• Title/Summary/Keyword: Nonlinear equations

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Numerical Simulation of Two-dimensional Nonlinear Waves on Beaches Using a Smoothed Particle Hydrodynamics Method (SPH법을 이용한 해안에서의 2차원 비선형파 수치시뮬레이션)

  • Kim, Cheol-Ho;Lee, Young-Gill;Jeong, Kwang-Leol
    • Journal of the Society of Naval Architects of Korea
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    • v.47 no.4
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    • pp.525-532
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    • 2010
  • In this paper, wave breakers which occur in two dimensional coasts are simulated using a SPH(Smoothed Particle Hydrodynamics) method which represents the movement of fluidic physical volume with particles. As continuative fluid is approximated to the particles, the simulations are performed using fully Lagrangian method without any grid system. Two-dimensional Navier-Stokes equations and continuity equation are used for the numerical simulations. To generate incident waves, a piston type wavemaker is employed. The accuracy of the wave which is numerically generated by the wavemaker is verified by comparing with analytical results. The computations are carried out with various wave heights and slopes. The wave patterns generated through the numerical simulations are compared with several existing experimental and computational results. Agreement between the experimental data and the computation results is comparatively good. Also, the breaker depth index and the breaker height index from the present calculations are compared with the existing experimental results, and the tendency is very similar.

Use of Composite Tailoring Techniques for a Low Vibration Rotor (복합재료 테일러링 기법을 이용한 저진동 로터 개발)

  • 이주영;박일주;정성남
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2004.05a
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    • pp.575-580
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    • 2004
  • In this work, the effect of composite couplings and mass distributions on hub loads of a hingeless rotor in forward flight is investigated. 1'he hingeless composite rotor is idealized as a laminated thin-walled box-beam. The nonclassical effects such as transverse shear and torsion warping are considered in the structural formulation. The nonlinear differential equations of motion are obtained by applying Hamilton's principle. The blade responses and hub loads are calculated using a finite element formulation both in space and time. The aerodynamic forces acting on the blade are calculated using the quasi-steady strip theory. The theory includes the effects of reversed flow and compressibility The magnitude of elastic couplings obtained by MSC/NASTRAN is compared with the classical pitch-flap($\delta$$_{3}$) coupling. It is observed that the elastic couplings and mass distributions of the blade have a substantial effect on the behavior of $N_{b/}$rev hub loads. About 40% hub loads is reduced by tailoring or redistributing the structural properties of the blade.f the blade.

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Effect of Strength and Age on Stress-Strain Curves in Low-, Medium-, and High-Strength Concretes (강도와 재령이 저강도, 중간강도, 및 고강도 콘크리트의 응력-변형률 곡선에 미치는 영향)

  • 오태근;이성태;양은익;최홍식;김진근
    • Proceedings of the Korea Concrete Institute Conference
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    • 2003.05a
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    • pp.53-58
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    • 2003
  • Many researchers have rigorously studied the nonlinear behavior of stress-strain relationship of concrete using mathematical curves. Most of model equations for stress-strain relationship, however, have been focused on old age concrete, and were not able to adequately represent the behavior of concrete at an early age. A wide understanding on the behavior of concrete from early age to old age is very important in evaluating the durability and service life of concrete structures. In previous study by authors of this paper, a stress-strain model equation for low- and medium-strength concretes was suggested. In this paper, to extend the application region of compressive stress-strain curve to high-strength concrete, an analytical research was performed. An analytical expression of stress-strain curve with strength and age was developed using regression analyses on the experimental results. For the verification of the proposed model equation, it was compared to the experimental data. The result showed that the proposed model equation was not only compatible with the experimental data quite satisfactorily but also describing well the effect of strength and age on stress-strain curve.

