Prediction of nonlinear panel response using proper orthogonal decomposition

Abstract

Boundaries of limit-cycle oscillation onset are computed using proper orthogonal decomposition for a nonlinear panel in supersonic flow. The governing structural dynamics equation is the large-deflection, nonlinear, von Karman equation for a pinned panel, and the governing flow equations are the Euler equations. Onset of limit-cycle oscillation is accurately and efficiently predicted with bifurcation analysis, as applied to a coupled set of reduced-order aerodynamic and structural dynamics equations. Nonlinear responses of panels away from critical onset conditions are obtained from reduced-order, time-domain, aeroelastic analyses and shown to compare well with published data. Static bifurcations in the transonic regime are also accurately predicted with reduced-order aeroelastic models. At Mach 0.95, an interesting array of nonlinear behaviors is found to occur over a range of scaled dynamic pressures, including limit-cycle oscillations, pitchfork bifurcation, and limit-point singularity. This paper describes a framework by which reduced-order models can be constructed and then applied to the rapid prediction of static and Hopf bifurcations in aeroelastic systems.