Theoretical analysis for the effect of static pressure differential on aeroelastic stability of flexible panel

The static pressure differentials have been neglected in almost all of theoretical analysis models for panel flutter in the supersonic flow, which are established on the basis of the classic aeroelastic model by Dowell in 1966. However, in actual engineering, flexible panels are still subjected to the static pressure differentials under some circumstances. By using the numerical methods, Dowell et al. found that the static pressure differentials as small as 10⁻² psi may significantly alter the flutter boundary. In this paper, a novel strategy for a theoretical analysis model is proposed to study the effect of static pressure differential on aeroelastic stability of flexible panel in the supersonic airflow. We regard the final total displacement of the panel as the superposition of dynamic displacement and static deformation, which is in accord with the actual situation of physicality. The static deformation is obtained by solving the static aeroelastic equation. Using the curve/surface fitting method, the static deformations are described by two approaches with/without considering the interaction between the static deformation and steady aerodynamic loads. And then the static deformation is introduced into the dynamic aeroelastic equations in the form of the stiffness through the nonlinear induced loading. The dynamic aeroelastic equation is solved by using the Galerkin discrete method, which can truncate the partial differential equations into a set of ordinary equations. Lyapunov indirect method is utilized to evaluate the aeroelastic stability of the flexible panel. According to the known expression of static deformation and Routh-Hurwitz criterion, a theoretical solution for the aeroelastic stability boundary under the action of the arbitrary static pressure differentials is derived. The theoretical results show that (1) The static pressure differential can significantly enhance the aeroelastic stability of the flexible panel, which is consistent with the numerical results. (2) Whether the actual coupling between the static deformation and aerodynamic loads is considered or not, the stability boundaries obtained are quite different. (3) The increase of the stiffness of structure induced by the static deformation can increase the critical flutter dynamic pressures, but it is not the dominant factor to lead to such a remarkable improvement of the stability of the flexible panel under the action of the static pressure differential. The actual coupling between the static deformation and aerodynamic loads plays a significant role in substantially improving the aeroelastic stability of the flexible panel.