Model Order Reduction of Viscously Damped Vibration Systems Using Accelerated Iterative Dynamic Condensation

[+] Author and Article Information
Zu-Qing Qu

 Michelin America R&D Corporation, 515 Michelin Road, Greenville, SC 29605zuqing.qu@us.michelin.comDepartment of Civil Engineering, University of Arkansas, 4190 Bell Engineering Center, Fayetteville, AR 72701zuqing.qu@us.michelin.com

Panneer Selvam

 Michelin America R&D Corporation, 515 Michelin Road, Greenville, SC 29605rps@engr.uark.eduDepartment of Civil Engineering, University of Arkansas, 4190 Bell Engineering Center, Fayetteville, AR 72701rps@engr.uark.edu

J. Appl. Mech 72(5), 761-771 (May 23, 2005) (11 pages) doi:10.1115/1.1993668 History: Received May 23, 2003; Revised May 23, 2005

An accelerated iterative dynamic condensation method for the model order reduction of vibration systems with viscous damping is proposed. A group of governing equations for dynamic condensation matrix are derived from the eigenvalue equations defined in the state space. Two iterative schemes for solving these governing equations are provided. Based on different state space formulations, two more groups of governing equations are developed. A comparison of the present method with three iterative approaches proposed recently is provided. The present approach is implemented into two practical vibration systems, a tall building with one tuned mass damper and a floating raft isolation system. The results show that the proposed method has much higher accuracy than the other three approaches while the computational effort is almost the same.

Copyright © 2005 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Comparison of relative errors of damped frequencies: (a) sixth damped frequency; (b) seventh damped frequency; (c) eighth damped frequency; (d) ninth damped frequency; and (e) tenth damped frequency

Grahic Jump Location
Figure 2

Comparison of relative errors of damping ratios: (a) sixth damping ratio; (b) seventh damping ratio; (c) eighth damping ratio; (d) ninth damping ratio; and (e) tenth damping ratio



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