• Title/Summary/Keyword: Euler number

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Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory

  • Kaci, Abdelhakim;Houari, Mohammed Sid Ahmed;Bousahla, Abdelmoumen Anis;Tounsi, Abdelouahed;Mahmoud, S.R.
    • Structural Engineering and Mechanics
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    • v.65 no.5
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    • pp.621-631
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    • 2018
  • In this paper, an exact analytical solution is developed for the analysis of the post-buckling non-linear response of simply supported deformable symmetric composite beams. For this, a new theory of higher order shear deformation is used for the analysis of composite beams in post-buckling. Unlike any other shear deformation beam theories, the number of functions unknown in the present theory is only two as the Euler-Bernoulli beam theory, while three unknowns are needed in the case of the other beam theories. The theory presents a parabolic distribution of transverse shear stresses, which satisfies the nullity conditions on both sides of the beam without a shear correction factor. The shear effect has a significant contribution to buckling and post-buckling behaviour. The results of this analysis show that classical and first-order theories underestimate the amplitude of the buckling whereas all the theories considered in this study give results very close to the static response of post-buckling. The numerical results obtained with the novel theory are not only much more accurate than those obtained using the Euler-Bernoulli theory but are almost comparable to those obtained using higher order theories, Accuracy and effectiveness of the current theory.

Axial Turbine Aerodynamic Design of Small Heavy-Duty Gas Turbines (발전용 소형가스터빈의 축류터빈 공력설계)

  • Kim, Joung Seok;Lee, Wu Sang;Ryu, Je Wook
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.37 no.4
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    • pp.415-421
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    • 2013
  • This study describes the aerodynamic design procedure for the axial turbines of a small heavy-duty gas turbine engine being developed by Doosan Heavy Industries. The design procedure mainly consists of three parts: namely, flowpath design, airfoil design, and 3D performance calculation. To design the optimized flowpath, through-flow calculations as well as the loss estimation are widely used to evaluate the effect of geometric variables, for example, shape of meridional plane, mean radius, blades axial gap, and hade angle. During the airfoil design procedure, the optimum number of blades is calculated by empirical correlations based on the in/outlet flow angles, and then 2D airfoil planar sections are designed carefully, followed by 2D B2B NS calculations. The designed planar sections are stacked along the spanwise direction, leading to a 3D surfaced airfoil shape. To consider the 3D effect on turbine performance, 3D multistage Euler calculation, single row, and multistage NS calculations are performed.

Semi-automatic 3D Building Reconstruction from Uncalibrated Images (비교정 영상에서의 반자동 3차원 건물 모델링)

  • Jang, Kyung-Ho;Jang, Jae-Seok;Lee, Seok-Jun;Jung, Soon-Ki
    • Journal of Korea Multimedia Society
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    • v.12 no.9
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    • pp.1217-1232
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    • 2009
  • In this paper, we propose a semi-automatic 3D building reconstruction method using uncalibrated images which includes the facade of target building. First, we extract feature points in all images and find corresponding points between each pair of images. Second, we extract lines on each image and estimate the vanishing points. Extracted lines are grouped with respect to their corresponding vanishing points. The adjacency graph is used to organize the image sequence based on the number of corresponding points between image pairs and camera calibration is performed. The initial solid model can be generated by some user interactions using grouped lines and camera pose information. From initial solid model, a detailed building model is reconstructed by a combination of predefined basic Euler operators on half-edge data structure. Automatically computed geometric information is visualized to help user's interaction during the detail modeling process. The proposed system allow the user to get a 3D building model with less user interaction by augmenting various automatically generated geometric information.

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Computation of Dynamic Fluid-Structure Interaction in a 2-Dimensional Laminar Channel Flow Divided by a Plate (판으로 나뉘어진 2차원 충류 채널유동에서 동적 유체-구조물 상호작용 수치해석)

