On the aeroelastic bifurcation of a flexible panel subjected to cavity pressure and inviscid oblique shock

The aeroelasticity of a panel in the presence of a shock is a fundamental issue of great significance in the development of hypersonic vehicles. In practical engineering, cavity pressure emerges as a crucial factor that influences the nonlinear dynamical characteristics of the panel. This study focuses on the aeroelastic bifurcation of a flexible panel subjected to both cavity pressure and oblique shock. To this end, a computational method is devised, coupling a high-fidelity reduced-order model for unsteady aerodynamic loads with nonlinear structural equations. The solution is meticulously tracked by continuous calculations. The obtained results indicate that cavity pressure plays a pivotal role in determining the bifurcation and stability characteristics of the system. First, the system exhibits hysteresis behaviour in response to the ascending and descending dynamic pressures. The evolution of hysteresis behaviour originates from the phenomenon of cusp catastrophe. Second, variations in cavity pressure induce three types of bifurcation phenomena, exhibiting characteristics akin to supercritical Hopf bifurcation, subcritical Hopf bifurcation and saddle-node bifurcation of cycles. The system's response at the critical points of these bifurcations manifests as long-period asymptotic flutter or explosive flutter. Lastly, the evolution of the dynamical system among these three types of bifurcations is an important factor contributing to the discrepancies observed in certain research results. This study enhances the understanding of the nonlinear dynamical behaviour of panel aeroelasticity in complex practical environments and provides new explanations for the discrepancies observed in certain research results.