• Title/Summary/Keyword: Matrix Equations

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Stability and parameters influence study of fully balanced hoist vertical ship lift

  • Cheng, Xionghao;Shi, Duanwei;Li, Hongxiang;Xia, Re;Zhang, Yang;Zhou, Ji
    • Structural Engineering and Mechanics
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    • v.66 no.5
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    • pp.583-594
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    • 2018
  • A theoretical formulation based on the linearized potential theory, the Descartes' rule and the extremum optimization method is presented to calculate the critical distance of lifting points of the fully balanced hoist vertical ship lift, and to study pitching stability of the ship lift. The overturning torque of the ship chamber is proposed based on the Housner theory. A seven-free-degree dynamic model of the ship lift based on the Lagrange equation of the second kind is then established, including the ship chamber, the wire rope, the gravity counterweights and the liquid in the ship chamber. Subsequently, an eigenvalue equation is obtained with the coefficient matrix of the dynamic equations, and a key coefficient is analyzed by innovative use of the minimum optimization method for a stability criterion. Also, an extensive influence of the structural parameters contains the gravity counterweight wire rope stiffness, synchronous shaft stiffness, lifting height and hoists radius on the critical distance of lifting points is numerically analyzed. With the Runge-Kutta method, the four primary dynamical responses of the ship lift are investigated to demonstrate the accuracy/reliability of the result from the theoretical formulation. It is revealed that the critical distance of lifting points decreases with increasing the synchronous shaft stiffness, while increases with rising the other three structural parameters. Moreover, the theoretical formulation is more applicable than the previous criterions to design the layout of the fully balanced hoist vertical ship lift for the ensuring of the stability.

Bending, buckling, and free vibration analyses of carbon nanotube reinforced composite beams and experimental tensile test to obtain the mechanical properties of nanocomposite

  • Mohammadimehr, M.;Mohammadi-Dehabadi, A.A.;Akhavan Alavi, S.M.;Alambeigi, K.;Bamdad, M.;Yazdani, R.;Hanifehlou, S.
    • Steel and Composite Structures
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    • v.29 no.3
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    • pp.405-422
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    • 2018
  • In this research, experimental tensile test and manufacturing of carbon nanotube reinforced composite beam (CNTRC) is presented. Also, bending, buckling, and vibration analysis of CNTRC based on various beam theories such as Euler-Bernoulli, Timoshenko and Reddy beams are considered. At first, the experimental tensile tests are carried out for CNTRC and composite beams in order to obtain mechanical properties and then using Hamilton's principle the governing equations of motion are derived for Euler Bernoulli, Timoshenko and Reddy theories. The results have a good agreement with the obtained results by similar researches and it is shown that adding just two percent of carbon nanotubes increases dimensionless fundamental frequency and critical buckling load as well as decreases transverse deflection of composite beams. Also, the influences of different manufacturing processes such as hand layup and industrial methods using vacuum pump on composite properties are investigated. In these composite beams, glass fibers used in an epoxy matrix and for producing CNTRC, CNTs are applied as reinforcement particles. Applying two percent of CNTs leads to increase the mechanical properties and increases natural frequencies and critical buckling load and decreases deflection. The obtained natural frequencies and critical buckling load by theoretical method are higher than other methods, because there are some inevitable errors in industrial and hand layup method. Also, the minimum deflection occurs for theoretical methods, in bending analysis. In this study, Young's and shear modulli as well as density are obtained by experimental test and have not been used from the results of other researches. Then the theoretical analysis such as bending, buckling and vibration are considered by using the obtained mechanical properties of this research.

Extraction of Electrical Parameters for Single and Differential Vias on PCB (PCB상 Single 및 Differential Via의 전기적 파라미터 추출)

  • Chae Ji Eun;Lee Hyun Bae;Park Hon June
    • Journal of the Institute of Electronics Engineers of Korea SD
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    • v.42 no.4 s.334
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    • pp.45-52
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    • 2005
  • This paper presents the characterization of through hole vias on printed circuit board (PCB) through the time domain and frequency domain measurements. The time domain measurement was performed on a single via using the TDR, and the model parameters were extracted by the fitting simulation using HSPICE. The frequency domain measurement was also performed by using 2 port VNA, and the model parameters were extracted by fitting simulation with ADS. Using the ABCD matrices, the do-embedding equations were derived probing in the same plane in the VNA measurement. Based on the single via characterization, the differential via characterization was also performed by using TDR measurements. The time domain measurements were performed by using the odd mode and even mode sources in TDR module, and the Parameter values were extracted by fitting with HSPICE. Comparing measurements with simulations, the maximum calculated differences were $14\%$ for single vias and $17\%$ for differential vias.

