• Title/Summary/Keyword: State equation

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A state space method for coupled flutter analysis of long-span bridges

  • Ding, Quanshun;Chen, Airong;Xiang, Haifan
    • Structural Engineering and Mechanics
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    • v.14 no.4
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    • pp.491-504
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    • 2002
  • A state-space method is proposed to analyze the aerodynamically coupled flutter problems of long-span bridges based on the modal coordinates of structure. The theory about complex modes is applied in this paper. The general governing equation of the system is converted into a complex standard characteristic equation in a state space format, which contains only two variables. The proposed method is a single-parameter searching method about reduced velocity, and it need not choose the participating modes beforehand and has no requirement for the form of structure damping matrix. The information about variations of system characteristics with reduced velocity and wind velocity can be provided. The method is able to find automatically the lowest critical flutter velocity and give relative amplitudes, phases and energy ratios of the participating modes in the flutter motion. Moreover, the flutter analysis of Jiangyin Yangtse suspension bridge with 1385 m main span is performed. The proposed method has proved reliable in its methodology and efficient in its use.

The State of Charge Estimation for Lithium-Polymer Battery using a PI Observer (PI 상태관측기를 이용한 리튬폴리머 배터리 SOC 추정)

  • Lee, Junwon;Jo, Jongmin;Kim, Sungsoo;Cha, Hanju
    • The Transactions of the Korean Institute of Power Electronics
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    • v.20 no.2
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    • pp.175-181
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    • 2015
  • In this study, a lithium polymer battery (LiPB) is simply expressed by a primary RC equivalent model. The PI state observer is designed in Matlab/Simulink. The non-linear relationship with the OCV-SOC is represented to be linearized with 0.1 pu intervals by using battery parameters obtained by constant-current pulse discharge. A state equation is configured based on battery parameters. The state equation, which applied Peukert's law, can estimate SOC more accurately. SOC estimation capability was analyzed by utilizing reduced Federal Test Procedure (FTP-72) current profile and using a bi-directional DC-DC converter at temperature ($25^{\circ}C$). The PI state observer, which is designed in this study, indicated a SOC estimation error rate of ${\pm}2%$ in any of the initial SOC states. The PI state observer confirms a strong SOC estimation performance despite disturbances, such as modeling errors and noise.

Nonrelativistic Solutions of Morse Potential from Relativistic Klein-Gordon Equation

  • Sun, Ho-Sung
    • Bulletin of the Korean Chemical Society
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    • v.31 no.12
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    • pp.3573-3578
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    • 2010
  • Recently it is suggested that it may be possible to obtain the approximate or exact bound state solutions of nonrelativistic Schr$\ddot{o}$dinger equation from relativistic Klein-Gordon equation, which seems to be counter-intuitive. But the suggestion is further elaborated to propose a more detailed method for obtaining nonrelativistic solutions from relativistic solutions. We demonstrate the feasibility of the proposed method with the Morse potential as an example. This work shows that exact relativistic solutions can be a good starting point for obtaining nonrelativistic solutions even though a rigorous algebraic method is not found yet.

The Time Correlation Function Near (and at) a Stable Steady State, When a Chemical System Relaxes from the Unstable Steady State$^*$

  • Lee, Dong-Jae;Ryu, Moon-Hee;Lee, Jong-Myung
    • Bulletin of the Korean Chemical Society
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    • v.6 no.2
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    • pp.91-95
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    • 1985
  • The dynamic properties near (and at) a stable steady state are discussed, when a chemical system relaxes from the unstable steady state. The time-dependent correlation length for the fluctuating variable near a stable steady state is explicitly obtained by introducing the probability average for the variable satisfying the rate equation. The study is carried out about the effect of nonlinearity on the correlation length near (and at) a stable steady state.

Estimation of Density of Methane and Ethane and Vapor-Liquid Equilibrium Predictions for Methane-Ethane Binary System Using PR and PC-SAFT Equations of State (PR 및 PC-SAFT 상태방정식을 이용한 메탄과 에탄의 기상과 액상의 밀도 추산 및 이성분계의 기-액 상평형 계산)

  • Park, Jong-Kee;Choi, Kun-Hyung;Lee, Sang-Gyu;Yang, Young-Myung;Cho, Jung-Ho
    • Journal of the Korean Institute of Gas
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    • v.14 no.2
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    • pp.22-26
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    • 2010
  • In this study, experimental vapor pressures and densities of vapor and liquid phases versus temperature were estimated using PC-SAFT equation. The estimated results were compared with those using PR equation of state. For the vapor phase densities, both equations well predicted the literature data. However, PC-SAFT equation showed better prediction capability for liquid phase densities. In the comparison of vapor-liquid equilibrium prediction capability for the binary systems of methane and ethane, PC-SAFT equation was better than the PR equation.

