• Title/Summary/Keyword: Cubic equation

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Higher order flutter analysis of doubly curved sandwich panels with variable thickness under aerothermoelastic loading

  • livani, Mostafa;MalekzadehFard, Keramat;Shokrollahi, Saeed
    • Structural Engineering and Mechanics
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    • v.60 no.1
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    • pp.1-19
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    • 2016
  • In this study, the supersonic panel flutter of doubly curved composite sandwich panels with variable thickness is considered under aerothermoelastic loading. Considering different radii of curvatures of the face sheets in this paper, the thickness of the core is a function of plane coordinates (x,y), which is unique. For the first time in the current model, the continuity conditions of the transverse shear stress, transverse normal stress and transverse normal stress gradient at the layer interfaces, as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of the sandwich panel are satisfied. The formulation is based on an enhanced higher order sandwich panel theory and the vertical displacement component of the face sheets is assumed as a quadratic one, while a cubic pattern is used for the in-plane displacement components of the face sheets and the all displacement components of the core. The formulation is based on the von $K{\acute{a}}rm{\acute{a}}n$ nonlinear approximation, the one-dimensional Fourier equation of the heat conduction along the thickness direction, and the first-order piston theory. The equations of motion and boundary conditions are derived using the Hamilton principle and the results are validated by the latest results published in the literature.

Optimal Design of a Piezoelectric Smart Structure for Cabin Noise Control (실내 소음제어를 위한 압전지능구조물의 최적 설계)

  • 고범진;이중근;김재환;최승복;정재천
    • Journal of KSNVE
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    • v.8 no.3
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    • pp.428-434
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    • 1998
  • Optimal design of a piezoelectric smart structure is studied for cabin noise control. A cubic shaped acoustic cavity with a flat plate which covers one side is taken as the problem. The sensor signal is returned to the actuator through a negative gain. The acoustic cavity is modeled using the modal approach which represents the pressure fields in the cavity as a sum of mode shapes of the cavity with unknown coefficients. By using orthogonality of the mode shapes of the cavity, finite element equation for the structure with the influence of the acoustic cavity is derived. The objective function is the average pressure at a certain region, so-called silent zone, in the cavity and the design variables are the locations and sizes of the piezoelectirc actuator and sensor. The optimal design is performed at several frequencies and the results show a remarkable noise reduction. To see the robustness of the optimally designed result, the configuration is used to examine the noise reduction at different frequencies. By adjusting the gain at each frequencies, it is possible to reduce the noise in comparison with the result when the actuator is not activated.

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A Numerical Study of Smoke Movement In Atrium Space (아트리움 공간에 있어서 연기 유동에 관한 수치해석적 연구)

  • 노재성;유홍선;정연태;김충익;윤명오
    • Fire Science and Engineering
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    • v.11 no.4
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    • pp.3-14
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    • 1997
  • The smoke filling process for the atrium space containing a fire source is simulated using two types of deterministic fire model : Zone model and Field model. The zone model used is the CFAST(version 1.6) model developed at the Building and Fire Research Laboratories, NIST in the USA. The field model is a self-developed frie field model based on Computational Fluid Dynamic (CFD) theories. This article is focused on finding out the smoke movement and temperature distribution in atrium space which is cubic in shape. For solving the liked set of velocity and pressure equation, the PISO algorithm, which strengthened the velocity-pressure coupling, was used. Since PISO algorithm is a time-marching procedure, computing time si very fast. A computational procedure for predicting velocity and temperature distribution in fire-induced flow is based on the solution, in finite volume method and non-staggered grid system, of 3-dimensional equations for the conservation of mass, momentum, energy, species and so forth. The fire model i.e Zone model and Field model predicted similar results for clear heights and the smoke layer temperature.