Constitutive Analysis of the High-temperature Deformation Behavior of Two Phase Ti-6Al-4V Near-α Ti-6.85Al-1.6V and Single Phase-α Ti-7.0Al-1.5V Alloy (2상 Ti-6Al-4V 합금, 준단상 Ti-6.85Al-1.6V 및 단상 Ti-7.0Al-1.5V 합금의 고온 변형거동에 관한 연구)

  • Kim Jeoung Han;Yeom Jong Taek;Park Nho Kwang;Lee Chong Soo
    • Transactions of Materials Processing
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    • v.14 no.8 s.80
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    • pp.681-688
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    • 2005
  • The high-temperature deformation mechanisms of a ${\alpha}+{\beta}$ titanium alloy (Ti-6Al-4V), near-a titanium alloy (Ti-6.85Al-1.6V) and a single-phase a titanium alloy (Ti-7.0Al-1.5V) were deduced within the framework of inelastic-deformation theory. For this purpose, load relaxation tests were conducted on three alloys at temperatures ranging from 750 to $950^{\circ}C$. The stress-versus-strain rate curves of both alloys were well fitted with inelastic-deformation equations based on grain matrix deformation and grain-boundary sliding. The constitutive analysis revealed that the grain-boundary sliding resistance is higher in the near-${\alpha}$ alloy than in the two-phase ${\alpha}+{\beta}$ alloy due to the difficulties in relaxing stress concentrations at the triple-junction region in the near-${\alpha}$ alloy. In addition, the internal-strength parameter (${\sigma}^*$) of the near-${\alpha}$ alloy was much higher than that of the ${\alpha}+{\beta}$ alloy, thus implying that dislocation emission/ slip transfer at ${\alpha}/{\alpha}$ boundaries is more difficult than at ${\alpha}/{\beta}$ boundaries.

Locking-free Straight Beam Element by a Modified Transverse Displacement Field (수정 횡변위장에 의한 강성과잉이 없는 직선 보 요소)

  • 이팔갑;신효철
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.12
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    • pp.2287-2297
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    • 1992
  • The Formulation of a new Hermite straight beam element to eliminate the shear locking is presented. All the kinematic variables in Timoshenko beam are reinterpreted by the consideration of equilibrium equations together. It shows that when the modified transverse displacement field is used the Timoshenko beam looks apparently the same as the Euler beam. The element is formulated for the modified transverse displacement field to have the same interpolation scheme as that in the Hermite element. Transformation Matrix which relates a modified nodal vector with nonmodified one is also introduced to deal with general boundary conditions. Several examples are demonstrated and discussed for the purpose of verification of the concepts employed. The solutions obtained reveal that the element describes of the beam quite correctly, showing no locking and that it is also applicable to the analysis of both thin and thick beams.

Transport of Colloids and Contaminant in Riverbank Filtration (강변여과에서 콜로이드 물질과 오염물의 거동에 관한 연구)

  • Lee Sang-Il;Kim Dae-Hwan;Lee Sang-Sin;You Sang-Yeon
    • Journal of Korea Water Resources Association
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    • v.39 no.6 s.167
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    • pp.511-520
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    • 2006
  • Riverbank filtration is a natural process, using alluvial aquifers to remove contaminants and pathogens in river water for the production of drinking water. In Korea, most of the drinking water is supplied by surface water in-take. However, maintaining the quality of the drinking water becomes more and more difficult due to the increase of contamination. In riverbank filtration, the understanding of contaminant transport is an important task for the production of high quality drinking water and for the maintenance of facilities. In this paper, the transport behavior of hydrophobic organic contaminants is investigated when contaminants coexist with dissolved organic matter (DOM) and bacteria. In the developed model, the aquifer is thought of as a four phase system: two mobile colloidal phases, an aqueous phase, and a stationary solid matrix phase. The model equations are solved numerically for various situations. Results indicate that the presence of colloidal matters can enhance the mobility of contaminant significantly and that partitioning coefficients play an important role in the process.

A linear program approach for a global optimization problem of optimizing a linear function over an efficient set (글로벌최적화 문제인 유효해집합 위에서의 최적화 문제에 대한 선형계획적 접근방법)

  • 송정환
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2000.04a
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    • pp.53-56
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    • 2000
  • The problem ( Ρ ) of optimizing a linear function d$\^$T/x over the set of efficient set for a multiple objective linear program ( Μ ) is difficult because the efficient set is nonconvex. There some interesting properties between the objective linear vector d and the matrix of multiple objectives C and those properties lead us to establish criteria to solve ( Ρ ) with a linear program. In this paper we investigate a system of the linear equations C$\^$T/${\alpha}$=d and construct two linearly independent positive vectors ${\mu}$, ν such that ${\alpha}$=${\mu}$-ν. From those vectors ${\mu}$, ν, solving an weighted sum linear program for finding an efficient extreme point for the ( Μ ) is a way to get an optimal solution ( Ρ ). Therefore our theory gives an easy way of solving nonconvex program ( Ρ ) with a weighted sum linear program.

