• Title/Summary/Keyword: Non-linear Equation

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A Study on Channel Flood Routing Using Nonlinear Regression Equation for the Travel Time (비선형 유하시간 곡선식을 이용한 하도 홍수추적에 관한 연구)

  • Kim, Sang Ho;Lee, Chang Hee
    • Journal of Wetlands Research
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    • v.18 no.2
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    • pp.148-153
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    • 2016
  • Hydraulic and hydrological flood routing methods are commonly used to analyze temporal and spatial flood influences of flood wave through a river reach. Hydrological flood routing method has relatively more simple and reasonable performance accuracy compared to the hydraulic method. Storage constant used in Muskingum method widely applied in hydrological flood routing is very similar to the travel time. Focusing on this point, in this study, we estimate the travel time from HEC-RAS results to estimate storage constant, and develop a non-linear regression equation for the travel time using reach length, channel slope, and discharge. The estimated flow by Muskingum model with storage constant of nonlinear equation is compared with the flow calculated by applying the HEC-RAS 1-D unsteady flow simulation. In addition, this study examines the effect on the weighting factor changes and interval reach divisions; peak discharge increases with the bigger weighting factor, and RMSE decreases with the fragmented division.

Obtaining 3-D Depth from a Monochrome Shaded Image (단시안 명암강도를 이용한 물체의 3차원 거리측정)

  • Byung Il Kim
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.29B no.7
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    • pp.52-61
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    • 1992
  • An iterative scheme for computing the three-dimensional position and the surface orientation of an opaque object from a singel shaded image is proposed. This method demonstrates that calculating the depth(distance) between the camera and the object from one shaded video image is possible. Most previous research works on $'Shape from Shading$' problem, even in the $'Photometric Stereo Method$', invoved the determination of surface orientation only. To measure the depth of an object, depth of the object, and the reflectance properties of the surface. Assuming that the object surface is uniform Lambertian the measured intensity level at a given image pixel*x,y0becomes a function of surface orientation and depth component of the object. Derived Image Irradiance Equation can`t be solved without further informations since three unknown variables(p,q and D) are in one nonlinear equation. As an additional constraints we assume that surface satisfy smoothness conditions. Then equation can be solved relaxatively using standard methods of TEX>$'Calculus of VariationTEX>$'. After checking the sensitivity of the algorithm to the errors ininput parameters, the theoretical results is tested by experiments. Three objects (plane, cylinder, and sphere)are used. Thees initial results are very encouraging since they match the theoretical calculations within 20$\%$ error in simple experiments.> error in simple experiments.

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Finite Element Modal Analysis of a Spinning Flexible Disk-spindle System Supported by Hydro Dynamic Bearings and Flexible Supporting Structures in a HDD (유연한 지지 구조와 유체 동압 베어링으로 지지되는 HDD의 회전 유연 디스크-스핀들 시스템에 대한 유한 요소 고유 진동 해석)

  • Han, Jaehyuk;Jang, Gunhee
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.3 s.96
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    • pp.251-258
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    • 2005
  • The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings (HDB) in an HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Reynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigen value problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

Study on Wear of Journal Bearings during Start-up and Coast-down Cycles of a Motoring Engine - I. Theory and Analysis Procedure (모터링 엔진의 시동 사이클 및 시동 정지 사이클에서 저어널베어링의 마모 연구 − I. 이론 및 해석 절차)

  • Chun, Sang Myung
    • Tribology and Lubricants
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    • v.31 no.3
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    • pp.109-124
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    • 2015
  • This paper presents a wear analysis procedure for the journal bearings on a stripped-down single-cylinder engine during start-up and coast-down by motoring. A journal bearing is in the mixed elastohydrodynamic (EHL) lubrication region when the shaft speed is less than the corresponding lift-off speed. Below the lift-off speed, a wear scar can form on bearing surfaces. In part 1 of this paper, we develop the appropriate formulations and the calculation procedure for the analysis. Specifically, we formulate an equation for modified film thickness in a journal bearing considering the additional wear volume. In order to obtain the modified specific wear rate induced by the modified Archard’s wear coefficient, we utilized the extended non-dimensional diagram for the specific wear rate, k, the fractional film defect coefficient, Ψ and the asperity load sharing factor, γ2. This asperity load sharing factor is newly calculated by setting the Zhao-Maietta-Chang (ZMC) asperity contact pressure equation coupled with the central film thickness equation derived by using the ZMC asperity contact model equal to the modified central contact pressure derived by using the central (or maximum) contact pressure at the dry rough line-contact configuration. We can use the procedure introduced in this paper to determine the lifetime (or longterm) linear wear in radial journal bearings that is a result of repeated stop-start cycles.

