• Title/Summary/Keyword: Non-linear Equation

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Time-frequency analysis of a coupled bridge-vehicle system with breathing cracks

  • Wang, W.J.;Lu, Z.R.;Liu, J.K.
    • Interaction and multiscale mechanics
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    • v.5 no.3
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    • pp.169-185
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    • 2012
  • The concrete bridge is likely to produce fatigue cracks during long period of service due to the moving vehicular loads and the degeneration of materials. This paper deals with the time-frequency analysis of a coupled bridge-vehicle system. The bridge is modeled as an Euler beam with breathing cracks. The vehicle is represented by a two-axle vehicle model. The equation of motion of the coupled bridge-vehicle system is established using the finite element method, and the Newmark direct integration method is adopted to calculate the dynamic responses of the system. The effect of breathing cracks on the dynamic responses of the bridge is investigated. The time-frequency characteristics of the responses are analyzed using both the Hilbert-Huang transform and wavelet transform. The results of time-frequency analysis indicate that complicated non-linear and non-stationary features will appear due to the breathing effect of the cracks.

Laminar Convective Heat Transfer from a Horizontal Flat Plate of Phase Change Material Slurry Flow

  • Kim Myoung-Jun
    • Journal of Advanced Marine Engineering and Technology
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    • v.29 no.7
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    • pp.779-784
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    • 2005
  • This paper presents the theory of similarity transformations applied to the momentum and energy equations for laminar, forced, external boundary layer flow over a horizontal flat plate which leads to a set of non-linear, ordinary differential equations of phase change material slurry(PCM Slurry). The momentum and energy equation set numerically to obtain the non-dimensional velocity and temperature profiles in a laminar boundary layer are solved. The heat transfer characteristics of PCM slurry was numerically investigated with similar method. It is clarified that the similar solution method of Newtonian fluid can be used reasonably this type of PCM slurry which has low concentration. The data of local wall heat flux and convective heat transfer coefficient of PCM slurry are higher than those of water more than 150$\~$200$\%$, approximately.

Analyses on the Behaviour of Ocean Structure Due to Ship Collision (선박의 충돌로 인한 해양구조물의 거동 해석)

  • 이호영;박종환;곽영기
    • Journal of Ocean Engineering and Technology
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    • v.15 no.4
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    • pp.115-119
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    • 2001
  • The simulation of motion responses of a dolphin-moored ocean structure in shallow water when it cllides with a ship, has been carried out. The equation of motion in the time domain according to Cummin's theory is employed, and solved by making use of the Newmark-${\beta}$ method. The added mass and damping coefficients involved in the equations are abtained from a three-dimensional panel method in the frequency domain. The impact forces due to ship collision are calculated using both the elastic and non-elastic modelings. The mooring forces for dolphin systems of ocean structure are regarded as linear spring forces.

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Ellipsoidal bounds for static response of framed structures against interactive uncertainties

  • Kanno, Yoshihiro;Takewaki, Izuru
    • Interaction and multiscale mechanics
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    • v.1 no.1
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    • pp.103-121
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    • 2008
  • This paper presents an optimization-based method for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain braced frame. Based on a non-stochastic modeling of uncertainty, we assume that the parameters both of brace stiffnesses and external forces are uncertain but bounded. A brace member represents the sum of the stiffness of the actual brace and the contributions of some non-structural elements, and hence we assume that the axial stiffness of each brace is uncertain. By using the $\mathcal{S}$-lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. The minimum bounding ellipsoids are computed for a braced frame under several uncertain circumstances.

On the post-buckling behaviour of plates under stress gradient

  • Bedair, Osama K.
    • Structural Engineering and Mechanics
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    • v.4 no.4
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    • pp.397-413
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    • 1996
  • In this paper the elastic post-buckling behaviour of plates under non-uniform compressive edge stress is investigated. The compatibility differential equations is first solved analytically and then an approximate solution of the equilibrium equation is obtained using the Galerkin method. Explicit expressions are derived for the load-deflection, ultimate strength and membrane stress distributions. Analytical effective width formulations, based on the characteristics of the stress field of the buckled plate, are proposed for this general loading condition. The predicted load-deflection expression is compared with independent test results. Results are also presented detailing the load-deflection behaviour and stress distribution for various aspect ratios.