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Drift Motion Analysis on Horizontal Plane of a Two-Point Moored Oil Tanker (2점 계류된 선박에 대한 수평면상 표류운동 해석)

  • 이호영;임춘규
    • Journal of Ocean Engineering and Technology
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    • v.18 no.3
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    • pp.8-12
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    • 2004
  • The anchor is laid on the seabed, and the main engine is working against incident environmental loads in a typhoon. As the main engine is broken Mum in the storm, the anchor chain is cut and the vessel drifts. Although a ship is moored by two-point mooring lines to maintain her position, it has crashed into a rock because of a typhoon, resulting in a possible accidental oil spillage. In this paper, we studied maintenance of a ship's position, which is analyzed based on the slow motion maneuvering equations considering wave, current, and wind. To estimate wave loads, the direct integration method is employed. The current forces are calculated, using MMG (Mathematical Modeling Group). Th two-point mooring forces are quasi-statistically evaluated, using the catenary equation. Th coefficients of wind forces are modeled from Isherwood's empirical data, and the variation of wind speed is estimated by wind spectrum. The nonlinear motions of a two-point moored ship are simulated, considering wave, current, and wind load, in specific domain of time.

A Study on Towing Characteristics of Barge Considering Wind Force (풍하중에 의한 바지선의 예인 시 거동특성 변화에 관한 연구)

  • Nam, Bo Woo;Choi, Young-Myoung;Hong, Sa Young
    • Journal of Ocean Engineering and Technology
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    • v.29 no.4
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    • pp.283-290
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    • 2015
  • This paper presents the results of a numerical study on the towing characteristics of a barge under various wind conditions. First, stability criteria, including the wind force, were derived based on the linear motion equations of a towed vessel. The effect of the wind force on the towing stability was investigated using stability criteria. Next, towing simulations were carried out using a nonlinear time-domain simulation method. In this case, the towline was modeled as a simple spring-damper, and the wind force was computed using the wind coefficient from CFD calculations. Simulations were conducted for a barge under a constant towing speed and constant wind speed conditions. The effect of the wind direction on the slewing motion was also observed. In addition, a series of numerical simulations using variable wind speeds were performed for the present barge with and without a skeg.

Modified cyclic steel law including bond-slip for analysis of RC structures with plain bars

  • Caprili, Silvia;Mattei, Francesca;Gigliotti, Rosario;Salvatore, Walter
    • Earthquakes and Structures
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    • v.14 no.3
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    • pp.187-201
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    • 2018
  • The paper describes a modified cyclic bar model including bond-slip phenomena between steel reinforcing bars and surrounding concrete. The model is focused on plain bar and is useful, for its simplicity, for the seismic analyses of RC structures with plain bars and insufficient constructive details, such as in the case of '60s -'70s Mediterranean buildings. The model is based on an imposed exponential displacements field along the bar including both steel deformation and slip; through the adoption of equilibrium and compatibility equations a stress-slip law can be deducted and simply applied, with opportune operations, to RC numerical models. This study aims to update and complete the original monotonic model published by the authors, solving some numerical inconsistencies and, mostly, introducing the cyclic formulation. The first aim is achieved replacing the imposed linear displacement field along the bar with an exponential too, while the cyclic behaviour is described through a formulation based on the results of parametric analyses concerning a large range of steel and concrete properties and geometric configurations. Validations of the proposed model with experimental results available in the current literature confirm its accuracy and the reduced computational burden, highlighting its suitability in performing nonlinear analyses of RC structures.

Vibration Analysis of Rotating Disk-Spindle System Using Finite Element Method and Substructure Synthesis (유한 요소법과 부분 구조 합성법을 이용한 회전 디스크-스핀들 계의 진동 해석)

  • Jeong, Myeong-Su;Jang, Geon-Hui
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.9 s.180
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    • pp.2201-2210
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    • 2000
  • Vibration of a rotating disk-spindle system is analyzed by using Hamilton's principle, FEM and substructure synthesis. A rotating disk undergoes the rigid body motion and the elastic deformation. It s equation of motion is derived by Kirchhoff plate theory and von Karman nonlinear strain. A rotating shaft is described by Rayleigh beam theory considering the axial rigid body motion. The stationay shaft supporting the rotating disk-spindle-bearing system is modeled by Euler beam theory, and the stiffness of ball bearing is determined by A.B.Jones' theory. FEM is used to solve the derived governing equations, and substructure synthesis is introduced to assemble each structure of the rotating disk-spindle system. The developed theory is applied to the spindle system of a 35' computer hard disk drive with 3 disks to verify the simulation results. The simulation results agree very well with the experimental ones. The proposed theory may be effectively expanded to the complex structure of a disk-spindle system.