Exact solution of a thick walled functionally graded piezoelectric cylinder under mechanical, thermal and electrical loads in the magnetic field

  • Arefi, M.;Rahimi, G.H.;Khoshgoftar, M.J.
    • Smart Structures and Systems
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    • v.9 no.5
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    • pp.427-439
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    • 2012
  • The present paper deals with the analytical solution of a functionally graded piezoelectric (FGP) cylinder in the magnetic field under mechanical, thermal and electrical loads. All mechanical, thermal and electrical properties except Poisson ratio can be varied continuously and gradually along the thickness direction of the cylinder based on a power function. The cylinder is assumed to be axisymmetric. Steady state heat transfer equation is solved by considering the appropriate boundary conditions. Using Maxwell electro dynamic equation and assumed magnetic field along the axis of the cylinder, Lorentz's force due to magnetic field is evaluated for non homogenous state. This force can be employed as a body force in the equilibrium equation. Equilibrium and Maxwell equations are two fundamental equations for analysis of the problem. Comprehensive solution of Maxwell equation is considered in the present paper for general states of non homogeneity. Solution of governing equations may be obtained using solution of the characteristic equation of the system. Achieved results indicate that with increasing the non homogenous index, different mechanical and electrical components present different behaviors along the thickness direction. FGP can control the distribution of the mechanical and electrical components in various structures with good precision. For intelligent properties of functionally graded piezoelectric materials, these materials can be used as an actuator, sensor or a component of piezo motor in electromechanical systems.

A Comparative Study on the Prediction of Vapor-Liquid Equilibria for the Ethanol-Benzene Mixture between Equation of State Model and Liquid Activity Coefficient Model (비이상적 상거동을 보이는 이성분계 혼합물의 기액 상평형 추산을 위한 상태방정식과 액체 활동도계수 모델 사이의 비교연구)

  • Cho, Jung-Ho;Lee, Ji-Hwan
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.11 no.5
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    • pp.1747-1753
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    • 2010
  • In this study, a comparative study was performed to predict the vapor-liquid equilibria with maximum azeotropic pressure for ethanol-benzene binary system between an equation of state model and a liquid activity coefficient model. Peng-Robinson equation of state model with a Panatiotopoulos mixing rules (PRP) was used and NRTL liquid activity coefficient model proposed by Renon was selected. The PRP model, even though it has only two binary adjustable parameters, was not inferior to the NRTL model to predict vapor-liquid equilibria for low pressure region of ethanol-benzene system and showed a better prediction capability for high pressure region of ethanol-benzene system than the NRTL model with three binary interaction parameters.

High-Pressure Phase Behavior of Polycaprolactone, Carbon Dioxide, and Dichloromethane Ternary Mixture Systems (Polycaprolactone, 디클로로메탄, 이산화탄소로 구성된 3성분계 고압 상거동 측정)

  • Gwon, JungMin;Shin, Hun Yong;Kim, Soo Hyun;Kim, Hwayong
    • Korean Chemical Engineering Research
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    • v.53 no.2
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    • pp.193-198
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    • 2015
  • The high-pressure phase behavior of a polycaprolactone (Mw=56,145 g/mol, polydispersity 1.2), dichloromethane, and carbon dioxide ternary system was measured using a variable-volume view cell. The experimental temperatures and pressures ranged from 313.15 K to 353.15 K and up to 300 bar as functions of the $CO_2$/dichloromethane mass ratio and temperature, at poly(D-lactic acid) weight fractions of 1.0, 2.0, and 3.0%. The correlation results were obtained from the hybrid equation of state (Peng-Robinson equation of state + SAFT equation of state) for the $CO_2$-polymer system using the van der Waals one-fluid mixing rule. The three binary interaction parameters were optimized by the simplex method algorithm.

Analytical Analysis of PT Ferroresonance in the Transient-State (과도상태에서 PT 철공진의 해석적 분석)

  • Kang, Yong-Cheol;Lee, Byung-Eun;Zheng, Tai-Ying;Kim, Yeon-Hee
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.59 no.5
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    • pp.860-865
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    • 2010
  • When a circuit breaker is opened, a large capacitance around the buses, the circuit breaker and the potential transformer (PT) might cause PT ferroresonance. During PT ferroresonance, the iron core repeats saturation and unsaturation even though the supplied voltage is a rated voltage. This paper describes an analytical analysis of PT ferroresonance in the transient-state. To analyze ferroresonance analytically, the iron core is modelled by a simplified two-segment core model in this paper. Thus, a nonlinear ordinary differential equation (ODE) for the flux linkage is changed into a linear ODE with constant coefficients, which enables an analytical analysis. In this simplified model, each state, which is either saturated or unsaturated state, corresponds to one of the three modes, i.e. overdamping, critical damping and underdamping. The flux linkage and the voltage in each state are obtained analytically by solving the linear ODE with constant coefficients. The proposed transient analysis is effective in the more understanding of ferroresonance and thus can be used to design a ferroresonance prevention or suppression circuit of a PT.

Anti-swing of the Nonlinear Overhead Crane Using Partial State Feedback Control (부분상태 궤환제어를 이용한 비선형 천정크레인의 진자각제어)

  • Lee, Jong-Kyu;Lee, Sang-Ryong
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.6
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    • pp.907-917
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    • 1997
  • The purpose of this study is to design an anti-sway motion for industrial overhead cranes which transport objects on a horizontal plane by adjusting movements of a trolley motor and a girder motor. The movement of a hoist motor has not been considered at this time since its role was assumed to move objects only vertically, therefore, not to affect the swing motion of objects. The dynamic behavior of the swing motion shows nonlinear characteristics, which makes the design of anti-sway motion controller difficult. First of all, the nonlinear state equation for the motion of industrial overhead cranes has been derived. Then they have been linearized about normal operating states determined by the dynamic characteristics of motor motion-acceleration, constant speed, and deceleration, and deceleration, during transportation. The partial state feedback control algorithm based on this linearized state equation has been developed on order to suppress the swing motion. The simulation results have demonstrated satisfactory performance of the proposed controller.