Electron Spin Resonance (ESR) and Microwave Absorption Studies of Superparamagnetic Iron Oxide Nanoparticles (SPIONs) for Hyperthermia Applications

  • Choi, Yong-Ho;Yi, Terry;Kim, Do-Kyung
    • Journal of the Korean Ceramic Society
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    • v.48 no.6
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    • pp.577-583
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    • 2011
  • Stabilized biocompatible superparamagnetic iron oxide nanoparticles (SPIONs) were prepared by controlled coprecipitation method for hyperthermia application. ESR measurements determined that all of the interactions in the individual SPIONs (1 nm and 11 nm) were antiferromagnetic in nature because the ions contributed to the magnetization with a range of magnetic moments. In-situ monitoring of the temperature increment was performed, showing that the microwave absorption rate of the SPIONs was dispersed in an appropriate host media (polar or non-polar solvents) during microwave irradiation. Microwave absorption energy rates and heat loss of SPIONs in solvent were calculated by non-linear data fitting with an energy balance equation. The microwave absorption rates of SPIONs dispersed in solvent linearly increases when the concentration of SPIONs increases, implying that the microwave absorption rate can be tunable by changing the concentration of SPIONs.

Fatigue-crack propagation behavior of 304 stainless steel by Moire grating (微小格子 를 利용한 304스테인레스鋼 의 피勞 크랙 進展擧動 에 관한 硏究)

  • 옹장우;임용호
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.6 no.3
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    • pp.197-203
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    • 1982
  • The fatigue crack propagation behavior or non-heat-treatment and thermally aged type 304 stainless steel was investigated on the basis of linear elastic fracture mechanics. This Study was concentrated on the relations between the crack propagation rate and the stress intensity factor range. The following results are obtained : The precision measurement and observation of fatigue crack propagation behavior is studied with moire grating. The effect of thermally aged type 304 stainless steel is investigated under small load. In the equation da/dN=c(.DELTA. k)/SUP m/, factor m of thermally aged steel is a little higher than non-heat-treatmented steel and its limit is m=1.35-4.2.

Gravity and Angular Velocity Profile Effects on the Balancing Performance of an Automatic Ball Balancer (자동볼평형장치의 밸런싱 성능에 대한 중력과 속도파형의 영향)

  • 정진태;정두한
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.11a
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    • pp.418-423
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    • 2003
  • The balancing performance of an automatic ball balancer (ABB) in the vertical or horizontal position is studied in this paper. Considering the effects of gravity and angular velocity profiles, a physical model for an ABB installed on the Jeffcott rotor is adopted. The non-linear equations of motion for the rotor with ABB are derived by using Lagrange's equation. Based on derived equations, dynamic responses for the rotor are computed by using the generalized-u method. From the computed responses, the effects of gravity and angular velocity profiles on the balancing performance are investigated. It is found that the rotor with ABB can be balanced regardless of the gravity effect. It is also shown that a smooth velocity profile yields relatively smaller vibration amplitude than a non-smooth velocity profile.

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A fast adaptive numerical solver for nonseparable elliptic partial differential equations

  • Lee, June-Yub
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.2 no.1
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    • pp.27-39
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    • 1998
  • We describe a fast numerical method for non-separable elliptic equations in self-adjoin form on irregular adaptive domains. One of the most successful results in numerical PDE is developing rapid elliptic solvers for separable EPDEs, for example, Fourier transformation methods for Poisson problem on a square, however, it is known that there is no rapid elliptic solvers capable of solving a general nonseparable problems. It is the purpose of this paper to present an iterative solver for linear EPDEs in self-adjoint form. The scheme discussed in this paper solves a given non-separable equation using a sequence of solutions of Poisson equations, therefore, the most important key for such a method is having a good Poison solver. High performance is achieved by using a fast high-order adaptive Poisson solver which requires only about 500 floating point operations per gridpoint in order to obtain machine precision for both the computed solution and its partial derivatives. A few numerical examples have been presented.

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A Design of Variable Structure Controller for the General Single Input Systems with Unmeasurable State Variables (측정불가능한 상태변수를 갖는 일반적인 단일 입력 계통에 대한 가변구조 제어기의 설계)

  • 박귀태;최중경
    • The Transactions of the Korean Institute of Electrical Engineers
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    • v.41 no.7
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    • pp.773-783
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    • 1992
  • There have been several control schemes for the single input systems with unmeasurable state variables using variable structure control(VSC) theory. However, each of them is a study on the systems which can be represented in the phase canonical form or non-phase canonical form dynamic equation separately. As these control algorithms have difficulties in practical application by its theoretical limitations, in this paper we propose a new VSC theory which overcomes those limitations, in this paper we propose a new VSC theory which overcomes those limitations of proposed schemes. This new control scheme can be realized for the general linear systems which have unmeasurable state variables. And the switching function of this VSS algorithm consists of measurable state variable function(reduced-order switching function) and its derivatives. Also in the construction of control imput only measurable state variables are used.

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