A Study on the Protecting Wall for Transferring Pipe of Waste Using Cast Basalt Tube (용융주조 현무암 튜브를 이용한 생활폐기물 이송관로의 보호벽에 관한 연구)

  • Wang, Jee-Seok;Kim, Jong-Do;Yoon, Hee-Jong
    • Journal of Advanced Marine Engineering and Technology
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    • v.34 no.6
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    • pp.816-824
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    • 2010
  • The forces applying to an object in the transferring pipe of waste are analyzed and the equation of motion is established in this paper. It is shown that the equation of motion becomes the 1st order non-linear differential equation. Using its general solution, the velocity of the object in the transferring pipe of waste can be expressed in the explicit form. Noting that the velocity of object is impact velocity to the elbow or curved part of the transferring pipe of waste, the kinetic energy of the object can be calculated and the necessary impact strength of inner wall is obtained. The velocity of object is also calculated and presented in the graphic forms with the condition of air velocity 30m/sec. The impact test of cast basalt tube is carried out by the free fall of a weight and the test results show that the impact strength of the cast basalt tube is sufficient to apply to protecting inner wall of the transferring pipe of waste.

Finite Element Modal Analysis of a Spinning Flexible Disk-Spindle System Supported by Hydro Dynamic Bearings and Flexible Supporting Structures In a HDD (유연한 지지 구조와 유체 동압 베어링으로 지지되는 HDD의 회전 유연 디스크-스핀들 시스템에 대한 유한 요소 고유 진동 해석)

  • 한재혁;장건희
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.11a
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    • pp.572-578
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    • 2003
  • The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings in a HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Raynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigenvalue problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

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Analysis of PIG Dynamics through Curved Section in Natural Gas Pipeline (천연가스 배관 곡관부에서의 피그 동적 거동 해석)

  • Kim D. K.;Nguyen T. T.;Yoo H. R.;Rho Y. W.;Kho Y.T.;Kim S. B.
    • Journal of the Korean Institute of Gas
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    • v.6 no.1 s.17
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    • pp.1-9
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    • 2002
  • This paper presents simple models for flow and the PIG dynamics when it passes through a $90^{\circ}$ curved section of pipeline. The simulation has been done with two different operational boundary conditions. The solution fur non-linear hyperbolic partial equations for flow is given by using MOC. The Runge-Kuta method is used to solve the initial condition equation fur flow and the PIG dynamics equation. The simulation results show that the proposed model and solution can be used fur estimating the PIG dynamics when the pig runs in the pipeline including curved section. In this paper, dynamic modeling and its analysis for the PIG flow through $90^{\circ}$ curved pipe with compressible and unsteady flow are studied. The PIG dynamics model is derived by using Lagrange equation under assumption that it passes through 3 different sections in the curved pipeline such that it moves into, inside and out of the curved section. The downstream and up stream flow dynamics including the curved sections are solved using MOC. The effectiveness of the derived mathematical models is estimated by simulation results fur a low pressure natural gas pipeline including downward and upward curved sections. The simulation results show that the proposed model and solution can be used for estimating the PIG dynamics when we pig the pipeline including curved section.

