• Title/Summary/Keyword: Approximate Solutions

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Analytic Solution to Mild Slope Equation for Transformation of Waves Propagating over an Axi-symmetric Pit (축대칭 함몰지형 위를 진행하는 파의 변형에 관한 완경사 방정식의 해석 해)

  • Jung, Tae-Hwa;Suh, Kyung-Duck
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.18 no.4
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    • pp.308-320
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    • 2006
  • An analytic solution to the mild-slope equation is derived for waves propagating over an axi-symmetric pit. The water depth inside the pit varies in proportion to a power of radial distance from the pit center. The governing equation is transformed into ordinary differential equations by using separation of variables, and the coefficients of the equations are transformed into explicit forms by using Hunt's (1979) approximate solution. Finally, by using the Frobenius series, the analytic solution is derived. Due to the feature of Hunt's equation, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth water. The validity of the analytic solution is demonstrated by comparison with numerical solutions. The analytic solution is also used to examine the effects of pit geometry and relative depth on wave transformation.

Weighted Averaged Flux Method for Computation of Shallow Water Equations (WAF 기법을 이용한 천수방정식 해석)

  • Kim, Woo-Gu;Jung, Kwan-Sue;Kim, Jae-Han
    • Journal of Korea Water Resources Association
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    • v.36 no.5
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    • pp.777-785
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    • 2003
  • A numerical model for the solution of two-dimensional free surface flow is developed on unstructured grid. By using fractional step method, the two-dimensional shallow water equations (SWE) are treated as two one-dimensional problems. Thus, it is possible to simulate computational hydraulic problems with higher computational efficiency. The one-dimensional problems are solved using upwind TVD version of second-order Weighted Averaged Flux (WAF) scheme with HLLC approximate Riemann solver. The numerical oscillations which are common with second-order numerical scheme are controlled by exploiting WAF flux limiter, Some idealized test problems are solved using this model and very accurate and stable solutions are obtained. It can be concluded as an efficient implement for the computation of SWE including dam break problems that concerning discontinuities, subcritical and supercritical flows and complex domain.

Voltammetric Determination of Copper(II) Using Glassy Carbon Electrodes Modified with Nafion-DTPA-Glycerol

  • Park, Chan-Ju;Park, Eun-Heui;Chung, Keun-Ho
    • Proceedings of the Korean Environmental Health Society Conference
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    • 2003.06a
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    • pp.177-180
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    • 2003
  • A glassy carbon electrode(GCE) modified with nafion-DTPA-glycerol was used for the highly selective and sensitive determination of a trace amount of Cu$\^$2+/. Various experimental parameters, which influenced the response of nafion-DTPA-glycerol modified electrode to Cu$\^$2+/, were optimized. The copper(II) was accumulated on the electrode surface by the formation of the complex in an open circuit, and the resulting surface was characterized by medium exchange, electrochemical reduction, and differential pulse voltammetry, A linear range was obtained in the concentration range 1.0${\times}$10$\^$-8/M∼1.0${\times}$10$\^$-6/M Cu(II) with 7 min preconcentration. Further, when an approximate amount of lead(II) is added to the test solution, nafion-DTPA-glycerol modified glassy carbon electrode has a dynamic range of 2 orders magnitude(1.0${\times}$10$\^$-9/M∼1.0${\times}$10$\^$-7/M). The detection limit(3 $\sigma$) was as low as 5.0${\times}$10$\^$-6/M(0.032ppb). The interferences from other metal ions could be reduced by adding KCN into the sample solutions. This method was applied to the determination of coppe,(II) in certified reference material(3.23${\times}$10$\^$-7/M, 21ppb), sea water(9.50${\times}$10/sup-7/M, 60ppb). The result agrees satisfactorily with the value measured by Korea Research Institute of Standard and Science.

