• Title/Summary/Keyword: linear differential equations

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Short- and long-term analyses of shear lag in RC box girders considering axial equilibrium

  • Xiang, Yiqiang;He, Xiaoyang
    • Structural Engineering and Mechanics
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    • v.62 no.6
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    • pp.725-737
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    • 2017
  • An analytical method considering axial equilibrium is proposed for the short- and long-term analyses of shear lag effect in reinforced concrete (RC) box girders. The axial equilibrium of box girders is taken into account by using an additional generalized displacement, referred to as the longitudinal displacement of the web. Three independent shear lag functions are introduced to describe different shear lag intensities of the top, bottom, and cantilever plates. The time-dependent material properties of the concrete are simulated by the age-adjusted effective modulus method (AEMM), while the reinforcement is assumed to behave in a linear-elastic fashion. The differential equations are derived based on the longitudinal displacement of the web, the vertical displacement of the cross section, and the shear lag functions of the flanges. The time-dependent expressions of the generalized displacements are then deduced for box girders subjected to uniformly distributed loads. The accuracy of the proposed method is validated against the finite element results regarding the short- and long-term responses of a simply-supported RC box girder. Furthermore, creep analyses considering and neglecting shrinkage are performed to quantify the time effects on the long-term behavior of a continuous RC box girder. The results show that the proposed method can well evaluate both the short- and long-term behavior of box girders, and that concrete shrinkage has a considerable impact on the concrete stresses and internal forces, while concrete creep can remarkably affect the long-term deflections.

Continuous Blood Pressure Prediction Using PTT During Exercise (PTT를 이용한 자전거 운동 중 지속적인 혈압의 예측)

  • Kim, Chul-Seung;Moon, Ki-Wook;Kwon, Jung-Hoon;Eom, Gwang-Moon
    • Journal of Biomedical Engineering Research
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    • v.27 no.6
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    • pp.370-375
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    • 2006
  • The purpose of this work is to predict the systolic blood pressure (BP) during exercise from pulse transit time (PTT) for warning of possible danger. PTT was calculated as the time between R-peak of ECG and the peak of differential photoplethysmograph (PPG). For the PTT-BP model, we used regress equations from previous studies and 3 kinds of new models combining linear and nonlinear regress equation. The model parameters were estimated with the data measured under low to middle intensity exercise, and then was tested with the data measured under high intensity exercise. Predicted BP values after high intensity exercise were compared with those measured by cuff-type sphygmomanometer. The results showed that the error between measured and predicted values were acceptable for the monitoring BP. We tested PTT-BP models 1 month after the identification without further calibration. Models could predict the BP and the errors between measured and predicted BP were about 5mmHg. The suggested system is expected to be helpful in recognizing any danger during exercise.

Experimental Study on Tip Clearance Effects for Performance Characteristics of Ducted Fan

  • Raza, Iliyas;Choi, Hyun-Min;Cho, Jin-Soo
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2009.11a
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    • pp.395-398
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    • 2009
  • Currently, a new generation of ducted fan UAVs (Unmanned Aerial Vehicles) is under development for a wide range of inspection, investigation and combat missions as well as for a variety of civil roles like traffic monitoring, meteorological studies, hazard mitigation etc. The current study presents extensive results obtained experimentally in order to investigate the tip clearance effects on performance characteristics of a ducted fan for small UAV systems. Three ducted fans having different tip clearance gap and with same rotor size were examined under three different yawed conditions of calibrated slanted hot-wire probe. Three dimensional velocity flow fields were measured from hub to tip at outlet of the ducted fan. The analysis of data were done by PLEAT (Phase locked Ensemble Averaging Technique) and three non-linear differential equations were solved simultaneously by using Newton -Rhapson numerical method. Flow field characteristics such as tip vortex and secondary flow were confirmed through axial, radial and tangential velocity contour plots. At the same time, the effects of tip clearance on axial thrust and input power were also investigated by using wind tunnel measurement system. For enhancing the performance of ducted fan, tip clearance level should be as small as possible.

