• 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.

• 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.

• Structural Monitoring and Maintenance
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• v.5 no.3
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• pp.417-428
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• 2018

In this paper, various model reduction methods were assessed using a shear frame, plane and space truss structures. Each of the structures is one-dimensional, two-dimensional and three-dimensional, respectively. Three scenarios of poor, better, and the best were considered for each of the structures in which 25%, 40%, and 60% of the total degrees of freedom (DOFs) were measured in each of them, respectively. Natural frequencies of the full and reduced order structures were compared in each of the numerical examples to assess the performance of model reduction methods. Generally, it was found that system equivalent reduction expansion process (SEREP) provides full accuracy in the model reduction in all of the numerical examples and scenarios. Iterated improved reduced system (IIRS) was the second-best, providing acceptable results and lower error in higher modes in comparison to the improved reduced system (IRS) method. Although the Guyan's method has very low levels of accuracy. Structures were classified with the excitation frequency. High-frequency structures compared to low-frequency structures have been poor performance in the model reduction methods (Guyan, IRS, and IIRS).

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.3
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• pp.281-285
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• 2008

Eigenvalue reduction schemes approximate the lower eigenmodes that represent the global behavior of the structures. In the previous study, we proposed a two-level condensation scheme (TLCS) for the construction of a reduced system. And we have improved previous TLCS with combination of the iterated improved reduced system method (IIRS) to increase accuracy of the higher modes intermediate range. In this study, we apply previous improved TLCS to multi-level sub-structuring scheme. In the first step, the global system is recursively partitioned into a hierarchy of sub-domain. In second step, each uncoupled sub-domain is condensed by the improved TLCS. After assembly process of each reduced sub-eigenvalue problem, eigen-solution is calculated by Lanczos method (ARPACK). Finally, Numerical examples demonstrate performance of proposed method.