• Title/Summary/Keyword: Nonlinear Systems of Equations

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Design of Tidal Basin Using Automatically Controlled Manifold System (분기관의 자동제어를 통한 조석수조의 설계)

  • 전인식;오영민;이달수
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.6 no.4
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    • pp.327-334
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    • 1994
  • The manifold designates a pipe system discharging or absorbing water through multiple holes installed along the finite length of the pipe. The proper design of the manifold requires the pre-analysis of the hydraulic characteristics such as system head and flow rate. head loss and hole discharges, etc. On the contrary to the general pipe systems. the head loss along the pipe is hardly quantified in an explicit way since it is complicately varied by the size and arrangement of the holes. In the present study, both energy and continuity equations are employed to analyze the hydraulic characteristics, constituting nonlinear simultaneous equations which are solved by Newton method. In addition, a hydraulic experiment utilizing the manifold system equipped with an automatically controlled valve is performed to reproduce model tide. The result shows that the manifold system can be effectively used in a tidal basin where water flow should be maintained uniformly over the basin width.

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Stability/instability of the graphene reinforced nano-sized shell employing modified couple stress model

  • Yao, Zhigang;Xie, Hui;Wang, Yulei
    • Wind and Structures
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    • v.32 no.1
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    • pp.31-46
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    • 2021
  • The current research deals with, stability/instability and cylindrical composite nano-scaled shell's resonance frequency filled by graphene nanoplatelets (GPLs) under various thermal conditions (linear and nonlinear thermal loadings). The piece-wise GPL-reinforced composites' material properties change through the orientation of cylindrical nano-sized shell's thickness as the temperature changes. Moreover, in order to model all layers' efficient material properties, nanomechanical model of Halpin-Tsai has been applied. A functionally modified couple stress model (FMCS) has been employed to simulate GPLRC nano-sized shell's size dependency. It is firstly investigated that reaching the relative frequency's percentage to 30% would lead to thermal buckling. The current study's originality is in considering the multifarious influences of GPLRC and thermal loading along with FMCS on GPLRC nano-scaled shell's resonance frequencies, relative frequency, dynamic deflection, and thermal buckling. Furthermore, Hamilton's principle is applied to achieve boundary conditions (BCs) and governing motion equations, while the mentioned equations are solved using an analytical approach. The outcomes reveal that a range of distributions in temperature and other mechanical and configurational characteristics have an essential contribution in GPLRC cylindrical nano-scaled shell's relative frequency change, resonance frequency, stability/instability, and dynamic deflection. The current study's outcomes are practical assumptions for materials science designing, nano-mechanical, and micromechanical systems such as micro-sized sensors and actuators.

Nonlinear Analysis of a Forced Circular Plate with Internal Resonance (내부공진을 가진 원판의 비선형 강제진동해석)

  • 김철홍;이원경
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.11
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    • pp.2098-2110
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    • 1992
  • An analysis is presented for the combination resonance of a clamped circular plate, which occurs when the frequency of the excitation is near the combination of the natural frequencies, that is, when ohm.=2.0mega./sub 1/+omega./sub 2/. The internal resonance, Omega./sub 3/=omega./sub 1/+2.omega./sub 2/, is considered and its influence on the response is studied. The clamped circular plate experiencing mid-plane stretching is governed by a nonlinear partial differential equation. By using Galerkin's method the governing equation is reduced to a system of nonautonomous ordinary differential equations. The method of multiple scales is used to obtain steady-state responses of the system. Results of numerical investigations show that the increase of the excitation amplitude can reduce the amplitudes of steady-state responses. We can not find this kind of results in linear systems.

Shaking Table Test for Analysis of Effect on Vibration Control of the Piping System by Steel Coil Damper (강재 코일 댐퍼의 배관시스템 진동제어 효과 분석을 위한 진동대시험)

  • Choi, Song Yi;So, Gi Hwan;Cho, Sung Gook
    • Journal of the Earthquake Engineering Society of Korea
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    • v.26 no.1
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    • pp.39-48
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    • 2022
  • Many piping systems installed in the power plant are directly related to the safety and operation of the plant. Various dampers have been applied to the piping system to reduce the damage caused by earthquakes. In order to reduce the vibration of the piping system, this study developed a steel coil damper (SCD) with a straightforward structure but excellent damping performance. SCD reduces the vibration of the objective structure by hysteretic damping. The new SCD damper can be applied to high-temperature environments since it consists of steel members. The paper introduces a design method for the elastoplastic coil spring, which is the critical element of SCD. The practical applicability of the design procedure was validated by comparing the nonlinear force-displacement curves calculated by design equations with the results obtained from nonlinear finite element analysis and repeated loading test. It was found that the designed SCD's have a damping ratio higher than 25%. In addition, this study performed a set of seismic tests using a shaking table with an existing piping system to verify the vibration control capacity on the piping system by SCD. Test results prove that the SCD can effectively control the displacement vibration of the piping system up to 80%.

Prediction of Inelastic Force-Displacement Relationships of Reinforced Concrete Shear Wall Systems Based on Prescribed Ductilities (강성저하 실험식 및 연성계수를 이용한 철근콘크리트 전단벽 구조시스템의 비탄성 하중-변위 관계식 예측)

  • 홍원기
    • Computational Structural Engineering
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    • v.8 no.4
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    • pp.159-171
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    • 1995
  • The parameters describing a complete hysteresis loop include pinch force, drift offset, effective stiffness, unloading and reloading trangential stiffness. Analytical equations proposed to quantify the nonlinear, inelastic behavior of reinforced shear walls can be used to predict these parameters as a function of axial load and drift ratio. For example, drift offset, effective stiffness, and first and second unloading and reloading tangential stiffness are calculated using equations obtained from test data for a desired drift ratio or ductility level. Pinch force can also be estimated for a given drift ratio and axial load. The effective virgin stiffness at the first yield and its post yield reduction can be estimated. The load deflection response of flexural reinforced concrete shear walls can now be estimated based on the effective wall stiffness that is a function of axial force and drift ratio.