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A method to evaluate the frequencies of free transversal vibrations in self-anchored cable-stayed bridges

  • Monaco, Pietro;Fiore, Alessandra
    • Computers and Concrete
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    • v.2 no.2
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    • pp.125-146
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    • 2005
  • The objective of this paper is setting out, for a cable-stayed bridge with a curtain suspension, a method to determine the modes of vibration of the structure. The system of differential equations governing the vibrations of the bridge, derived by means of a variational formulation in a nonlinear field, is reported in Appendix C. The whole analysis results from the application of Hamilton's principle, using the expressions of potential and kinetic energies and of the virtual work made by viscous damping forces of the various parts of the bridge (Monaco and Fiore 2003). This paper focuses on the equation concerning the transversal motion of the girder of the cable-stayed bridge and in particular on its final form obtained, restrictedly to the linear case, neglecting some quantities affecting the solution in a non-remarkable way. In the hypotheses of normal mode of vibration and of steady-state, we propose the resolution of this equation by a particular method based on a numerical approach. Respecting the boundary conditions, we derive, for each mode of vibration, the corresponding frequency, both natural and damped, the shape-function of the girder axis and the exponential function governing the variability of motion amplitude in time. Finally the results so obtained are compared with those deriving from the dynamic analysis performed by a finite elements calculation program.

Pyrolysis Reaction for the Treatment of Hazardous Halogenated Hydrocarbon Waste (유해 할로겐화 탄화수소 폐기물 처리를 위한 열분해 반응)

  • 조완근
    • Journal of Environmental Science International
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    • v.6 no.4
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    • pp.399-407
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    • 1997
  • The pyrolysis reactions of atomic hydrogen with chloroform were studied In a 4 cm 1.6. tubular flow reactor with low flow velocity 1518 cm/sec and a 2.6 cm 1.4. tubular flow reactor with high flow velocity (1227 cm/sec). The hydrogen atom concentration was measured by chemiluminescence titration with nitrogen dioxide, and the chloroform concentrations were determined using a gas chromatography. The chloroform conversion efficiency depended on both the chloroform flow rate and linear flow velocity, but 416 not depend on the flow rate of hydrogen atom. A computer model was employed to estimate a rate constant for the initial reaction of atomic hydrogen with chloroform. The model consisted of a scheme for chloroform-hydrogen atom reaction, Runge-Kutta 4th-order method for Integration of first-order differential equations describing the time dependence of the concentrations of various chemical species, and Rosenbrock method for optimization to match model and experimental results. The scheme for chloroform-hydrogen atom reaction Included 22 elementary reactions. The rate constant estimated using the data obtained from the 2.6 cm 1.4. reactor was to be 8.1 $\times$ $10^{-14}$ $cm^3$/molecule-sec and 3.8 $\times$ $10^{-15}$ cms/molecule-sec, and the deviations of computer model from experimental results were 9% and 12% , for the each reaction time of 0.028 sec and 0.072 sec, respectively.

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Dynamic responses of a beam with breathing cracks by precise integration method

  • Cui, C.C.;He, X.S.;Lu, Z.R.;Chen, Y.M.;Liu, J.K.
    • Structural Engineering and Mechanics
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    • v.60 no.5
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    • pp.891-902
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    • 2016
  • The beam structure with breathing cracks subjected to harmonic excitations was modeled by FEM based on Euler-Bernoulli theory, and a piecewise dynamical system was deduced. The precise integration method (PIM) was employed to propose an algorithm for analyzing the dynamic responses of the deduced system. This system was first divided into linear sub-systems, between which there are switching points resulted from the breathing cracks. The inhomogeneous terms due to the external excitations were tackled by introducing auxiliary variables to express the harmonic functions, hence the sub-systems are homogeneous. The PIM was then applied to solve the homogeneous sub-systems one by one. During the procedures, a predictor-corrector algorithm was presented to determine the switching points accurately. The presented method can provide solutions with an accuracy to a magnitude of $10^{-12}$ compared with exact solutions obtained by the theories of ordinary differential equations. The PIM results are much more accurate than Newmark ones with the same time step. Moreover, it is found that the PIM can maintain a high level of accuracy even when the time step increases within a relatively wide range.

