Coherent structures and their influence on the dynamics of aeroelastic panels

TLDR: In this paper, a panel forced by a supersonic unsteady flow is numerically investigated using a finite difference method, a Galerkin approach, and proper orthogonal decomposition (POD).

Abstract: A panel forced by a supersonic unsteady flow is numerically investigated using a finite difference method, a Galerkin approach, and proper orthogonal decomposition (POD). The aeroelastic model investigated is based on piston theory for modeling the flow-induced forces, and von Karman plate theory for modeling the panel. Structural non-linearity is considered, and it is due to the non-linear coupling between bending and stretching. Several novel facets of behavior are explored, and key aspects of using a Galerkin method for modeling the dynamics of the panel exhibiting limit cycle oscillations and chaos are investigated. It is shown that multiple limit cycles may co-exist, and they are both symmetric and asymmetric. Furthermore, the level of spatial coherence in the dynamics is estimated by means of POD. Reduced order models for the dynamics are constructed. The sensitivity to initial conditions of the non-linear aeroelastic system in the chaotic regime limits the capability of the reduced order models to identically model the time histories of the system. However, various global characteristics of the dynamics, such as the main attractor governing the dynamics, are accurately predicted by the reduced order models. For the case of limit cycle oscillations and stable buckling, the reduced order models are shown to be accurate and robust to parameter variations.