Affiliations: Institute of Sound and Vibration Research, University
of Southampton, Highfield, Southampton, UK | School of Engineering, University of Liverpool, The
Quadrangle, Liverpool, UK
Note: [] Corresponding author: H. Ouyang, School of Engineering,
University of Liverpool, The Quadrangle, Liverpool L69 3GH, UK. E-mail:
[email protected]
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.
Keywords: Partial pole assignment, asymmetric system, friction-induced vibration, flutter instability, receptance, state feedback