An Improved Poincaré-like Carleman Linearization Approach for Power System Nonlinear Analysis

  • Wang, Zhou-Qiang;Huang, Qi;Zhang, Chang-Hua
    • Journal of Electrical Engineering and Technology
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    • v.8 no.2
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    • pp.271-281
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    • 2013
  • In order to improve the performance of analysis, it is important to consider the nonlinearity in power system. The Carleman embedding technique (linearization procedure) provides an effective approach in reduction of nonlinear systems. In the approach, a group of differential equations in which the state variables are formed by the original state variables and the vector monomials one can build with products of positive integer powers of them, is constructed. In traditional Carleman linearization technique, the tensor matrix is truncated to form a square matrix, and then regular linear system theory is used to solve the truncated system directly. However, it is found that part of nonlinear information is neglected when truncating the Carleman model. This paper proposes a new approach to solve the problem, by combining the Poincar$\acute{e}$ transformation with the Carleman linearization. Case studies are presented to verify the proposed method. Modal analysis shows that, with traditional Carleman linearization, the calculated contribution factors are not symmetrical, while such problems are avoided in the improved approach.

Optimum Inverse Design of 2-D Cascade Airfoil (2차원 익렬 익형의 최적역설계)

  • 조장근;박원규
    • Journal of the Society of Naval Architects of Korea
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    • v.39 no.4
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    • pp.17-23
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    • 2002
  • The present paper describes the optimum inverse design of 2-D linear cascade airfoil. The pressure coefficient of an airfoil surface is taken as the objective function, and non-orthogonal incompressible Navier-Stokes equation is applied to calculate the pressure coefficient. Both of steepest descent and conjugate gradient method have been used to make the objective function go to zero. The 1st order finite differential method is applied to the searching direction and the golden section method is used to compute the searching distance. As a result of the present work, a good convergence to the target airfoil has been obtained.

Passive control of seismically excited structures by the liquid column vibration absorber

  • Konar, Tanmoy;Ghosh, Aparna Dey
    • Structural Engineering and Mechanics
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    • v.36 no.5
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    • pp.561-573
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    • 2010
  • The potential of the liquid column vibration absorber (LCVA) as a seismic vibration control device for structures has been explored in this paper. In this work, the structure has been modeled as a linear, viscously damped single-degree-of-freedom (SDOF) system. The governing differential equations of motion for the damper liquid and for the coupled structure-LCVA system have been derived from dynamic equilibrium. The nonlinear orifice damping in the LCVA has been linearized by a stochastic equivalent linearization technique. A transfer function formulation for the structure-LCVA system has been presented. The design parameters of the LCVA have been identified and by applying the transfer function formulation the optimum combination of these parameters has been determined to obtain the most efficient control performance of the LCVA in terms of the reduction in the root-mean-square (r.m.s.) displacement response of the structure. The study has been carried out for an example structure subjected to base input characterized by a white noise power spectral density function (PSDF). The sensitivity of the performance of the LCVA to the coefficient of head loss and to the tuning ratio have also been examined and compared with that of the liquid column damper (LCD). Finally, a simulation study has been carried out with a recorded accelerogram, to demonstrate the effectiveness of the LCVA.

Computational Study on the Hemodynamic Behaviors of the Human Cardiovascular System with an Acute Arteriovenous Fistula (급성 동정맥루를 포함하는 인체 심혈관계의 혈류역학적 거동에 관한 수치 해석적 연구)

  • 변수영;손정락;심은보;노승탁
    • Journal of Biomedical Engineering Research
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    • v.24 no.4
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    • pp.329-337
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    • 2003
  • Blood in congenital or acquired AY fistula(arteriovenous fistula) flows from arteries directly to veins. detouring peripheral micro-circulation. This makes a great effect on the hemodynamics of human cardiovascular system. In this study, a computational method using lumped parameter mode) was proposed to simulate the cardiovascular hemodynamics of patients with acute AV fistula The cardiovascular system model with a fistula compartment in left lower limb was built using 17 standard lumped compartments. Using fourth order Runge-Kutta method. we solved numerically the unsteady linear set of the ordinary differential equations resulting from application of Kirchhoff's law to the lumped parameter hemodynamic model. The baroreceptor reflex system was implemented to explain the auto-regulation effect of the cardiovascular system with acute AV fistula.