• Title/Summary/Keyword: Superposition Theory

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Density Functional Theoretical Study on Intermolecular Interactions of 3,6-Dihydrazino-1,2,4,5-tetrazine Dimers

  • Hu, Yin;Ma, Hai-Xia;Li, Jun-Feng;Gao, Rong;Song, Ji-Rong
    • Bulletin of the Korean Chemical Society
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    • v.31 no.10
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    • pp.2897-2902
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    • 2010
  • Seven fully optimized geometries of 3,6-dihydrazino-1,2,4,5-tetrazine (DHT) dimers have been obtained with density functional theory (DFT) method at the B3LYP/$6-311++G^{**}$ level. The intermolecular interaction energy was calculated with zero point energy (ZPE) correction and basis set superposition error (BSSE) correction. The greatest corrected intermolecular interaction energy of the dimers is $-23.69\;kJ{\cdot}mol^{-1}$. Natural bond orbital (NBO) analysis is performed to reveal the origin of the interaction. Based on the vibrational analysis, the changes of thermodynamic properties from the monomers to dimer with the temperature ranging from 200.0 K to 800.0 K have been obtained using the statistical thermodynamic method. It was found that the hydrogen bonds dominantly contribute to the dimers, while the binding energies are not only determined by hydrogen bonding. The dimerization process can not occur spontaneously at given temperatures.

Finite Element Analysis of Unbalance Response of a High Speed Flexible Polygon Mirror Scanner Motor Considering the Flexibility of Supporting Structure (지지구조의 유연성을 고려한 고속 유연 폴리곤 미러 스캐너 모터의 유한 요소 불평형 응답 해석)

  • Jung, Kyung-Moon;Seo, Chan-Hee;Kim, Myung-Gyu;Jang, Gun-Hee
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.05a
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    • pp.859-865
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    • 2007
  • This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered bearing and flexible supporting structures by using the finite element method and the mode superposition method. The appropriate finite element equations for polygon mirror are described by rotating annular sector element using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. The rotating components except for the polygon mirror are modeled by Timoshenko beam element including the gyroscopic effect. The flexible supporting structures are modeled by using a 4-node tetrahedron element and 4-node shell element with rotational degrees of freedom. Finite element equations of each component of the polygon mirror scanner motor and the flexible supporting structures are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between sleeve and sintered bearing to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. Unbalance responses in time and frequency domain are performed by superposing the eigenvalues and eigenvectors from the free vibration analysis. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results. This research also shows that the flexibility of supporting structures plays an important role in determining the unbalance response of the polygon mirror scanner motor.

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On the eigenvalues of a uniform rectangular plate carrying any number of spring-damper-mass systems

  • Chen, Der-Wei
    • Structural Engineering and Mechanics
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    • v.16 no.3
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    • pp.341-360
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    • 2003
  • The goal of this paper is to determine the eigenvalues of a uniform rectangular plate carrying any number of spring-damper-mass systems using an analytical-and-numerical-combined method (ANCM). To this end, a technique was presented to replace each "spring-damper-mass" system by a massless equivalent "spring-damper" system with the specified effective spring constant and effective damping coefficient. Then, the mode superposition approach was used to transform the partial differential equation of motion into the matrix equation, and the eigenvalues of the complete system were determined from the associated characteristic equation. To verify the reliability of the presented theory, all numerical results obtained from the ANCM were compared with those obtained from the conventional finite element method (FEM) and good agreement was achieved. Since the order of the property matrices for the equation of motion obtained from the ANCM is much lower than that obtained from the FEM, the CPU time required by the ANCM is much less than that by the FEM.

Calculation of weight functions in single edge notched specimen (SEN시편에서의 무게함수 계산)

  • 안득만
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.15 no.2
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    • pp.604-610
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    • 1991
  • In this paper, the weight functions for the Mode I and Mode II in SEN(single edge notched) specimen are obtained by superposition of the displacement in the singular field of the Buckner type and the displacements by opposite tractions induced by the singular field. The stress intensity factors, $K_{I}$ and $K_{II}$ are calculated by the weight function theory in SEN specimen under the loading equivalent to uniform tension and shear at infinity in Griffith crack. And the results are compared with the exact solutions.s.

Variation of Internal arch Trajectory with Type of Load in RC Beams (RC 보에서 하중형태에 따른 내부아치궤적 변화에 대한 연구)

  • Oh, Se-Wang;Park, Dae-Sung;Kim, Woo
    • Proceedings of the Korea Concrete Institute Conference
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    • 2001.11a
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    • pp.483-488
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    • 2001
  • The RC beams subjected to bending and shear are an important substructure. After flexural cracking, the internal stress state in the beam could not be explained by the classical beam theory. In this study the internal force state factor is introduced to explain the stress state change in the RC beams. The internal force state factor of uniform load was expanded by superposition method using infernal force state factor of point load. As the load types change, the operator that would be calculated the internal force state factor was proposed.

