www.elsevier.nl/locate/jnlabr/yjfls Journal of Fluids and Structures 19 (2004) 575–590 Reduced-order modelling of limit-cycle oscillation for aeroelastic systems $ P.S. Beran a, *, D.J. Lucia b , C.L. Pettit a a Multidisciplinary Technologies Center, Air Vehicles Directorate, AFRL/VASD, Building 146, 2210 Eighth Street, WPAFB, OH 45433, USA b Structures Division, Air Vehicles Directorate, AFRL/VAS, Building 45, 2130 Eighth Street, WPAFB, OH 45433, USA Received 23 September 2003; accepted 19 January 2004 Abstract Limit-cycle oscillations (LCOs) of a nonlinear panel in supersonic flow are computed using a reduced-order aeroelastic model. Panel dynamics are governed by the large-deflection, nonlinear, von Ka´rma´n equation as expressed in low-order form through a Galerkin approximation. The aerodynamics are described by the Euler equations, which are reduced in order using proper orthogonal decomposition. The coupled system of equations is implicitly time integrated with second-order temporal accuracy to predict LCO amplitude, and linearly analyzed to predict LCO onset. The fluid is synchronized with the structure in time through subiteration, using only 18 dof to describe the aeroelastic system. The Jacobian employed in the fully implicit analysis is of equivalently low rank, enabling rapid analysis. Using the reduced-order model, LCO onset is predicted directly at a computational cost of approximately 400 time steps with a high accuracy verified by full-order analysis. Published by Elsevier Ltd. 1. Introduction Over the last several years, Karhunen–Loe`ve (K–L) analysis, or proper orthogonal decomposition (POD), has been used to accelerate greatly the time integration of aeroelastic configurations by reducing system order (Romanowski, 1996; Hall et al., 2000; Thomas et al., 2001). While the application of POD to aeroelastic systems has been primarily limited to linearized aerodynamic analysis, these studies show the tremendous potential of POD-based reduced-order models (ROMs) for the economical stability analysis of aeroelastic configurations. POD-based ROMs have also been applied in different forms to problems in many disciplines. Noteworthy achievements with POD-based ROMs include: the development of control models for unsteady flow (Park and Lee, 1998; Rediniotis et al., 1999), airfoil shape optimization (LeGresley and Alonso, 2000, 2001), Euler analysis of unsteady flows driven by structural vibration (Pettit and Beran, 2000), and the study of nonlinear oscillations in flexible panels (Mortara and Beran, 2000). A review of relevant work is given by Beran and Silva, 2001. The determination of aeroelastic behavior in the transonic regime is an especially demanding problem owing to the capture of essential nonlinearities in the aerodynamics. System nonlinearities, which may include structural nonlinearities, also play a key role in the aeroelastic phenomenon of limit-cycle oscillation (LCO) (Dobbs et al., 1985; ARTICLE IN PRESS $ The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air Force, the Department of Defense, or the US Government. *Corresponding author. E-mail address: philip.beran@wpafb.af.mil (P.S. Beran). 0889-9746/$-see front matter Published by Elsevier Ltd. doi:10.1016/j.jfluidstructs.2004.04.002