• 제목/요약/키워드: Nonlinear differential equations

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Temperature dependent buckling analysis of graded porous plate reinforced with graphene platelets

  • Wei, Guohui;Tahouneh, Vahid
    • Steel and Composite Structures
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    • 제39권3호
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    • pp.275-290
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    • 2021
  • The main purpose of this research work is to investigate the critical buckling load of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using generalized differential quadrature (GDQ) method at thermal condition. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the plate thickness direction. Generally, the thermal distribution is considered to be nonlinear and the temperature changing continuously through the thickness of the nanocomposite plates according to the power-law distribution. To model closed cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme are used, through which mechanical properties of the structures can be extracted. Based on the third order shear deformation theory (TSDT) and the Hamilton's principle, the equations of motion are established and solved for various boundary conditions (B.Cs). The fast rate of convergence and accuracy of the method are investigated through the different solved examples and validity of the present study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns through the thickness, porosity coefficient and distribution of porosity on critical buckling load. Results reveal that the importance of thermal condition on of the critical load of FGP-GPL reinforced nanocomposite plates.

Numerical and statistical analysis of Newtonian/non-Newtonian traits of MoS2-C2H6O2 nanofluids with variable fluid properties

  • Manoj C Kumar;Jasmine A Benazir
    • Advances in nano research
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    • 제16권4호
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    • pp.341-352
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    • 2024
  • This study investigates the heat and mass transfer characteristics of a MoS2 nanoparticle suspension in ethylene glycol over a porous stretching sheet. MoS2 nanoparticles are known for their exceptional thermal and chemical stability which makes it convenient for enhancing the energy and mass transport properties of base fluids. Ethylene glycol, a common coolant in various industrial applications is utilized as the suspending medium due to its superior heat transfer properties. The effects of variable thermal conductivity, variable mass diffusivity, thermal radiation and thermophoresis which are crucial parameters in affecting the transport phenomena of nanofluids are taken into consideration. The governing partial differential equations representing the conservation of momentum, energy, and concentration are reduced to a set of nonlinear ordinary differential equations using appropriate similarity transformations. R software and MATLAB-bvp5c are used to compute the solutions. The impact of key parameters, including the nanoparticle volume fraction, magnetic field, Prandtl number, and thermophoresis parameter on the flow, heat and mass transfer rates is systematically examined. The study reveals that the presence of MoS2 nanoparticles curbs the friction between the fluid and the solid boundary. Moreover, the variable thermal conductivity controls the rate of heat transfer and variable mass diffusivity regulates the rate of mass transfer. The numerical and statistical results computed are mutually justified via tables. The results obtained from this investigation provide valuable insights into the design and optimization of systems involving nanofluid-based heat and mass transfer processes, such as solar collectors, chemical reactors, and heat exchangers. Furthermore, the findings contribute to a deeper understanding of stretching sheet systems, such as in manufacturing processes involving continuous casting or polymer film production. The incorporation of MoS2-C2H6O2 nanofluids can potentially optimize temperature distribution and fluid dynamics.

Daily Stock Price Prediction Using Fuzzy Model (퍼지 모델을 이용한 일별 주가 예측)

  • Hwang, Hee-Soo
    • The KIPS Transactions:PartB
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    • 제15B권6호
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    • pp.603-608
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    • 2008
  • In this paper an approach to building fuzzy model to predict daily open, close, high, and low stock prices is presented. One of prior problems in building a stock prediction model is to select most effective indicators for the stock prediction. The problem is overcome by the selection of information used in the analysis of stick-chart as the input variables of our fuzzy model. The fuzzy rules have the premise and the consequent, in which they are composed of trapezoidal membership functions, and nonlinear equations, respectively. DE(Differential Evolution) searches optimal fuzzy rules through an evolutionary process. To evaluate the effectiveness of the proposed approach numerical example is considered. The fuzzy models to predict open, high, low, and close prices of KOSPI(KOrea composite Stock Price Index) on a daily basis are built, and their performances are demonstrated and compared with those of neural network.