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Steady-State Solution of Forced Symmetric Piecewise-Linear Oscillator (强制 對稱 偏的 線型 振動子의 定常解)

  • 최연선
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.13 no.4
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    • pp.583-594
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    • 1989
  • The strong nonliner dynamic behavior of mechanical systems in the presence of clearances are studied. The nonlinearity is induced from the assumed symmetric piecewise-linear characteristics for stiffness and damping by the contact and uncontact. Based on Stoker's assertion concering the reasoning beyond the occurrence of subharmonics, the nonlinear differential equation is converted to four nonlinear algebraic equations form the boundary conditions at the contact points. For a single contact per half exciting period, under the assumption of symmetric response, the steady-state solutions obtained are in agreement with those of numerical integration. Also a nondimen-sionalized formulation is made for the purpose of parametric studies.

Waveform Relaxation Method for Reactor Transient Analysis (원자로 천이해석을 위한 파형완화법)

  • Park, Keon-Woo;Co, Nam-Zin
    • Nuclear Engineering and Technology
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    • v.27 no.6
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    • pp.845-852
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    • 1995
  • We investigate the concurrent solution of differential equations by the waveform relaxation (WR) method, an iterative method for analyzing linear and nonlinear dynamical systems in the time do-main. The method, at each iteration, decomposes the dynamical system into several subsystems, each of which is analyzed for the entire given time interval. The method, when efficiently implemented, results in algorithms with a highly parallelizable concurrent fraction. In this paper, the waveform relaxation method is introduced and applied to two types of reactor dynamics problems. It is concluded that the U method can be applied to reactor dynamics equations, but that its parallel performance on the KMRR dynamics is only modest.

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Optimal Temperature Tracking Control of a Polymerization Batch Reactor by Adaptive Input-Output Linearization

  • Noh, Kap-Kyun;Dongil Shin;Yoon, En-Sup;Rhee, Hyun-Ku
    • Transactions on Control, Automation and Systems Engineering
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    • v.4 no.1
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    • pp.62-74
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    • 2002
  • The tracking of a reference temperature trajectory in a polymerization batch reactor is a common problem and has critical importance because the quality control of a batch reactor is usually achieved by implementing the trajectory precisely. In this study, only energy balances around a reactor are considered as a design model for control synthesis, and material balances describing concentration variations of involved components are treated as unknown disturbances, of which the effects appear as time-varying parameters in the design model. For the synthesis of a tracking controller, a method combining the input-output linearization of a time-variant system with the parameter estimation is proposed. The parameter estimation method provides parameter estimates such that the estimated outputs asymptotically follow the measured outputs in a specified way. Since other unknown external disturbances or uncertainties can be lumped into existing parameters or considered as another separate parameters, the method is useful in practices exposed to diverse uncertainties and disturbances, and the designed controller becomes robust. And the design procedure and setting of tuning parameters are simple and clear due to the resulted linear design equations. The performances and the effectiveness of the proposed method are demonstrated via simulation studies.

Camera Calibration for Machine Vision Based Autonomous Vehicles (머신비젼 기반의 자율주행 차량을 위한 카메라 교정)

  • Lee, Mun-Gyu;An, Taek-Jin
    • Journal of Institute of Control, Robotics and Systems
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    • v.8 no.9
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    • pp.803-811
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    • 2002
  • Machine vision systems are usually used to identify traffic lanes and then determine the steering angle of an autonomous vehicle in real time. The steering angle is calculated using a geometric model of various parameters including the orientation, position, and hardware specification of a camera in the machine vision system. To find the accurate values of the parameters, camera calibration is required. This paper presents a new camera-calibration algorithm using known traffic lane features, line thickness and lane width. The camera parameters considered are divided into two groups: Group I (the camera orientation, the uncertainty image scale factor, and the focal length) and Group II(the camera position). First, six control points are extracted from an image of two traffic lines and then eight nonlinear equations are generated based on the points. The least square method is used to find the estimates for the Group I parameters. Finally, values of the Group II parameters are determined using point correspondences between the image and its corresponding real world. Experimental results prove the feasibility of the proposed algorithm.

Investigation of the semi-active electromagnetic damper

  • Montazeri-Gh, Morteza;Kavianipour, Omid
    • Smart Structures and Systems
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    • v.13 no.3
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    • pp.419-434
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    • 2014
  • In this paper, the electromagnetic damper (EMD), which is composed of a permanent-magnet rotary DC motor, a ball screw and a nut, is considered to be analyzed as a semi-active damper. The main objective pursued in the paper is to study the two degrees of freedom (DOF) model of the semi-active electromagnetic suspension system (SAEMSS) performance and energy regeneration controlled by on-off and continuous damping control strategies. The nonlinear equations of the SAEMSS must therefore be extracted. The effects of the EMD characteristics on ride comfort, handling performance and road holding for the passive electromagnetic suspension system (PEMSS) are first analyzed and damping control strategies effects on the SAEMSS performance and energy regeneration are investigated next. The results obtained from the simulation show that the SAEMSS provides better performance and more energy regeneration than the PEMSS. Moreover, the results reveal that the on-off hybrid control strategy leads to better performance in comparison with the continuous skyhook control strategy, however, the energy regeneration of the continuous skyhook control strategy is more than that of the on-off hybrid control strategy (except for on-off skyhook control strategy).