mm$) and S3 ($315{\times}473mm$), respectively. The experimental results show that all specimens represent diagonal tensile failure. For $S^*-1$ specimens (d/s=0), the shear strength decreased by 33% and 46% with increasing the beam effective depth, 26% and 33% for $S^*-2$ specimens (d/s=1.5) and 16% and 20% for $S^*-3$ specimens (d/s=2.0) respectively. As the shear reinforcement ratio increases, the decrease range in shear strength decreases. In other words, this means that as the shear reinforcement ratio increases, the size effect of concrete decreases. In the S1 series, the shear strength increased by 39% and 41% as the shear reinforcement ratio increased, 54% and 76% in the S2 series and 66% and 100% in the S3 series, respectively. As the effective depth of beam increases, the increase range of shear strength increases. This means that the effect of shear reinforcement increases as the beam effective depth increases. As a result of comparing experimental values with theoretical values by standard equation and proposed equation, the ratio by Zsutty and Bazant's equation is 1.30 ~ 1.36 and the ratio by KBC1 and KBC2 is 1.55~.163, respectively. Therefore, Zsutty and Bazant's proposed equation is more likely to reflect the experimental data. The current standard for shear reinforcement ratio (i.e., $S_{max}=d/2$) is expected to be somewhat relaxed because the ratio of experimental values to theoretical values was found to be 1.01 ~ 1.44 for most specimens.

Six Sigma Robust Design of Composite Hand for LCD Glass Transfer Robot (LCD 유리 이송용 복합재료 로봇 핸드의 식스 시그마 강건설계)

  • Nam Hyunwook
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.29 no.3 s.234
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    • pp.455-461
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    • 2005
  • This research studied robust design of composite hand for LTR (LCD glass Transfer Robot). $1^{st}$ DOE (Design of Experiment) was conducted to find out vital few Xs. 108 experiments were performed and their results were statistically analyzed. Pareto chart analysis shows that the geometric parameters (height and width of composite beam) are more important than material parameters $(E_{1},\;E_{2})$ or stacking sequence angle. Also, the stacking sequence of mid-layer is more important than that of outer-layer. The main effect plots shows that the maximum deflection of LTR hand is minimized with increasing height, width of beam and layer thickness. $2^{nd}$ DOE was conducted to obtain RSM (Response Surface Method) equation. 25 experiments were conducted. The CCD (Central Composite Design) technique with four factors was used. The coefficient of determination $(R^{2})$ for the calculated RSM equation was 0.989. Optimum design was conducted using the RSM equation. Multi-island genetic algorithm was used to optimum design. Optimum values for beam height, beam width, layer thickness and beam length were 24.9mm, 186.6mnL 0.15mm and 2402.4mm respectively. An approximate value of 0.77mm in deflection was expected to be a maximum under the optimum conditions. Six sigma robust design was conducted to find out guideline for control range of design parameter. To acquire six sigma level reliability, the standard deviation of design parameter should be con trolled within $2{\%}$ of average design value