• Structural Engineering and Mechanics
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• v.30 no.5
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• pp.603-617
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• 2008

Three dimensional coupled bending-torsion dynamic vibrations of thin-walled open section beam subjected to moving vehicle are investigated by transfer matrix method. Through adopting the idea of Newmark-${\beta}$ method, the partial differential equations of structural vibration can be transformed to the differential equations. Then, those differential equations are solved by transfer matrix method. An iterative scheme is proposed to deal with the coupled bending-torsion terms in the governing vibration equations. The accuracy of the presented method is verified through two numerical examples. Finally, with different eccentricities of vehicle, the torsional vibration of thin-walled open section beam and vertical and rolling vibration of truck body are investigated. It can be concluded from the numerical results that the torsional vibration of beam and rolling vibration of vehicle increase with the eccentricity of vehicle. Moreover, it can be observed that the torsional vibration of thin-walled open section beam may have a significant nonlinear influence on vertical vibration of truck body.

• International Journal of Control, Automation, and Systems
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• v.3 no.2
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• pp.159-165
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• 2005

This paper designs observers for matrix second-order linear systems on the basis of generalized eigenstructure assignment via unified parametric approach. It is shown that the problem is closely related with a type of so-called generalized matrix second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass system is utilized to show the effect of the proposed approaches.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.7
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• pp.739-748
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• 1992

A CGM iterative systolic algorithm to solve large sparse linear systems of equations is presented. For implementation of the algorithm, a systolic array using the stripe structure is proposed. The matrix A is decomposed into a strictly lower triangular matrix, a diagonal matrix, and a strictly up-per triangular matrix, and the two formers and the tatter· are concurrently computed by different linear arrays. Hence, the execution time of this approach Is reduced to half of the execution time of the that a linear array is used. computation of the Irregularly distributed sparse matrix can be executed effectively by using the stripe structure.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.774-781
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• 2006

This paper presents a study on the analytical prediction of vibration transmission from helical gears to the bearing. The proposed method is based on the application of the three dimensional helical gear behaviors and complete description of shaft by the spectral method. Helical gear system used in this paper consists of the driving element, helical gears, shafts, bearings, couplings and load element. In order to describe all translation and rotation motion of helical gears twelve degree of freedom equations of motion by the transmission error excitation are derived. Using these equations, transfer matrix for the helical gear is derived. For the detail behavior of shaft motion, the $12{\times}12$ transfer matrix for the shaft is derived. Transfer matrix for the bearing, coupling, driving element, and load is also derived. Application of the boundary conditions in the assembled transfer matrix produces the forces and displacements in each element of the helical gear system. The effect of the proposed method is shown by numerical example.

• Journal of the Korean Chemical Society
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• v.16 no.6
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• pp.349-353
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• 1972

The Faddeev-type equations for systems of more than four particles are derived from Weinberg's equation. The derivation is considerably simpler than that by others. The Faddeev-type equations thus derived can be expressed in a matrix form and the rules for constructing the inhomogeneous term and the matrix kernel of the matrix integral equation are formulated and verified explicitly for N=3, 4, and 5.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.4
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• pp.455-459
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• 1986

A large set of linear equations which arise in many applications, such as in digital signal processing, image filtering, estimation theory, numerical analysis, etc. involve the problem of a tridiagonal matrix. In this paper, the determinant, eigenvalue and inverse matrix of a tridiagoanl matrix are analytically evaluated.

• Korean Journal of Computational Design and Engineering
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• v.15 no.6
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• pp.411-417
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• 2010

In this paper, the boom of a floating crane is modeled as a 3-dimensional elastic beam in order to analyze the dynamic response of the crane and its cargo. The boom is divided into more than two elements based on finite element formulation, and deformation of each element is expressed in terms of shape matrix and nodal coordinates. The equations of motion for the elastic boom consist of a mass matrix, a stiffness matrix, and a quadratic velocity vector that contains the gyroscopic and Coriolis forces. The size and complicity of the matrices increase in proportion with the number of elements. Therefore, it is not possible to derive the equations of motion explicitly for different number of elements. To overcome this difficulty, matrices for one 3-dimensional element are expressed with elementary sub-matrices. In particular, the quadratic velocity vector is derived as a product of a shape matrix and a 3-dimensional rotation matrix. By using the derived matrices, the equations of motion for the multi-element boom are automatically constructed. To verify the implementation of the elastic boom based on finite element formulation, we simulated a simple vibration of the elastic boom and compared the average deformation with the analytic solution. Finally, heave motion of the floating crane and surge motion of the cargo are presented as application examples of the elastic boom.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.3
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• pp.169-176
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• 1998

A method for the dynamic analysis of multibody systems undertaking impulsive force is introduced in this paper. A partial velocity matrix based on Kane's method is introduced to reduce the number of equations to be solved. Only minimum number of equations of motion can be obtained by using the partial velocity matrix. This reduces the computational effort significantly to obtain the dynamic response of the system. At the very moment of the impulse, instead of using the numerical integrator to solve the equations of motion, the impulse and momentum principle is used to obtain the dynamic response. The impulse as wall as the reaction force acting on the kinematic joints can easily calculated too.

• The Journal of the Korean dental association
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• v.54 no.11
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• pp.850-864
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• 2016

The Generalized Estimating Equations (GEE) approach is a widely used statistical method for analyzing longitudinal data and clustered data in clinical studies. In dentistry, due to multiple outcomes obtained from one patient, the outcomes produced from an individual patient are correlated with one another. This study focused on the basic ideas of GEE and introduced the types of covariance matrix and working correlation matrix. The quasi-likelihood information criterion (QIC) and quasi-likelihood information criterion approximation ($QIC_u$) were used to select the best working correlation matrix and the best fitting model for the correlated outcomes. The purpose of this study is to show a detailed process for the GEE analysis using SPSS software along with an orthodontic miniscrew example, and to help understand how to use GEE analysis in dental research.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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• pp.2483-2490
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• 1993

This paper presents a systematic formulation for the kinematic and dynamic analysis of flexible multibody systems. The system equations of motion are derived in terms of relative and elastic coordinates using velocity transformation technique. The position transformation equations that relate the relative and elastic coordinates to the Cartesian coordinates for the two contiguous flexible bodies are derived. The velocity transformation matrix is derived systematically corresponding to the type of kinematic joints connecting the bodies and system path matrix. This matrix is employed to represent the equations of motion in relative coordinate space. Two examples are taken to test the method developed here.