Parametric study of aeroelastic stability and response of flexible panel in Mach shock reflection

Abstract

This paper presents a parametric study of aeroelastic stability and response of a two-dimensional panel in Mach shock reflection, revealing the effects of shock parameters, static pressure differential, and thermal stress. The analytical model of Mach reflection is established based on the three-shock theory, providing an accurate description of the flowfield with the quasi-one-dimensional flow assumption introduced, which enables the aeroelastic model to reflect the impacts of shock angles. The results indicate that the shock impingement location plays a crucial role in the panel aeroelastic performance, determining the instability form of the panel. The flow acceleration of quasi-one-dimensional flow aggravates the divergence instability but has a limited influence on the flutter instability. The increase in shock angle pushes the sonic throat downstream, limiting the acceleration of the flow above the panel, leading to a smaller post-divergence amplitude but a larger post-flutter amplitude. The exertion of static pressure differential aggravates the divergence instability, but suppresses the flutter instability. Similar to the situation in the supersonic flow without shock impingement, the thermal stress excites complicated nonlinear behaviors in the panel response, featured by the chaotic motions. Additionally, the Lyapunov indirect method is found to be inaccurate when evaluating the impacts of shock impingement location on the stability boundary of panel in Mach reflection.