Time Series Stock Prices Prediction Based On Fuzzy Model (퍼지 모델에 기초한 시계열 주가 예측)

  • Hwang, Hee-Soo;Oh, Jin-Sung
    • Journal of the Korean Institute of Intelligent Systems
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    • 제19권5호
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    • pp.689-694
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    • 2009
  • In this paper an approach to building fuzzy models for predicting daily and weekly stock prices is presented. Predicting stock prices with traditional time series analysis has proven to be difficult. Fuzzy logic based models have advantage of expressing the input-output relation linguistically, which facilitates the understanding of the system behavior. In building a stock prediction model we bear a burden of selecting most effective indicators for the stock prediction. In this paper information used in traditional candle stick-chart analysis is considered as input variables of our fuzzy models. The fuzzy rules have the premises and the consequents composed of trapezoidal membership functions and nonlinear equations, respectively. DE(Differential Evolution) identifies optimal fuzzy rules through an evolutionary process. The fuzzy models to predict daily and weekly open, high, low, and close prices of KOSPI(KOrea composite Stock Price Index) are built, and their performances are demonstrated.

Development of a Dynamic Model for Double-Effect LiBr-$H_2O$ Absorption Chillers and Comparison with Experimental Data. (이중효용 흡수식 냉온수기 동특성 모델 개발 및 실험결과 비교)

  • Shin, Young-gi;Seo, Jung-A;Cho, Hyun-Wook;Nam, Sang-Chul;Jeong, Jin-Hee
    • Proceedings of the SAREK Conference
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    • 대한설비공학회 2008년도 하계학술발표대회 논문집
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    • pp.109-114
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    • 2008
  • A dynamic model has been developed to simulate dynamic operation of a real double-effect absorption chiller. Dynamic behavior of working fluids in main components was modeled in first-order nonlinear differential equations based on heat and mass balances. Mass transport mechanisms among the main components were modeled by valve throttling, 'U' tube overflow and solution sub-cooling. The nonlinear dynamic equations coupled with the subroutines to calculate thermodynamic properties of working fluids were solved by a numerical method. The dynamic performance of the model was compared with the test data of a commercial medium chiller. The model showed a good agreement with the test data except for the first 5,000 seconds during which different flow rates of the weak solution caused some discrepancy. It was found that the chiller dynamics is governed by the inlet temperatures of the cooling water and the chilled water when the heat input to the chiller is relatively constant.

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Development of a Dynamic Model for Double-Effect LiBr-$H_{2}O$ Absorption Chillers and Comparison with Experimental Data (이중효용 흡수식 냉온수기 동특성 모델 개발 및 실험결과 비교)

  • Shin, Young-Gy;Seo, Jung-A;Cho, Hyun-Wook;Nam, Sang-Chul;Jeong, Jin-Hee
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • 제20권12호
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    • pp.781-788
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    • 2008
  • A dynamic model has been developed to simulate dynamic operation of a real double-effect absorption chiller. Dynamic behavior of working fluids in main components was modeled in first-order nonlinear differential equations based on heat and mass balances. Mass transport mechanisms among the main components were modeled by valve throttling, 'U' tube overflow and solution sub-cooling. The nonlinear dynamic equations coupled with the subroutines to calculate thermodynamic properties of working fluids were solved by a numerical method. The dynamic performance of the model was compared with the test data of a commercial medium chiller. The model showed a good agreement with the test data except for the first 5,000 seconds during which different flow rates of the weak solution caused some discrepancy. It was found that the chiller dynamics is governed by the inlet temperatures of the cooling water and the chilled water when the heat input to the chiller is relatively constant.