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Free Torsional Vibration of Linearly Tapered I-Beams (선형(線形) 변단면(變斷面) I-형(型) 보의 비틂진동(振動))

  • Lee, Yong Woo;Min, Kyung Ju
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.5
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    • pp.1013-1021
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    • 1994
  • The stiffness and mass matrices are developed for free torsional vibration analysis in linearly tapered thin-walled I-beams that takes into account the effect of warping torsion. The approximate shape functions are used for formulating stiffness and mass matrices. Significant improvements of accuracy and efficiency of free vibration analysis are achieved by using the stiffness and mass matrices developed in this study. Frequencies of free vibration of tapered members are compared with solutions based upon stepped representation of beam element and also are verified with model tests. The stiffness and mass matrices presented in this study can be used for the free vibration analysis of tapered and prismatic thin walled I-beams and space structures involving warping torsion.

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Thermo-optic Characteristics of Micro-structured Optical Fiber Infiltrated with Mixture Liquids

  • Wang, Ran;Wang, Yuye;Miao, Yinping;Lu, Ying;Luan, Nannan;Hao, Congjing;Duan, Liangcheng;Yuan, Cai;Yao, Jianquan
    • Journal of the Optical Society of Korea
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    • v.17 no.3
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    • pp.231-236
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    • 2013
  • We present both theoretically and experimentally the thermo-optic characteristics of micro-structured optical fiber (MOF) filled with mixed liquid. The performance of MOF depends on the efficient interaction between the fundamental mode of the transmitted light wave and the tunable thermo-optic materials in the cladding. The numerical simulation indicates that the confinement loss of MOF presents higher temperature dependence with higher air-filling ratios $d/{\Lambda}$, longer incident wavelength and fewer air holes in the cladding. For the 4cm liquid-filled grapefruit MOF, we demonstrate from experiments that different proportions of solutions lead to tunable temperature sensitive ranges. The insertion loss and the extinction ratio are 3~4 dB and approximate 20 dB, respectively. The proposed liquid-filling MOF will be developed as thermo-optic sensor, attenuator or optical switch with the advantages of simple structure, compact configuration and easy fabrication.

Solid Solution Phenomena of Al+Al3Ti Alloy and Al+10wt.%Ti Alloy using Mechanical Alloying Process (기계적 합금화법에 의해 제조된 Al+Al3Ti합금 및 Al+10wt.%Ti합금의 고용현상)

  • Kim, Hye-Sung;Lee, Jung-Ill;Kim, Gyeung-Ho;Kum, Dong-Wha;Shur, Dong-Soo
    • Journal of the Korean Society for Heat Treatment
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    • v.9 no.2
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    • pp.121-129
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    • 1996
  • The solubility of Ti in Al matrix was determined by X-ray diffraction method on two different mechanical alloying systems, i.e Al+$Al_3Ti$ and Al+Ti alloys. Starting powder compositions of two systems were chosen for final volume fraction of $Al_3Ti$ phase being 25%. The solubility of Ti in ${\alpha}$-Al was estimated by the lattice parameter measurement of Al. For Al+$Al_3Ti$ mixture, it appeared that some of $Al_3Ti$ particles decomposed during milling and maximum solubility of Ti in Al was about 0.99%. The majority of $Al_3Ti$ particles were dispersed uniformly in Al matrix, having approximate size of 100~200 nm. On the other hand, higher Ti solubility of 1.24 wt.% was found in Al+Ti system, with starting composition of Al+10 wt.%Ti. After 15 hours of milling, Ti phase was identified as 20 nm sized particles embedded in Al matrix. The annealing of mechanically alloyed powders from Al+$Al_3Ti$ and Al+10 wt.%Ti systems was followed in the temperature range of 200 to $600^{\circ}C$ to study thermal stability of supersaturated solution of Al(Ti). After annealing, the lattice parameter of Al reverted back to that of pure Al, and the peak intensity ratio of $Al_3Ti$/Al was increased more than the original value before annealing. These results suggest that Ti dissolve into alpha-Al solutions during milling, and by annealing, $Do_{22}-Al_3Ti$ phase forms from Al(Ti) solution.

