• Title/Summary/Keyword: Non-linear Equation

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Nonlinear Wave Forces on an Offshore Wind Turbine Foundation in Shallow Waters

  • Choi, Sung-Jin;Lee, Kwang-Ho;Hong, Keyyoung;Shin, Seong-Ho;Gudmestad, O.T.
    • International Journal of Ocean System Engineering
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    • v.3 no.2
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    • pp.68-76
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    • 2013
  • In this study, a 3D numerical model was used to predict nonlinear wave forces on a cylindrical pile installed in a shallow water region. The model was based on solving the viscous and incompressible Navier-Stokes equations for a two-phase flow (water and air) model and the volume of fluid method for treating the free surface of water. A new application was developed based on the cut-cell method to allow easy installation of complicated obstacles (e.g., bottom geometry and cylindrical pile) in a computational domain. Free-surface elevation, water particle velocities, and inline wave forces were calculated, and the results show good agreement with experimental data obtained by the Danish Hydraulic Institute. The simulation results revealed that the proposed model can, without the use of empirical formulas (i.e., Morison equation) and additional wave analysis models, reliably predict non-linear wave forces on an offshore wind turbine foundation installed in a shallow water region.

A new analytical model to determine dynamic displacement of foundations adjacent to slope

  • Varzaghani, Mehdi Imani;Ghanbari, Ali
    • Geomechanics and Engineering
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    • v.6 no.6
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    • pp.561-575
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    • 2014
  • Estimating seismic displacements has a great importance for foundations on or adjacent to slope surfaces. However, dynamic solution of the problem has received little attention by previous researchers. This paper presents a new analytical model to determine seismic displacements of the shallow foundations adjacent to slopes. For this purpose, a dynamic equilibrium equation is written for the foundation with failure wedge. Stiffness and damping at the sliding surface are considered variable and a simple method is proposed for its estimation. Finally, for different failure surfaces, the calculated dynamic displacement and the surfaces with maximum strain are selected as the critical failure surface. Analysis results are presented as curves for different slope angles and different foundation distances from edge of the slope and are then compared with the experimental studies and software results. The comparison shows that the proposed model is capable of estimating seismic displacement of the shallow foundations adjacent to slopes. Also, the results demonstrate that, with increased slope angle and decreased foundation distances from the slope edge, seismic displacement increases in a non-linear trend. With increasing the slope angle and failure wedge angle, maximum strain of failure wedge increases. In addition, effect of slope on foundation settlement could be neglected for the foundation distances over 3B to 5B.

Comparison of Models to Describe Growth of Green Algae Chlorella vulgaris for Nutrient Removal from Piggery Wastewater (양돈폐수의 영양염류 제거를 위한 녹조류 Chlorella vulgaris 성장 모형의 비교)

  • Lim, Byung-Ran;Jutidamrongphan, Warangkana;Park, Ki-Young
    • Journal of The Korean Society of Agricultural Engineers
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    • v.52 no.6
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    • pp.19-26
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    • 2010
  • Batch experiments were conducted to investigate growth and nutrient removal performance of microalgae Chlorella vulgaris by using piggery wastewater in different concentration of pollutants and the common growth models (logistic, Gompertz and Richards) were applied to compare microalgal growth parameters. Removal of nitrogen (N) and phosphorus (P) by Chlorella vulgaris showed correlation with biomass increase, implying nutrient uptake coupled with microalgae growth. The higher the levels of suspended solids (SS), COD and ammonia nitrogen were in the wastewater, the worse growth of Chlorella vulgaris was observed, showing the occurrence of growth inhibition in higher concentration of those pollutants. The growth parameters were estimated by non-linear regression of three growth curves for comparative analyses. Determination of growth parameters were more accurate with population as a variable than the logarithm of population in terms of R square. Richards model represented better fit comparing with logistic and Gompertz model. However, Richards model showed some complexity and sensitivity in calculation. In the cases tested, both logistic and Gompertz equation were proper to describe the growth of microalgae on piggery wastewater as well as easy to application.