  • Namkoong, Kak;Choi, Hyoung-Gwon;Yoo, Jung-Yul
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.26 no.12
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    • pp.1738-1746
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    • 2002
  • In the FSI (Fluid-Structure Interaction) problems, two different governing equations are to be solved together. One is fur the fluid and the other for the structure. Furthermore, a kinematic constraint should be imposed along the boundary between the fluid and the structure. We use the combined formulation, which incorporates both the fluid and structure equations of motion into a single coupled variational equation so that it is not necessary to calculate the fluid force on the surface of structure explicitly when solving the equations of motion of the structure. A two-dimensional channel flow divided by a Bernoulli-Euler beam is considered and the dynamic response of the beam under the influence of channel flow is studied. The Navier-Stokes equations are solved using a P2P1 Galerkin finite element method with ALE (Arbitrary Lagrangian-Eulerian) algorithm. The internal structural damping effect is not considered in this study and numerical results are compared with a previous work fer steady case. In addition to the Reynolds number, two non-dimensional parameters, which govern this fluid-structure system, are proposed. It is found that the larger the dynamic viscosity and density of the fluid are, the larger the damping of the beam is. Also, the added mass is found to be linearly proportional to the density of the fluid.

Vibration of Rectangular Plates (직사각형판(直四角形板)의 진동해석(振動解析))

  • Keuck-Chun,Kim;Tae-Young,Chung
    • Bulletin of the Society of Naval Architects of Korea
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    • v.14 no.1
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    • pp.1-10
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    • 1977
  • The major objects of this report are to supplement data of natural frequencies of thin elastic rectangular plates to the available data, and to give an experimental verification for natural frequencies obtained by Rayleigh-Ritz method, the generation set of which are eigenfunctions of Euler beams. For the first object the following five models, for which data only for the fundamental mode or data only for square plates are available, are adopted; (1) two opposed edges are clamped and the other two opposed edges simply supported (C-C, S-S), (2) one edge is simply supported and the other three edges clamped (C-C, C-S), (3) one edge is free and the other three edges clamped (C-C, C-F), (4) two adjacent edges are clamped and the other two adjacent edges free (C-F, C-F). For the (C-C, S-S) model the frequency equation obtained with the mode shapes assumed as of a single trigonometric series is solved. And for the other four models Rayleigh-Ritz method taking eigenfunctions of Euler beams as the generating set is applied. The numerical examples are obtained up to the fourth, the fifth or the sixth order depending on the range of the aspect ratio (0.1-10.0). The number of terms in the generating set for Rayleigh-Ritz method is fifteen for all models. For the experiment three models made of 3.2mm thickness mild steel plate for general structure use were prepared in following size; $300mm{\times}600mm,\;600mm{\times}600mm\;and\;900mm{\times}600mm$. Their boundary conditions are made to fit (C-C, C-F) condition. From the experiment mechanical impedance curves based on the frequency response method were obtained together with phase relation diagrams. The experimental data are resulted in good conformity to calculated values.

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Bayesian estimation of tension in bridge hangers using modal frequency measurements

  • Papadimitriou, Costas;Giakoumi, Konstantina;Argyris, Costas;Spyrou, Leonidas A.;Panetsos, Panagiotis
    • Structural Monitoring and Maintenance
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    • v.3 no.4
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    • pp.349-375
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    • 2016
  • The tension of an arch bridge hanger is estimated using a number of experimentally identified modal frequencies. The hanger is connected through metallic plates to the bridge deck and arch. Two different categories of model classes are considered to simulate the vibrations of the hanger: an analytical model based on the Euler-Bernoulli beam theory, and a high-fidelity finite element (FE) model. A Bayesian parameter estimation and model selection method is used to discriminate between models, select the best model, and estimate the hanger tension and its uncertainty. It is demonstrated that the end plate connections and boundary conditions of the hanger due to the flexibility of the deck/arch significantly affect the estimate of the axial load and its uncertainty. A fixed-end high fidelity FE model of the hanger underestimates the hanger tension by more than 20 compared to a baseline FE model with flexible supports. Simplified beam models can give fairly accurate results, close to the ones obtained from the high fidelity FE model with flexible support conditions, provided that the concept of equivalent length is introduced and/or end rotational springs are included to simulate the flexibility of the hanger ends. The effect of the number of experimentally identified modal frequencies on the estimates of the hanger tension and its uncertainty is investigated.

