• Title/Summary/Keyword: Stiff equations

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Dynamic analysis of magnetic head slider at ultra low clearance (마그네틱 헤드 슬라이더의 극소 공기막에 대한 동특성 해석)

  • 장인배;한동철
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.14 no.6
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    • pp.1487-1494
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    • 1990
  • In this paper the dynamic characteristics of self acting air lubricated slider bearing of hard disk/head system are investigated. The dynamic equations of magnetic head mechanism considering both parallel and pitch motion and the time dependent modified Reynolds equation are analyzed and the dynamic pressure distribution of air film is numerically calculated in frequency domain by small perturbation method and finite difference scheme with variable grid. The dynamic response of the slider spacing is obtained accordingly as the moving recording surface vibrates in parallel mode.

Static and dynamic analysis of circular beams using explicit stiffness matrix

  • Rezaiee-Pajand, Mohammad;Rajabzadeh-Safaei, Niloofar
    • Structural Engineering and Mechanics
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    • v.60 no.1
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    • pp.111-130
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    • 2016
  • Two new elements with six degrees of freedom are proposed by applying the equilibrium conditions and strain-displacement equations. The first element is formulated for the infinite ratio of beam radius to thickness. In the second one, theory of the thick beam is used. Advantage of these elements is that by utilizing only one element, the exact solution will be obtained. Due to incorporating equilibrium conditions in the presented formulations, both proposed elements gave the precise internal forces. By solving some numerical tests, the high performance of the recommended formulations and also, interaction effects of the bending and axial forces will be demonstrated. While the second element has less error than the first one in thick regimes, the first element can be used for all regimes due to simplicity and good convergence. Based on static responses, it can be deduced that the first element is efficient for all the range of structural characteristics. The free vibration analysis will be performed using the first element. The results of static and dynamic tests show no deficiency, such as, shear and membrane locking and excessive stiff structural behavior.

Buckling of restrained steel columns due to fire conditions

  • Hozjan, Tomaz;Planinc, Igor;Saje, Miran;Srpcic, Stanislav
    • Steel and Composite Structures
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    • v.8 no.2
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    • pp.159-178
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    • 2008
  • An analytical procedure is presented for the determination of the buckling load and the buckling temperature of a straight, slender, geometrically perfect, axially loaded, translationally and rotationally restrained steel column exposed to fire. The exact kinematical equations of the column are considered, but the shear strain is neglected. The linearized stability theory is employed in the buckling analysis. Behaviour of steel at the elevated temperature is assumed in accordance with the European standard EC 3. Theoretical findings are applied in the parametric analysis of restrained columns. It is found that the buckling length factor decreases with temperature and depends both on the material model and stiffnesses of rotational and translational restraints. This is in disagreement with the buckling length for intermediate storeys of braced frames proposed by EC 3, where it is assumed to be temperature independent. The present analysis indicates that this is a reasonable approximation only for rather stiff rotational springs.

Layer-wise numerical model for laminated glass plates with viscoelastic interlayer

  • Zemanova, Alena;Zeman, Jan;Janda, Tomas;Sejnoha, Michal
    • Structural Engineering and Mechanics
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    • v.65 no.4
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    • pp.369-380
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    • 2018
  • In this paper, a multi-layered finite element model for laminated glass plates is introduced. A layer-wise theory is applied to the analysis of laminated glass due to the combination of stiff and soft layers; the independent layers are connected via Lagrange multipliers. The von $K{\acute{a}}rm{\acute{a}}n$ large deflection plate theory and the constant Poisson ratio for constitutive equations are assumed to capture the possible effects of geometric nonlinearity and the time/temperature-dependent response of the plastic foil. The linear viscoelastic behavior of a polymer foil is included by the generalized Maxwell model. The proposed layer-wise model was implemented into the MATLAB code and verified against detailed three-dimensional models in ADINA solver using different hexahedral finite elements. The effects of temperature, load duration, and creep/relaxation are demonstrated by examples.

Thermal buckling analysis of functionally graded carbon nanotube-reinforced composite sandwich beams

  • Ebrahimi, Farzad;Farazmandnia, Navid
    • Steel and Composite Structures
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    • v.27 no.2
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    • pp.149-159
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    • 2018
  • Thermo-mechanical buckling of sandwich beams with a stiff core and face sheets made of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) within the framework of Timoshenko beam theory is presented. The material properties of FG-CNTRC are supposed to vary continuously in the thickness direction and are estimated through the rule of mixture. Also the properties of these materials should be considered temperature dependent. The governing equations and boundary conditions are derived by using Hamilton's principle and solved using an efficient technique called the Differential Transform Method (DTM) to achieve the critical buckling of the sandwich beam in uniform thermal environment. A detailed parametric study is guided to investigate the effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, and clamped-clamped, simply-simply and clamped-simply end supports on the critical buckling behavior of sandwich beams with FG-CNTRC face sheets. Numerical results for comparison of sandwich beams with uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) face sheets with those with FG-CNTRC face sheets are also presented.