Analysis and Modeling of Wireless Power Transfer Systems using Magnetically Coupled Resonator Scheme with Relay Coils (릴레이 코일을 포함한 자기 공명 방식 무선 전력 전송 시스템의 분석 및 모델링)

  • Park, Hee-Su;Kwon, Min-Sung;Kim, Min-Ji;Park, Hyeon-Min;Ku, Hyun-Chul
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.28 no.1
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    • pp.69-78
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    • 2014
  • In this paper, characteristics of wireless power transfer (WPT) systems using magnetically coupled resonance scheme with relay coils are investigated and modeled. Especially, asymmetric frequency splitting characteristics in over-coupled region of WPT with relays are measured and accurately modeled. Transmitter, receiver, and relay coils are modeled with R, L, C equivalent circuits. Using these circuit models and mutual inductances between coils, a WPT system is described with a linear matrix equation. For under-coupled region, a matrix is simplified considering only mutual inductances between adjacent coils. An analytical transfer characteristic of WPT system vs. distance is extracted using an inverse matrix that is acquired by Gauss elimination method for the simplified matrix. For over-coupled region, a matrix considering mutual inductances between non-adjacent coils is used to predict a frequency splitting characteristics accurately. A 6.3MHz WPT system with relay coils is implemented and measured. An accuracy of the model is investigated by comparing the output of the model with the measured results.

Simulation of the Dynamic Interactions between Catenary and Pantograph (전차선과 팬터그래프 사이의 동적 상호작용 시뮬레이션)

  • Kwon, Sam-Young;Kim, Gil-Sang
    • Proceedings of the KIEE Conference
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    • 1995.07a
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    • pp.455-459
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    • 1995
  • Catenary/pantograph system consists of overhead lines which have non-uniform elasticity and pantographs which move at high speed and give force to the lines, therefore happen to be failed in contacts between both from time to time. In this study, as the first step to develop a dynamic simulation program, the general theory is discussed for catenary/pantograph system and appropriate modelling. And comparison is conducted with the references after making a program which referred to the contact force equation algorithm. On this algorithm, the unknown contact force is computed by the equations which was induced as combining catenary and pantograph motion equations expressed in finite difference form. Another simulation program based on the assumed contact forces algorithm was developed. In this algorithm, numerical integraion of both the overhead line and pantograph equations, which without combining, are effected for two assumed values of contact force. The correct contact force is then obtained from these two sets of results by linear interpolation to satisfy the contact condition. Through the comparative review on the outputs from this program, it is verified that this algorithm is reliable.

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Numerical Analysis in Unsteady State on variation of Diameter and Environmental Velocity of Carbon Heating Source (탄소발열체의 외부유속 및 직경변화에 대한 비정상상태에서의 수치해석적 연구)

  • Bae, K.Y.;Lee, Y.H.;Lee, S.Y.;Lee, C.S.;Kim, B.G.;Lee, S.H.
    • Journal of Power System Engineering
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    • v.10 no.4
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    • pp.25-30
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    • 2006
  • This paper represents the numerical analysis in unsteady state on the variation of diameter and environmental velocity of carbon heating source. In general heating system, the oil and sheath heater is widely used, but these systems have many problems. So, the heating source with carbon ingredient has been researched in many country about manufacture, thermal and electrical properties. In this research, the carbon heating source was studied through numerical analysis on several conditions of unsteady state, heat generation, diameter and environmental velocity. The temperature distributions at steady state are appeared as a non-proportional linear pattern with variations of environmental velocity due to the Nesselt number with convective heat flux is proportioned to 0.805 of Reynolds number. As the radius is increasing, the temperature distributions is appeared the minus tilt because of the environmental condition is cooling by constant temperature. So, the correlation equation between temperature at steady state and environmental velocity was obtained.

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Free Vibration Analysis of Circular Strip Foundations (원호형 띠기초의 자유진동 해석)

  • Lee, Jong-Kook;Kang, Hee-Jong;Lee, Byoung-Koo
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2004.11a
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    • pp.898-901
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    • 2004
  • Since soil-structure interactions are one of the most important subjects in the structural/foundation engineering, much study concerning the soil-structure interactions had been carried out. One of typical structures related to the soil-structure interactions is the strip foundation which is basically defined as the beam or strip rested on or supported by the soils. At the present time, lack of studies on dynamic problems related to the strip foundations is still found in the literature. From these viewpoint, this paper aims to theoretically investigate dynamics of the circular strip foundations and also to present the practical engineering data for the design purpose. Differential equations governing the free, out-of-plane vibrations of such strip foundations are derived, in which effects of the rotatory and torsional inertias and also shear deformation are included although the warping of the cross-section is excluded. Governing differential equations subjected to the boundary conditions of corresponding end constraints are numerically solved for obtaining the natural frequencies and mode shapes by using the numerical integration technique and the numerical method of non-linear equation.

