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Technical Briefs

Model-Order Reduction by Simultaneous Realization of Eigenvalues and Mode Shapes (SREM)

[+] Author and Article Information
Fariborz Fariborzi

Mechanical Engineering Department,  Shahrood University of Technology, Semnan 3619995161, Iranbfariborzi@yahoo.com

Ramin Bighamian1

Department of Mechanical Engineering,  Isfahan University of Technology, Isfahan 8415683111, Iranr.bighamian@me.iut.ac.ir

Hamid Reza Mirdamadi

Department of Mechanical Engineering,  Isfahan University of Technology, Isfahan 8415683111, Iranhrmirdamadi@cc.iut.ac.ir

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(1), 014502 (Dec 05, 2011) (5 pages) doi:10.1115/1.4004573 History: Revised January 03, 2010; Received June 15, 2010; Accepted March 01, 2011; Published December 05, 2011; Online December 05, 2011

In this paper, a unique technique “cost function” has been presented to simultaneously realize eigenvalues and mode shape vectors to attain a reduced model. Differential evolution algorithm has been utilized in order to numerically optimize the nonlinear cost function instead of the least squares solution of the characteristic equation of the system. The modal matrix is reduced by effective independence distribution vector (EIDV) method to remove the slave degrees of freedom and retain the master ones which have the most contribution in the system response. EIDV retains those degrees of freedom (DOFs) in such a way as to reserve the system information content, as much as possible. This procedure has been verified with some examples and good results have been obtained. It is shown that the algorithm has several advantages, e.g., the coupling between selected modes of full-order model will be attained to guarantee the stability of closed-loop system.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

A 4-DOF proportional damped system

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Figure 2

Computational time-cost for optimization

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Figure 3

A 16-DOF proportional damped truss system

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Figure 4

Comparison between the full-model, SEREP, and SREM FRFs

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Figure 5

Comparison between the full-model, modal truncation, and SREM FRFs

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