A CAD-based Software for the Simulation of Lifting and Turnover of Ship Block (선박 블록의 이동 및 반전 시뮬레이션 프로그램 개발)

  • Lee, Soo-Beom;Shin, Sang-Beom;Kwak, Byung-Man
    • Proceedings of the KSME Conference
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    • 2000.04a
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    • pp.714-719
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    • 2000
  • In this paper, an application program is made to simulate the behavior of a ship block under various crane works and to generate data of lu9 reactions and wire tensions. The program is based on a CAD program, Pro/ENGINEER. A ship is composed of more than 100 ship blocks. In order to lift, move, turn, or put a ship block at a convenient location fur assembling, workers in a shipyard use cranes, wires, and lugs temporarily attached to the block. In the procedure of lifting and turning a ship block with a crane, it is important to find suitable lug points and wires to do the handling efficiently and prevent accidents. Evaluation of forces in lugs and wires is necessary, but the problem is rather complex due to nonlinearity and nonuniqueness. In the present development, the nonlinear system of equations for quasi-static equilibriums is derived and a Newton type solution method is adopted to solve the system. The importance of initial estimates to the solution is illustrated and two approaches are utilized and compared. With the program developed, users can assign lug points on the CAD model by mouse and choose various linking devices at each crane point. Users can try to simulate the motion for any prescribed conditions, compare the motion of the block and the reactions and choose appropriate lug points and the type of wires and lugs.

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A Study on the Nonlinearity of Chaotic Signal by Bispectral Analysis (바이스펙트럼 해석에 의한 카오스 신호의 비선형성에 관한 연구)

  • Lee, Hae-Jin;Lee, Gyeong-Tae;Park, Young-Sun;Cha, Kyung-Joon;Park, Moon-Il;Oh, Jae-Eung
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.31 no.8
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    • pp.817-825
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    • 2007
  • During thirty years, deterministic chaos has moved center stage in many areas of applied mathematics. One important stimulus for this, particularly in the early 1970s, was work on nonlinear aspects of the dynamics of plant and animal populations. There are many situations, at least to a crude first approximation, by a simple first-order difference equation. Past studies have shown that such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behavior, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. But higher-order spectral analyses of such behavior are usually not considered. Higher-order spectra of a signal contain important information that is not present in its power spectrum. So, if we find the spectral pattern and get information from it, it will be able to be used effectively in so many fields. Hence, this paper uses auto bicoherence and bicoherence residue which are sort of bispectrum. Applying these to behavior of logistic difference equation, which is typical chaotic signal, the phenomenon of phase coupling and the appearance of frequency band can be analyzed. Such information means that bispectral analysis is useful to detect nonlinearity of signal.

Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects

  • Golabchi, Hadi;Kolahchi, Reza;Bidgoli, Mahmood Rabani
    • Computers and Concrete
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    • v.21 no.4
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    • pp.431-440
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    • 2018
  • Fluid velocity analysis on the instability of pipes reinforced by silica nanoparticles ($SiO_2$) is presented in this paper. Mori-Tanaka model is used for obtaining the effective materials properties of the nanocomposite structure considering agglomeration effects. The well known Navier-Stokes equation is used for obtaining the applied force of fluid to pipe. Based on the Reddy higher-order shear deformation theory, the motion equations are derived based on energy method and Hamilton's principal. The frequency and critical fluid velocity of structure are calculated using differential quadrature method (DQM) so that the effects of different parameters such as volume fractions of SiO2 nanoparticles, SiO2 nanoparticles agglomeration, boundary conditions and geometrical parameters of pipes are considered on the nonlinear vibration and instability of the pipe. Results indicate that increasing the volume fractions of SiO2 nanoparticles, the frequency and critical fluid velocity of the structure are increased. Furthermore, considering SiO2 nanoparticles agglomeration, decreases the frequency and critical fluid velocity of the pipe.