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PFC and Zero Torque Control of SRM for EV Battery Charging (EV용 충전 인덕터용 PFC 및 제로 토크제어)

  • Rashidi, A.;Namazi, M.M.;Saghaian-nezhad, S.M.;Lee, D.H.;Ahn, J.W
    • Proceedings of the KIEE Conference
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    • 2015.07a
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    • pp.652-654
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    • 2015
  • Integrated switched reluctance motor drive as an electric vehicle battery charger is presented in this paper. The SRM, which is used as the traction power in the driving mode, is used in the charge circuit to improve the power factor of charging system. The charging circuit can share the power switches of the asymmetric converter and phase windings of SRM to charge the battery, and can reduce the size and cost of the system in the plug-in system. To keep the rotor at standstill, zero torque control method is proposed. Since the inductances of the SRM windings are not same at any stop position, the charger controller controls the reference current to satisfy the total charging current with PFC and zero torque condition. A novel cubic equation method is proposed as a current reference distributor of the charging controller. Simulations are performed by MATLAB software and results satisfy the Effectiveness of proposed battery charging system.

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Thermo-mechanically induced finite element based nonlinear static response of elastically supported functionally graded plate with random system properties

  • Lal, Achchhe;Jagtap, Kirankumar R.;Singh, Birgu N.
    • Advances in Computational Design
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    • v.2 no.3
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    • pp.165-194
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    • 2017
  • The present work proposes the thermo mechanically induced statistics of nonlinear transverse central deflection of elastically supported functionally graded (FG) plate subjected to static loadings with random system properties. The FG plate is supported on two parameters Pasternak foundation with Winkler cubic nonlinearity. The random system properties such as material properties of FG material, external loading and foundation parameters are assumed as uncorrelated random variables. The material properties are assumed as non-uniform temperature distribution with temperature dependent (TD) material properties. The basic formulation for static is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics through Newton-Raphson method. A second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are used to compute the nonlinear governing equation. The effects of load parameters, plate thickness ratios, aspect ratios, volume fraction, exponent, foundation parameters, and boundary conditions with random system properties are examined through parametric studies. The results of present approaches are compared with those results available in the literature and by employing direct Monte Carlo simulation (MCS).

NUMERICAL ANALYSIS FOR THE SHALLOW WATER EQUATIONS ON THE SPHERE BY CIP METHOD (CIP법을 이용한 구 좌표계에서의 천수 방정식 해석)

  • Yoon, Seong-Young;Kim, Soo-Youn;Kim, Hyun-Chul
    • Journal of computational fluids engineering
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    • v.10 no.2
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    • pp.7-14
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    • 2005
  • In this study, the shallow water equations on the sphere is simulated by the proposed method which has high spatial resolution and is based on the CIP(Cubic Interpolated Pseudoparticle) method. The governing equations are approximated on the longitude-latitudinal coordinate system. To avoid the problems resulting from the convergence of the meridians toward high-latitude and singularities on the poles, the semi-Lagrangian and finite volume method are employed. in addition, the CIP method is employed to solve the advection equations and is extended to apply on the equations in the polar coordinate system. The mathematical formulation and numerical results are also described. To verify of the efficiency, accuracy and capability of proposed algorithm, the standard test cases proposed bv Williamson et. al are simulated and the results are compared with other results. As a result, it is found that the present scheme gives a good properties in preserving shapes of solution and settles the pole problems in solving the shallow water equations on the sphere.

A Thoracic Model using Three-dimensional Finite Element Method (3차원 유한 요소법을 이용한 흉부 모델)

  • Deok-Won Kim
    • Journal of Biomedical Engineering Research
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    • v.8 no.1
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    • pp.57-62
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    • 1987
  • A three-dimensional thoracic model was constructed using 8-node trilinear hexahedron elements. A three-dimensional steady-state finite element code was developed using FORTRAN. Its output consists of potential at each node. current In each element, and total current In each layer in the z-direction. The thoracic model was Implemented to calculate basal impedance(Zo) In Impedance CardiograPhy Generalized Laplace's equation was solved with Dirlchlet(constant potentials) and homogeneous Neumann(no flux) boundary conditions. It was found that the con structed thoracic model was reasonable since the calculated potential differences between the adjacent electrodes and basal impedance were about the same as the measured ones.

