• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.2 s.257
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• pp.211-220
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• 2007

This work presents an iterated improved reduced system (IIRS) procedure combined with sub-structuring scheme for large structures. Iterated IRS methods are usually more efficient than others because the dynamic condensation matrix is updated repeatedly until the desired convergent values are obtained. However, using these methods simply for large structures causes expensive computational cost and even makes analyses intractable because of the limited computer storage. Therefore, the application of sub-structuring scheme is necessary. Because the large structures are subdivided into several (or more) sub-domains, the construction of dynamic condensation matrix does not require much computation cost in every iteration. This makes the present method much more efficient to compute the eigenpairs both in lower and intermediate modes. In Part I, iterated IRS method combined with sub-structuring scheme for undamped structures is presented. The validation of the proposed method and the evaluation of computational efficiency are demonstrated through the numerical examples.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.04a
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• pp.57-64
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• 1994

The purpose of this paper is to find minimum surface shape of pneumatic structure using the finite element method. The pneumatic membrane structure is a kind of large deformation problem and very flexible composite material, which mean geomatric nonlinearity. It is not to resist for compression and resultant moment. As the displacement due to internal pressure is getting bigger, it should be considered the direction of forces. It becomes non-linear problem with the non-conservative force. The follower-force depends on the deformation and the direction of force is normal to each element. The solution process is obtained the new stiffness matrix (load correction matrix) depending on deformation through each iterated step. However, the stiffness matrix have not the symmetry and influence on the time of covergence. So in this paper Newton-Rhapson method for solving non-linear problem and for using symmetic matrix, the load direction is changed in each iterated step using the transformation matrix.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.37-45
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• 2024

The aim of this article is to consider the sequences generated by repeatedly performing matrix multiplication operations, define the stable, amicable pair, sociable matrix sequences, and analyze the results obtained through iteration. Lastly, numbers are changed to colors to make them easier to understand.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.2 s.257
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• pp.221-230
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• 2007

An iterated improved reduced system (IIRS) procedure combined with sub-structuring scheme for nonclassically damped structural systems is presented. For dynamic analysis of such systems, complex eigenproperties are required to incorporate properly the nonclassical damping effect. In complex structural systems, the equations of motion are written in the state space from. Thus, the number of degrees of freedom of the new equations of motion and the size of the associated eigenvalue problem required to obtain the complex eigenvalues and eigenvectors are doubled. Iterated IRS method is an efficient reduction technique because the eigenproperties obtained in each iteration step improve the condensation matrix in the next iteration step. However, although this reduction technique reduces the size of problem drastically, it is not efficient to apply this technique to a single domain finite element model with degrees of freedom over several thousands. Therefore, for a practical application of the reduction method, accompanying sub-structuring scheme is necessary. In the present study, iterated IRS method combined with sub-structuring scheme for nonclssically damped structures is developed. Numerical examples demonstrate the convergence and the efficiency of a newly developed scheme.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.41-60
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• 2000

In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author's work. concerning parameter identification of linear dynamic stochastic system. Special attention is given of searching the solution of an equation in a neighbourhood of some initial approximation. The offered approaches and algorithms allow us to receive fast and quite exact solution. We give some recommendations for application of given algorithms.

• Honam Mathematical Journal
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• v.32 no.3
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• pp.493-514
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• 2010

The resultant and discriminant of composite polynomials were studied by McKay and Wang using some algebraic properties. In this paper we study the resultant and discriminant of iterate polynomials. We shall use elementary computations of matrices and block matrix determinants; this could provide not only the values but also the visual structure of resultant and discriminant from elementary matrix calculation.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.36 no.4
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• pp.77-83
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• 2013

This study is to develop a mathematical analysis model to grasp the behaviors of cartels. Cartels are formed tacitly and cause tremendous damage to consumers in modern society which is composed of advanced industry structure. The government authorities have instituted the leniency programs to respond cartels. However, cartels will continue unless there are legal sanctions against cartels based on an accurate analysis of leniency programs. The proposed cartel equilibrium analysis model is a mathematical behavior model which is based on the existing methods and the prison's dilemma of game theory. Therefore, the model has a form of pay off matrix of two players. We use a iterated polymatrix approximation (IPA) method to deduct a Nash equilibrium point. The model is validated by an empirical analysis as well.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.389-405
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• 2022

We study the Fisher Information (FI) of m-generalized order statistics (m-GOSs) and their concomitants about the shape-parameter vector of the Iterated Farlie-Gumbel-Morgenstern (IFGM) bivariate distribution. We carry out a computational study and show how the FI matrix (FIM) helps in finding information contained in singly or multiply censored bivariate samples from the IFGM. We also run numerical computations about the FIM for the sub-models of order statistics (OSs) and sequential order statistics (SOSs). We evaluate FI about the mean and the shape-parameter of exponential and power distributions, respectively. Finally, we investigate the Kullback-Leibler distance in concomitants of m-GOSs.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.4
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• pp.904-921
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• 2014

The main objective of this paper is to propose a new Finite Element (FE) model updating technique for damped beam structures. The present method consists of a FE model updating, a Degree of Freedom (DOF) reduction method and a damping matrix identification method. In order to accomplish the goal of this study, first, a sensitivity-based FE model updating method using the natural frequencies and the zero frequencies is introduced. Second, an Iterated Improved Reduced System (IIRS) technique is employed to reduce the number of DOF of FE model. Third, a damping matrix is estimated using modal damping ratios identified by a curve-fitting method and modified matrices which are obtained through the model updating and the DOF reduction. The proposed FE model updating method is verified using a real cantilever beam attached damping material on one side. The updated result shows that the proposed method can lead to accurate model updating of damped structures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.10a
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• pp.821-832
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• 2011

Recently, the noise of vehicle is the one of the key factors for customers to purchase a vehicle and the most important part which is related to the noise is the exhaust system. Thus, car makers have their own ways to assess this exhaust noise not only to decrease the level of noise but to enhance the feeling of it. Typically, to do these things in the early stage of development, the tuning code of the exhaust system has to be made by CAE tool, which is very reliable but expensive, and the prototype parts of this code would be made for the validation test. Then this process can be iterated to meet the target of the performance. In this study, a new algorithm which adapts the '3 dimensional convective sound wave theory 'and 'Doppler effect' has been developed. With this new algorithm, a brand new system for the calculation of tail pipe noise has been developed and validated by acoustic wind tunnel test. As a result of this study, various comparisons and have been carried out, for example, the comparison with other CAE tool has been performed for the validity and the improvement of the new calculation code could be achieved.