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Age and Growth of White Croaker Pennahia argentata in the Southern Sea of Korea by Otolith Analysis (한국 남해안에 서식하는 보구치(Pennahia argentata)의 이석을 이용한 연령 및 성장)

  • Jeon, Bok Soon;Choi, Jung Hwa;Kim, Doo Nam;Im, Yang Jae;Lee, Hae Won
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.54 no.1
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    • pp.53-63
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    • 2021
  • Age structure and growth of white croaker Pennahia argentata were estimated an analysis of otoliths. Fish specimens were collected from the Southern Sea of Korea from January to December 2018. A thin section method was used for age determination because otoliths of white croaker are oval in shape and large in size. Otoliths were cut vertically into 0.4-0.5 mm thick sections with an electric saw (Micracut 125). Monthly changes in the marginal index indicated that rings (opaque zone) were formed once a year in August. The estimated von Bertalanffy growth equation estimated by a non-linear regression were L∞=34.71 (1-e0.38(t+0.80)). In the present study, the oldest female was 8 years old and the male was 7 years old.

The Estimated Source of 2017 Pohang Earthquake Using Surface Deformation Modeling Based on Multi-Frequency InSAR Data

  • Fadhillah, Muhammad Fulki;Lee, Chang-Wook
    • Korean Journal of Remote Sensing
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    • v.37 no.1
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    • pp.57-67
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    • 2021
  • An earthquake occurred on 17 November 2017 in Pohang, South Korea with a strength of 5.4 Mw. This is the second strongest earthquake recorded by local authorities since the equipment was first installed. In order to improve understanding of earthquakes and surface deformation, many studies have been conducted according to these phenomena. In this research, we will estimate the surface deformation using the Okada model equation. The SAR images of three satellites with different wavelengths (ALOS-2, Cosmo SkyMed and Sentinel-1) were used to produce the interferogram pairs. The interferogram is used as a reference for surface deformation changes by using Okada to determine the source of surface deformation that occurs during an earthquake. The Non-linear optimization (Levemberg-Marquadrt algorithm) and Monte Carlo restart was applied to optimize the fault parameter on modeling process. Based on the modeling results of each satellite data, the fault geometry is ~6 km length, ~2 km width and ~5 km depth. The root mean square error values in the surface deformation model results for Sentinel, CSK and ALOS are 0.37 cm, 0.79 cm and 1.47 cm, respectively. Furthermore, the results of this modeling can be used as learning material in understanding about seismic activity to minimize the impacts that arise in the future.

The Effect of Slip on the Convective Instability Characteristics of the Stagnation Point Flow Over a Rough Rotating Disk

  • Mukherjee, Dip;Sahoo, Bikash
    • Kyungpook Mathematical Journal
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    • v.61 no.4
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    • pp.831-843
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    • 2021
  • In this paper we look at the three dimensional stagnation point flow problem over a rough rotating disk. We study the theoretical behaviour of the stagnation point flow, or forced flow, in the presence of a slip factor in which convective instability stationary modes appear. We make a numerical investigation of the effects of slip on the behaviour of the flow components of the stagnation point flow where the disk is rough. We provide, for the first time in the literature, a complete convective instability analysis and an energy analysis. Suitable similarity transformations are used to reduce the Navier-Stokes equations and the continuity equation into a system of highly non-linear coupled ordinary differential equations, and these are solved numerically subject to suitable boundary conditions using the bvp4c function of MATLAB. The convective instability analysis and the energy analysis are performed using the Chebyshev spectral method in order to obtain the neutral curves and the energy bars. We observe that the roughness of the disk has a destabilising effect on both Type-I and Type-II instability modes. The results obtained will be prominently treated as benchmarks for our future studies on stagnation flow.