Multistability and global stability analysis of heated viscoelastic panels under supersonic flow

Traditional linear stability theory has inherent limits in predicting the response of nonlinear systems under finite perturbations, which restricts its use in aeroelastic stability analysis of thin panels. To overcome this limitation, this study develops a global dynamics framework based on the composite cell coordinate system method and applies it to heated viscoelastic panels under supersonic flow. The geometric and aerodynamic nonlinearities are described by the von Kármán large deflection theory and third-order piston theory, respectively. Aerodynamic heating is modeled using quasi-steady thermal stress theory, and viscoelastic effects are included using the Kelvin model. The proposed framework can establish a mapping from parameters to global dynamic characteristics, quantify the fractal dimension of the boundaries separating distinct global responses in the parameter domain and enable accurate computation of high-dimensional basins of attraction. The results reveal broad multistability regions in the dynamic pressure and thermal stress parameter domain and show that increasing viscoelastic damping can compress the multistable and chaotic flutter regions and reduce the sensitivity of the panel's complex dynamics to parameter variations. Based on the analysis of basin structures and basin stability, the global stability of panels under different generalized coordinates and parameters is investigated. The results show that panel is found to be more sensitive to perturbations in generalized displacement coordinates. In the transition parameter region, the basin stability of the flat state is substantially lower than that of the buckled states, indicating a higher likelihood of convergence to buckling under random perturbations. These results complement linear stability analyses and support reliability evaluation and design of thin panels under realistic perturbations.