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Quantum-behaved Electromagnetism-like Mechanism Algorithm for Economic Load Dispatch of Power System

  • Zhisheng, Zhang;Wenjie, Gong;Xiaoyan, Duan
    • Journal of Electrical Engineering and Technology
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    • v.10 no.4
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    • pp.1415-1421
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    • 2015
  • This paper presents a new algorithm called Quantum-behaved Electromagnetism-like Mechanism Algorithm which is used to solve economic load dispatch of power system. Electromagnetism-like mechanism algorithm simulates attraction and repulsion mechanism for particles in the electromagnetic field. Every solution is a charged particle, and it move to optimum solution according to certain criteria. Quantum-behaved electromagnetism-like mechanism algorithm merges quantum computing theory with electromagnetism-like mechanism algorithm. Superposition characteristic of quantum methodology can make a single particle present several states, and the characteristic potentially increases population diversity. Probability representation of quantum methodology is to make particle state be presented according to a certain probability. And the quantum rotation gates are used to realize update operation of particles. The algorithm is tested for 13-generator system and 40-generator system, which validates it can effectively solve economic load dispatch problem. Through performance comparison, it is obvious the solution is superior to other optimization algorithm.

A Study on the Optimal Design for DC traction system of Light Rail Transit (경전철 급전시스템의 최적설계에 관한 연구)

  • Jeon, Yong-Joo;Cho, Sung-Joon;Baek, Byung-San;Kim, Kuk-Jin;Kim, Jong-Koo
    • Proceedings of the KIEE Conference
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    • 2001.07b
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    • pp.1251-1253
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    • 2001
  • This paper presents on capacity design of DC-fed-traction system. The system is introduced including a characteristics of train, feeding network configuration, and design method of substation arrangements. Optimal design procedures is described, and program for capacity computation of the system is presented using the nodal equation, K.C.L, K.V.L, Ohm's law and superposition theory. For the proof of the proposed algorithm, we accomplished the simulation of DC traction system for HA-Nam LRT. By considering whole component in DC traction system the conclusion will be much precise.

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A Experimental Study on the Hydroelastic Behavior of Large Floating Offshore Structures (대형부체구조물(大型浮體構造物)의 유(流).탄성(彈性) 연성거동에 관한 실험적 고찰)

  • Lee, Sang-Yeob
    • Journal of Korean Association for Spatial Structures
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    • v.1 no.2 s.2
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    • pp.101-110
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    • 2001
  • A large floating structure is attracting great attention in recent years from the view of ocean space utilization. Its huge scale in the horizontal directions compared with the wavelength and relatively shallow depth make this type of floating structure flexible and its wave-induced motion be characterized by the elastic deformation. In this paper, a boundary integral equation method is proposed to predict the wave-induced dynamic response mat-like floating offshore structure. The structure is modeled as an elastic plate and its elastic deformation is expressed as a superposition of free-vibration modes in air. This makes it straightforward to expand the well-established boundary integral technique for rigid floating bodies to include the hydroelastic effects. In order to validate the theoretical analysis, we compare with the experimental result of reduced model test. Satisfactory agreement is found between theory and experiment.

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Effects of Intramolecular Basis Set Superpositon Error on Conformational Energy Difference of 1,2-Difluoroethane and 1.2-Dimethoxyethane

  • Han, Young-Kyu;Kim, Kyoung-Hoon;Son, Sang-Kil;Lee, Yoon-Sup
    • Bulletin of the Korean Chemical Society
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    • v.23 no.9
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    • pp.1267-1271
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    • 2002
  • The conformation dependences of basis set superposition errors (BSSE) for 1,2-difluoroethane (DFE) and 1,2-dimethoxyethane (DME) molecules have been estimated using counterpoise method at the Moller-Plesset second order perturbation (MP2) level of theory with various basis sets, assuming that all BSSE dependences on conformations are due to the change in CC bond. The BSSE on the energy differences between eclipsed and gauche forms of DFE are in the range of 0.2-1.2 kcal/mol and those between local minima, gauche and anti forms, are less than 0.2 kcal/mol. For the larger DME molecule, the BSSE differences between local minima are still less than 0.4 kcal/mol, but may not be ignored compared to the energy differences of 0.2-3.0 kcal/mol between conformers.

A theoretical study on the hydroelastic behavior of Large floating offshore structures (대형부체구조물(大型浮體構造物)의 유체(流體)·탄성체(彈性體) 연성거동의 이론적 해석에 관한 연구(硏究))

  • Lee, Sang-Yeob;Rha, Young-Ho
    • Journal of the Korean Society of Industry Convergence
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    • v.4 no.4
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    • pp.433-439
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    • 2001
  • A large floating structure is attracting great attention in recent years from the view of ocean space utilization. Its huge scale in the horizontal directions compared with the wavelength and relatively shallow depth make this type of floating structure flexible and its wave-induced motion be characterized by the elastic deformation. In this paper, a boundary integral equation method is proposed to predict the wave-induced dynamic response mat-like floating offshore structure. The structure is modeled as an clastic plate and its elastic deformation is expressed as a superposition of free-vibration modes in air. This makes it straightforward to expand the well-established boundary integral technique for rigid floating bodies to include the hydroelastic effects. In order to validate the theoretical analysis, we compare with the experimental result of previous model test. Satisfactory agreement is found between theory and experiment.

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