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Shock and Vibration
Volume 19 (2012), Issue 5, Pages 1135-1142
http://dx.doi.org/10.3233/SAV-2012-0718

Receptance-Based Partial Pole Assignment for Asymmetric Systems Using State-Feedback

M. Ghandchi Tehrani1 and H. Ouyang2

1Institute of Sound and Vibration Research, University of Southampton, Highfield, Southampton, UK
2School of Engineering, University of Liverpool, The Quadrangle, Liverpool, UK

Received 25 April 2012; Accepted 25 April 2012

Copyright © 2012 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Many structures or machines interact with some internal nonconservative forces and present asymmetric systems in which the stiffness and damping matrices are asymmetric. Examples include friction-induced vibration and aeroelastic flutter. Asymmetric systems are prone to flutter instability as a result of the real parts of some poles becoming positive when certain system parameters vary.

This paper presents a receptance-based inverse method for assigning a number of complex poles of second-order damped asymmetric systems while keeping other unassigned poles unchanged. It uses state-feedback (active damping and active stiffness) to shift the poles to desired locations where all poles have negative real parts. Receptances at only a small, limited number of degrees-of-freedom of the underlying symmetric system are required. Simulated numerical examples indicate that this is an effective method and is capable of assigning negative real parts to unstable poles to stabilise an otherwise unstable second-order dynamic system.