Observer Theory Applied to the Optimal Control of Xenon Concentration in a Nuclear Reactor (옵저버 이론의 원자로 지논 농도 최적제어에의 응용)

  • Woo, Hae-Seuk;Cho, Nam-Zin
    • Nuclear Engineering and Technology
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    • v.21 no.2
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    • pp.99-110
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    • 1989
  • The optimal control of xenon concentration in a nuclear reactor is posed as a linear quadratic regulator problem with state feedback control. Since it is not possible to measure the state variables such as xenon and iodine concentrations directly, implementation of the optimal state feedback control law requires estimation of the unmeasurable state variables. The estimation method used is based on the Luenberger observer. The set of the reactor kinetics equations is a stiff system. This singularly perturbed system arises from the interaction of slow dynamic modes (iodine and xenon concentrations) and fast dynamic modes (neutron flux, fuel and coolant temperatures). The singular perturbation technique is used to overcome this stiffness problem. The observer-based controller of the original system is effected by separate design of the observer and controller of the reduced subsystem and the fast subsystem. In particular, since in the reactor kinetics control problem analyzed in the study the fast mode dies out quickly, we need only design the observer for the reduced slow subsystem. The results of the test problems demonstrated that the state feedback control of the xenon oscillation can be accomplished efficiently and without sacrificing accuracy by using the observer combined with the singular perturbation method.

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Ambient Vibration Testing and System Identification for Tall Buildings (고층건물의 자연 진동실험 및 시스템판별)

  • Cho, Soon-Ho
    • Journal of the Earthquake Engineering Society of Korea
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    • v.16 no.3
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    • pp.23-33
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    • 2012
  • Dynamic response measurements from natural excitation were carried out for three 18-story office buildings to determine their inherent properties. The beam-column frame system was adopted as a typical structural form, but a core wall was added to resist the lateral force more effectively, resulting in a mixed configuration. To extract modal parameters such as natural frequencies, mode shapes and damping ratios from a series of vibration records at each floor, the most advanced operational system identification methods based on frequency- and time-domain like FDD, pLSCF and SSI were applied. Extracted frequencies and mode shapes from the different identification methods showed a greater consistency for three buildings, however the three lower frequencies extracted were 1.2 to 1.7 times as stiff as those obtained using the initial FE models. Comparing the extracted fundamental periods with those estimated from the code equations and FE analysis, the FE analysis results showed the most flexible behavior, and the most simple equation that considers the building height as the only parameter correlated fairly well with test results. It is recognized that such a discrepancy arises from the fact that the present tests exclude the stiffness decreasing factors like concrete cracking, while the FE models ignore the stiffness increasing factors, such as the contribution of non-structural elements and the actual material properties used.

Experimental Studies on Shear Strength of High-Strength Lightweight Concrete Beam using the Industrial by-products (산업부산물을 활용한 고강도 경량콘크리트 보의 전단강도에 대한실험 연구)

  • Lee, Seung-Jo;Park, Jung-Min;Kim, Wha-Jung
    • Journal of the Korea Concrete Institute
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    • v.18 no.5 s.95
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    • pp.621-630
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    • 2006
  • Twelve beams made of lightweight high-strength concrete were tested to determine their diagonal cracking and ultimate shear capacities. A total of 12 beams without(4 beams) and with lightweight(8 beams) were tested in a stiff testing facility, and complete load-midspan deflection curves, including the maximum capacities portion, were obtained. The variables in the test program were concrete strength, which varied 35.4 MPa, 65.3 MPa; shear span-depth ratios a/d=1.5, 2.5, 3.5, 4.5; and tensile steel ratio between 0.57 and 2.3 percent. Also, we divided beam by diagonal tension crack and ultimate shearing strength to propose an equation. In addition, it analyzed comparison mutually applying existing proposal and guide. $V_{cr}$ was as result that AIK recommendations and Zsutty proposal decrease more than a/d=2.5, increased some in Mathey's proposal equation. $V_{cr,\exp}/V_{cr,cal}$ showed tendency of overestimation according to increase of tensile steel ratio and compressive strength of concrete. On the other hand, $V_{cr,\exp}/V_{cr,cal}$ is superior in conformability with an experiment result Zsutty's proposal among other equations. The proposal equation hew that expect $V_{cr}/V_u$, rationally about shearing strength. Therefore, shear strength an equation is considered to be utilized usefully evaluating capacity by change of the shear span depth ratio of lightweight concrete, tensile steel ratio, and compressive strength of the concrete in this research.

Development of a Chinese cabbage model using Microsoft Excel/VBA (엑셀/VBA를 이용한 배추 모형 제작)

  • Moon, Kyung Hwan;Song, Eun Young;Wi, Seung Hwan;Oh, Sooja
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.20 no.2
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    • pp.228-232
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    • 2018
  • Process-based crop models have been used to assess the impact of climate change on crop production. These models are implemented in procedural or object oriented computer programming languages including FORTRAN, C++, Delphi, Java, which have a stiff learning curve. The requirement for a high level of computer programming is one of barriers for efforts to develop and improve crop models based on biophysical process. In this study, we attempted to develop a Chinese cabbage model using Microsoft Excel with Visual Basic for Application (VBA), which would be easy enough for most agricultural scientists to develop a simple model for crop growth simulation. Results from Soil-Plant-Atmosphere-Research (SPAR) experiments under six temperature conditions were used to determine parameters of the Chinese cabbage model. During a plant growing season in SPAR chambers, numbers of leaves, leaf areas, growth rate of plants were measured six times. Leaf photosynthesis was also measured using LI-6400 Potable Photosynthesis System. Farquhar, von Caemmerer, and Berry (FvCB) model was used to simulate a leaf-level photosynthesis process. A sun/shade model was used to scale up to canopy-level photosynthesis. An Excel add-in, which is a small VBA program to assist crop modeling, was used to implement a Chinese cabbage model under the environment of Excel organizing all of equations into a single set of crop model. The model was able to simulate hourly changes in photosynthesis, growth rate, and other physiological variables using meteorological input data. Estimates and measurements of dry weight obtained from six SPAR chambers were linearly related ($R^2=0.985$). This result indicated that the Excel/VBA can be widely used for many crop scientists to develop crop models.