A Study on the Variable Structure Adaptive Control Systems for a Nuclear Reactor (가변구조 적응제어이론에 의한 원자로부하추종 출력제어에 관한 연구)

  • Sung Ha Kwon;Hee Young Chun;Hyun Kook Shin
    • Nuclear Engineering and Technology
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    • 제17권4호
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    • pp.247-255
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    • 1985
  • This paper describes a new method for the design of variable structure model-following control systems(VSMFC). This design concept is developed using the theory of variable structure systems (VSS) and slide mode. The new results are presented on the sliding control methodology to achieve accurate tracking for a class of nonlinear, multi-input multi-output(MIMO), time varying systems in the presence of parameter variations. The design requires little computational effort. The dynamic response is insensitive to parameter variations. The feasibility and the advantages of the method are illustrated by applying it to a 1000 MWe boiling water reactor(BWR). The control is studied in the range of 85%∼90% of rated power for load-following control. A set of 12 nonlinear differential equations is used to simulate the total plant. A 6-th order linear model has been developed from these equations at 85% of rated power. The obtained controller is shown by simulations to be able to compensate for a plant parameter variation over a wide power range.

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Aerodynamic and Aeroelastic Tool for Wind Turbine Applications

  • Viti, Valerio;Coppotelli, Giuliano;De Pompeis, Federico;Marzocca, Pier
    • International Journal of Aeronautical and Space Sciences
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    • 제14권1호
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    • pp.30-45
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    • 2013
  • The present work focuses on the unsteady aerodynamics and aeroelastic properties of a small-medium sized wind-turbine blade operating under ideal conditions. A tapered/twisted blade representative of commercial blades used in an experiment setup at the National Renewable Energy Laboratory is considered. The aerodynamic loads are computed using Computational Fluid Dynamics (CFD) techniques. For this purpose, FLUENT$^{(R)}$, a commercial finite-volume code that solves the Navier-Stokes and the Reynolds-Averaged Navier-Stokes (RANS) equations, is used. Turbulence effects in the 2D simulations are modeled using the Wilcox k-w model for validation of the CFD approach. For the 3D aerodynamic simulations, in a first approximation, and considering that the intent is to present a methodology and workflow philosophy more than highly accurate turbulent simulations, the unsteady laminar Navier-Stokes equations were used to determine the unsteady loads acting on the blades. Five different blade pitch angles were considered and their aerodynamic performance compared. The structural dynamics of the flexible wind-turbine blade undergoing significant elastic displacements has been described by a nonlinear flap-lag-torsion slender-beam differential model. The aerodynamic quasi-steady forcing terms needed for the aeroelastic governing equations have been predicted through a strip-theory based on a simple 2D model, and the pertinent aerodynamic coefficients and the distribution over the blade span of the induced velocity derived using CFD. The resulting unsteady hub loads are achieved by a first space integration of the aeroelastic equations by applying the Galerkin's approach and by a time integration using a harmonic balance scheme. Comparison among two- and three- dimensional computations for the unsteady aerodynamic load, the flap, lag and torsional deflections, forces and moments are presented in the paper. Results, discussions and pertinent conclusions are outlined.

Formulation of Fully Coupled THM Behavior in Unsaturated Soil (불포화지반에 대한 열-수리-역학 거동의 수식화)

  • Shin, Ho-Sung
    • Journal of the Korean Geotechnical Society
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    • 제27권3호
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    • pp.75-83
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    • 2011
  • Emerging issues related with fully coupled Thermo-Hydro-Mechanical (THM) behavior of unsaturated soil demand the development of a numerical tool in diverse geo-mechanical and geo-environmental areas. This paper presents general governing equations for coupled THM processes in unsaturated porous media. Coupled partial differential equations are derived from three mass balances equations (solid, water, and air), energy balance equation, and force equilibrium equation. With Galerkin formulation and time integration of these governing equations, finite element code is developed to find nonlinear solution of four main variables (displacement-u, gas pressure-$P_g$), liquid pressure-$P_1$), and temperature-T) using Newton's iterative scheme. Three cases of numerical simulations are conducted and discussed: one-dimensional drainage experiments (u-$P_g-P_1$), thermal consolidation (u-$P_1$-T), and effect of pile on surrounding soil due to surface temperature variation (u-$P_1$-T).

Stochastic vibration suppression analysis of an optimal bounded controlled sandwich beam with MR visco-elastomer core

  • Ying, Z.G.;Ni, Y.Q.;Duan, Y.F.
    • Smart Structures and Systems
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    • 제19권1호
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    • pp.21-31
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    • 2017
  • To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.