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A Comparative Study on Mechanical Behavior of Low Temperature Application Materials for Ships and Offshore Structures (선박 및 해양구조물용 극저온 재료의 기계적 거동 특성)

  • Park, Woong-Sup;Kang, Ki-Yeob;Chun, Min-Sung;Lee, Jae-Myung
    • Journal of the Society of Naval Architects of Korea
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    • v.48 no.3
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    • pp.189-199
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    • 2011
  • Austenite stainless steel(ASS), aluminum alloy and nickel steel alloy are the most widely used in many cryogenic applications due to superior mechanical properties at low temperature. The Face-Centered Cubic(FCC) and Hexagonal Close-Packed(HCP) materials are used for the primary and secondary insulation barrier of Liquefied Natural Gas(LNG) carrier tank and various kinds of LNG applications currently. In this study, tensile tests of ASS, aluminum alloy and nickel steel alloy were carried out for the acquisition of quantitative mechanical properties under the cryogenic environment. The range of thermal condition was room temperature to $-163^{\circ}C$ and strain rate range was 0.00016/s to 0.01/s considering the dependencies of temperatures and strain rates. The comprehensive test data were analyzed in terms of the characteristics of mechanical behavior for the development of constitutive equation and its application.

A Studyon Synthesis of High Purity $\beta$-SiC Fine Particles from Ethyl Silicate(II) (Powder Properties, Reaction Type and Activation Energy) (Ethyl Silicate를 이용한 고순도 $\beta$-SiC미분말 합성에 관한 연구(II) (분말의 특성, 반응형식 및 활성화에너지))

  • 최용식;박금철
    • Journal of the Korean Ceramic Society
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    • v.26 no.2
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    • pp.195-200
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    • 1989
  • The Silica-Carbon mixture was made with addition of carbon black in the composition which monodispersed spherical fine silica was formed by the hydrolysis of ethylsilicate, mole ratio of Carbon/Alkoxide was 3.1 and $\beta$-SiC powder was synthesized by reacting this mixture at 1,350~1,50$0^{\circ}C$ in Ar atmosphere. The results of this study are as follow : (1) The purity of synthesized $\beta$-SiC powder was above 99.98% and it was in cubic modification with lattice constant of 4.3476$\AA$. (2) The rate-controlling steps varied with the reaction temperature for the syntehsis of $\beta$-SiC in this study ; nucleation and growth of $\beta$-SiC at 1,350~1,40$0^{\circ}C$, interfacial reaction at 1,45$0^{\circ}C$ and diffusion described by Jander Equation at 1,50$0^{\circ}C$. (3) When the rate-determining step was nucleation and growth, the activation energy was about 87.8kcal/mol.

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An Experimental Study on the Flow Characteristics with the Impinging Angles of Defrost Nozzle Jet Inside a Vehicle Passenger Compartment (차실내 Defrost 노즐 분류의 충돌각 변화에 따른 유동특성에 관한 실험적 연구)

  • Kim, Duck-Jin;Kim, Hyun-Joo;Rho, Byung-Joon;Lee, Jee-Keun
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.31 no.12
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    • pp.1024-1032
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    • 2007
  • The flow characteristics with the impinging angles of defrost nozzle jet inside a commercial vehicle passenger compartment were investigated experimentally by using the two-dimensional duct-nozzle model. The shape of the nozzle contraction was designed according to the curved line of cubic equation to the vertical plan of the flow direction. The impinging angles, defined as the angle between nozzle axis and a vertical line to the windshield, were varied from the $0^{\circ}\;to\;80^{\circ}$. The mean velocity distributions, the half-widths, and the momentum distributions with the cases of both the free jet and the impinging jet onto the dummy windshield were measured. The impinging jet flows similarly with wall jet from $X/b_o=20$, and the impinging angle has an effect on the half-width of the impinging jet. The momentum distributions onto the windshield increased with the increase of impinging angle, and then their inflection point was observed around the impinging angle of $60^{\circ}$.