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Compression Lap Splice Length in Concrete of Compressive Strength from 40 to 70 MPa (40-70 MPa 콘크리트에서의 철근 압축이음 길이)

  • Chun, Sung-Chul;Lee, Sung-Ho;Oh, Bo-Hwan
    • Journal of the Korea Concrete Institute
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    • v.21 no.4
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    • pp.401-408
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    • 2009
  • A compression lap splice becomes an important issue due to development of ultra-high strength concrete. Current design codes regarding compression lap splice do not utilize merits of the improved strength of ultra-high strength concrete. Especially, a compression lap splice can be calculated longer than a tension lap splice according to the codes because they do not consider effects of compressive strength of concrete and transverse reinforcement. This anomaly confuses engineers in practice. Design equation is proposed for compression lap splice in 40 to 70 MPa of compressive strength of concrete. The proposed equation is based on 51 specimens conducted by authors. Basic form of the equation includes main parameters which are derived from investigating test results. Through two-variable non-linear regression analysis of measured splice strengths, a strength equation of compression lap splices is then derived. A specified splice strength is defined using a 5% fractile coefficient and a lap length equation is constructed. By the proposed equation, the anomaly of lap lengths in tension and compression is got rid of. In addition, the equation has a reliability equivalent to those of the specified strengths of materials.

Nonlinear Moment-Curvature Relations and Numerical Structural Analysis of High-Strength PSC Flexural Members (고강도 PSC 휨부재의 비선형 모멘트-곡률 관계와 전산구조해석)

  • 연정흠;이제일
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.15 no.1
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    • pp.95-104
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    • 2002
  • A methods to calculate non-linear moment-curvature relations of high-strength PSC flexural members for numerical analysis has been proposed. The moment-curvature relations were calculated with assumptions of design codes and by the layer method. The results of the proposed procedures for moment-curvature relations and numerical analysis were compared with those of pre-existing tests. The absorption energy rate of the design codes was about 30% larger than that of the layer method. The ultimate load and the external work of the layer method were 90% and 85% of those of tests, respectively The ultimate load of the strength design method was 97% of that of tests, but the external work was over-estimated with 122%. The ultimate load and external work by the proposed equation of the CEB-FIP Model Code were 113% and 173% of those of tests, respectively. It show that the use of ultimate strain of 0.0035 should be over-estimated for high-strength concrete. The procedure of non-linear numerical analysis of this research could be stably simulated the behavior of concrete flexural members until the ultimate state, and calculate results of the load-deflection relation and cracking pattern were very similar with those of tests.

2-D Axisymmetric Non-linear Finite Strain Consolidation Model Considering Self-weight Consolidation of Dredged Soil (준설매립지반의 자중압밀을 고려한 2차원 축대칭 비선형 유한변형 압밀 모델)

  • Kwak, Tae-Hoon;Lee, Dong-Seop;Lim, Jee-Hee;Stark, T.D.;Choi, Eun-Seok;Choi, Hang-Seok
    • Journal of the Korean Geotechnical Society
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    • v.28 no.8
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    • pp.5-19
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    • 2012
  • Vertical drains along with the preloading technique have been commonly used to enhance the consolidation rate of dredged placement formation. In practice, vertical drains are usually installed in the process of self-weight consolidation of a dredged soil deposit because this process takes considerable time to be completed, which makes conventional analytical or numerical models difficult to quantify the consolidation behavior. In this paper, we propose a governing partial differential equation and develop a numerical model for 2-D axisymmetric non-linear finite strain consolidation considering self-weight consolidation to predict the behavior of a vertical drain in the dredged placement foundation which is installed during the self-weight consolidation. In order to verify the developed model in this paper, results of the numerical analysis are compared with that of the lab-scaled self-weight consolidation test. In addition, the model verification has been carried out by comparing with the simplified method. The comparisons show that the developed model can properly simulate the consolidation of the dredged placement formation with the vertical drains installed during the self-weight consolidation. Finally, the effect of construction schedule of vertical drains and of pre-loading during the self-weight consolidation is examined by simulating an imaginary dredged material placement site with a thickness of 10 m and 20 m, respectively. This simulation infers the applicability of the proposed method in this research for designing a soil improvement in a soft dredged deposit when vertical drains and pre-loading are implemented before the self-weight consolidation ceases.