Numerical Prediction of Unsteady Transitional Boundary Layer Flows due to Rotor-Stator Interaction(II)-Characteristics of Unsteady Transitional Boundary Layer Flow- (정익과 동익의 상호작용에 의한 비정상 천이 경계층 유동의 수치해석에 관한 연구 (II))

  • Kang, Dong-Jin;Lakshminarayana, Budugur
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.22 no.6
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    • pp.771-787
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    • 1998
  • A Navier-Stokes code with a modified low Reynolds number k-.epsilon. turbulence model was used to study the unsteady transitional boundary layer flow due to rotor-stator interaction. The modification, proposed by Launder, to improve prediction of stagnation flows was incorporated to the low Reynolds number k-.epsilon. turbulence model by Fan-Lakshminarayana-Barnett. Numerical solution is shown to capture well the calmed laminar flow as well as the wake induced transitional strip due to rotor-stator interaction and shows improvement, in terms of onset of transition and its length, over previous Euler/boundary layer solution. The turbulent kinetic energy shows local maximum along the upstream rotor wake in the wake induced transitional strip and this characteristics is observed untill the end of transition. The wake induced strip also shown apparent even in the laminar sublayer as the upstream rotor wake penetrates inside the boundary layer.

A Study of the Twin Impulse Wave Discharged from the Exit of Two Parallel Tubes (두 평행한 관의 출구로부터 방출되는 트윈파에 관한 연구)

  • Kang, Sung-hwang;Kim, Jae-Ho;Kim, Heuy-dong
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.8 s.101
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    • pp.962-967
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    • 2005
  • The twin-impulse wave discharged from two parallel tubes is investigated to see flow patterns, compared with the single impulse wave. In the present study, the merging phenomena and propagation characteristics of the impulse waves are investigated by experiment and numerical computation. The Harten-Yee's total variation diminishing scheme is used to solve the unsteady, two-dimensional, compressible, Euler equations. The Mach number Ms of incident shock wave is lower than 1.5 and the distance between the tubes is between 1.2 and 4.0. In the shock tube experiment, the twin impulse waves are visualized by a Schlieren optical system in order to validate the computational result. It is shown that on the symmetric axis between two parallel tubes, the peak pressure produced by the twin impulse waves and its location strongly depend upon the tube distance and the incident shock Mach number, Ms. The predicted Schlieren images show a good agreement with the measured twin-impulse wave.

Sound Radiation Analysis for Structure Vibration Noise Control of Vehicle Tire under The Action of Random Moving Line Forces (불규칙 이동분포하중을 받는 차량 타이어의 구조 진동소음 제어를 위한 음향방사 해석)

  • Kim Byoung-sam
    • Proceedings of the Acoustical Society of Korea Conference
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    • autumn
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    • pp.221-224
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    • 2004
  • A theoretical model has been studied to describe the sound radiation analysis for structure vibration noise of vehicle tires under the action of random moving line forces. When a tire is analyzed, it had been modeled as curved beams with distributed springs and dash pots that represent the radial , tangential stiffness and damping of tire, respectively. The reaction due to fluid loading on the vibratory response of the curved beam is taken into account. The curved beam is assumed to occupy the plane y=0 and to be axially infinite. The curved beam material and elastic foundation are assumed to be lossless Bernoulli-Euler beam theory including a tension force, damping coefficient and stiffness of foundation will be employed. The expression for sound power is integrated numerically and the results examined as a function of Mach number, wave-number ratio and stiffness factor. The experimental investigation for structure vibration noise of vehicle tire under the action of random moving line forces has been made. Based on the Spatial Transformation of Sound Field techniques, the sound power and sound radiation are measured. Results strongly suggest that operation condition in the tire material properties and design factors of the tire govern the sound power and sound radiation characteristics.

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Secondary Instability in the Wake of a Circular Cylinder (원주 후류에서의 2차적 불안정성)

  • KNAG S. J.;TANAHASHI M.;MIYAUCHI T.;LEE Y. H.
    • 한국전산유체공학회:학술대회논문집
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    • 2001.10a
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    • pp.84-90
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    • 2001
  • Secondary instability of flow past a circular cylinder is examined using direct numerical simulation at Reynolds number 220 and 250. The higher-order finite difference scheme is employed for the spatial distributions along with the second order Adams-Bashforth and the first order backward-Euler time integration. In x-y plane, the convection term is applied by the 5th order upwind scheme, and the pressure and viscosity terms are applied by the 4th order central difference. In spanwise, Navier-Stokes equation is distributed using Spectral Method. The critical Reynolds number for this instability is found to be about Re=190. The secondary instability leads re three-dimensionality with a spanwise wavelength about 4 cylinder diameters at onset (A-mode). Results of three-dimensional effect in wake of a circular cylinder are represented with spanwise and streamwise vorticity contours as Reynolds numbers.

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