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Sensitivity Approach of Sequential Sampling Using Adaptive Distance Criterion (적응거리 조건을 이용한 순차적 실험계획의 민감도법)

  • Jung, Jae-Jun;Lee, Tae-Hee
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.29 no.9 s.240
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    • pp.1217-1224
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    • 2005
  • To improve the accuracy of a metamodel, additional sample points can be selected by using a specified criterion, which is often called sequential sampling approach. Sequential sampling approach requires small computational cost compared to one-stage optimal sampling. It is also capable of monitoring the process of metamodeling by means of identifying an important design region for approximation and further refining the fidelity in the region. However, the existing critertia such as mean squared error, entropy and maximin distance essentially depend on the distance between previous selected sample points. Therefore, although sufficient sample points are selected, these sequential sampling strategies cannot guarantee the accuracy of metamodel in the nearby optimum points. This is because criteria of the existing sequential sampling approaches are inefficient to approximate extremum and inflection points of original model. In this research, new sequential sampling approach using the sensitivity of metamodel is proposed to reflect the response. Various functions that can represent a variety of features of engineering problems are used to validate the sensitivity approach. In addition to both root mean squared error and maximum error, the error of metamodel at optimum points is tested to access the superiority of the proposed approach. That is, optimum solutions to minimization of metamodel obtained from the proposed approach are compared with those of true functions. For comparison, both mean squared error approach and maximin distance approach are also examined.

A Study on the Vibration Analysis of Beam (보의 진동해석에 관한 연구)

  • Kim, Yeong-Sik;Moon, Duk-Hong
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.20 no.1
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    • pp.43-48
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    • 1984
  • The transfer matrix method is well-known and extensively used for finding solutions in vibration problems. At the final stage of this method natural frequencies are obtained by a trial and error search procedure. In this paper authors presented the method which needed only a few division number to yield an accurate solution and the most effective method to get an approximate solution in the case of beam vibrations. The methods which were presented by authors could be applied for the beam with nonuniform section and uniformly distributed load, and the values of numerical calculations by these methods have just agreed with those of experiments.

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The stress analysis of a shear wall with matrix displacement method

  • Ergun, Mustafa;Ates, Sevket
    • Structural Engineering and Mechanics
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    • v.53 no.2
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    • pp.205-226
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    • 2015
  • Finite element method (FEM) is an effective quantitative method to solve complex engineering problems. The basic idea of FEM for a complex problem is to be able to find a solution by reducing the problem made simple. If mathematical tools are inadequate to obtain precise result, even approximate result, FEM is the only method that can be used for structural analyses. In FEM, the domain is divided into a large number of simple, small and interconnected sub-regions called finite elements. FEM has been used commonly for linear and nonlinear analyses of different types of structures to give us accurate results of plane stress and plane strain problems in civil engineering area. In this paper, FEM is used to investigate stress analysis of a shear wall which is subjected to concentrated loads and fundamental principles of stress analysis of the shear wall are presented by using matrix displacement method in this paper. This study is consisting of two parts. In the first part, the shear wall is discretized with constant strain triangular finite elements and stiffness matrix and load vector which is attained from external effects are calculated for each of finite elements using matrix displacement method. As to second part of the study, finite element analysis of the shear wall is made by ANSYS software program. Results obtained in the second part are presented with tables and graphics, also results of each part is compared with each other, so the performance of the matrix displacement method is demonstrated. The solutions obtained by using the proposed method show excellent agreements with the results of ANSYS. The results show that this method is effective and preferable for the stress analysis of shell structures. Further studies should be carried out to be able to prove the efficiency of the matrix displacement method on the solution of plane stress problems using different types of structures.

Modeling Method of Receiving Radar Signals from Warhead and Decoy with Micro-Motion (미세운동을 가지는 탄두 및 기만체의 새로운 레이다 수신신호 모델링 방법)

  • Choi, In-Oh;Park, Sang-Hong;Kang, Ki-Bong;Kim, Kyung-Tae
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.30 no.3
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    • pp.243-251
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    • 2019
  • Recently, several studies were conducted on the micro-Doppler(MD) phenomenon to identify a warhead from decoys. Both, the warhead and decoy, can be modeled as various shapes and maneuver with their own micro-motion. Their MD phenomenon can be demonstrated by amplitude modulation and phase modulation. Most studies have utilized approximate solutions to express the amplitude modulation regardless of various warhead and decoy shapes. However, the exact solution of the amplitude modulation is required for more effective warhead identification. In this study, we proposed a new modeling method of receiving radar signals from warheads and decoys based on physical optics. The proposed solution was evaluated using an electromagnetic prediction technique and computer-aided design models.