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Airspeed Estimation of Course Correction Munitions by Using Extended Kalman Filter (확장 칼만필터를 이용한 탄도수정탄의 대기속도 추정)

  • Sung, Jaemin;Kim, Byoung Soo
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.43 no.5
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    • pp.405-412
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    • 2015
  • This paper represents a filter design to estimate the airspeed of a spin-stabilized, trajectory-correctible artillery ammunition. Due to the limited power and space in operational point of view, the airspeed sensor is not installed, and thus the airspeed need to be estimated using limited sensor measurements. The only IMU measurements(three-axis specific forces and angular rates) are used in this application. The extended Kalman filter algorithm is applied since a linear filter can not cover the its wide operational range in airspeed and altitude. In the implementation of the EKF, the state and measurement equations are transformed into the no-roll frame for simple form of Jacobian matrix. The simulation study is conducted to evaluate the performance of the filter under various environment conditions of sensor noise and wind turbulence. In addition, the effect of the choice in filter design parameters, i.e. process error covariance matrices is analyzed on the performance of the estimation of airspeed and angular rates.

Theoretical modelling of post - buckling contact interaction of a drill string with inclined bore-hole surface

  • Gulyayev, V.I.;Andrusenko, E.N.;Shlyun, N.V.
    • Structural Engineering and Mechanics
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    • v.49 no.4
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    • pp.427-448
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    • 2014
  • At present, the time of easy oil and gas is over. Now, the largest part of fossil fuels is concentrated in the deepest levels of tectonic structures and in the sea shelves. One of the most cumbersome operations of their extraction is the bore-hole drilling. In connection with austere tectonic and climate conditions, their drivage every so often is associated with great and diversified technological difficulties causing emergencies on frequent occasions. As a rule, they are linked with drill string accidents. A key role in prediction of these situations should play methods of theoretical modelling. For this reason, there is a growing need for development and implementation of new numerical methods for computer simulation of critical and post-critical behavior of drill strings (DSs). In this paper, the processes of non-linear deforming of a DS in cylindrical cavity of a deep bore-hole are considered. On the basis of the theory of curvilinear flexible rods, non-linear constitutive differential equations are deduced. The effects of the longitudinal non-uniform preloading, action of torque and interaction between the DS and the bore-hole surface are taken into account. Owing to the use of curvilinear coordinates in the constraining cylindrical surface and a specially chosen concomitant reference frame, it became possible to separate the desired variables and to reduce the total order of the equation system. To solve it, the method of continuation the solution by parameter and the transfer matrix technique are applied. As a result of the completed numerical analysis, the critical states of the DS loading in the cylindrical channels of inclined bore-holes are found. It is shown that the modes of the post-critical deforming of the DS are associated with its irregular spiral curving prevailing in the zone of bottom-hole-assembly. The possibility of invariant state generation during post-critical deforming is established, condition of its bifurcation is formulated. It is shown that infinite variety of loads can correspond to one geometrical configuration of the DS. They differ each from other by contact force functions.

Fundamental Study on Estimating Compressive Strength and Physical Characteristic of Heat insulation Lightweight Mortar With Foam Agent (기포제 혼입 단열형 경량모르타르의 물리적 특성 및 압축강도 추정에 관한 기초적 연구)

  • Min, Tae-Beom;Woo, Young-Je;Lee, han-Seung
    • KIEAE Journal
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    • v.10 no.3
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    • pp.89-96
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    • 2010
  • In comparison with ordinary or heavy-weight concrete, light-weight air void concrete has the good aspects in optimizing super tall structure systems for the process of design considering wind load and seismic load by lightening total dead load of buildings and reducing natural resources used. Light-weight air void concrete has excellent properties of heat and sound insulating due to its high amount porosity of air voids. So, it has been used as partition walls and the floor of Ondol which is the traditional Korean floor heating system. Under the condition of which the supply of light-weight aggregates are limited, the development of light-weight concrete using air voids is highly required in the aspects of reduced manufacturing prices and mass production. In this study, we investigated the physical properties and thermal behaviors of specimens that applied different mixing ratios of foaming agent to evaluate the possibility of use in the structural elements. We proposed the estimating equation for compressive strength of each mix having different ratio of foaming agent. We also confirmed that the density of cement matrix is decreased as the mixing amount of foaming agent increase up to 0.6% of foaming agent mixing ratio which was observed by SEM. Based on porosity and compressive strength of control mortar without foaming agent, we built the estimating equations of compressive strength for mortars with foaming agent. The upper limit of use in foaming agent is about 0.6% of the binder amount. Each air void is independent, and size of voids range from 50 to $100{\mu}m$.