Model reduction for nonlinear flutter analysis of panels in supersonic airflow based on mixed-mode spectral submanifolds

High fidelity analysis of nonlinear flutter in supersonic panels with complex configurations generally requires high-dimensional nonlinear dynamical models, whose direct simulation is prohibitively expensive. To reduce computational cost, this paper develops an equation-driven model reduction framework tailored to nonlinear panel flutter. Because the proposed reduction directly operates on the system matrices and nonlinear coefficient tensors of the full-order models (FOMs), a numerically stable finite element discretization is essential. To this end, a nonlinear Hermite-interpolation-based Bogner–Fox–Schmit element (HBE) is developed. By constructing explicit shape functions, the HBE inherently eliminates the numerical instability that traditional bicubic-interpolation-based Bogner–Fox–Schmit elements typically suffer during mesh refinement. Based on the spectral submanifold (SSM) theory, a master spectral subspace selection strategy incorporating both unstable and coupled stable modes is then formulated. The dimensionless dynamic pressure is embedded into an augmented system as a parameter coordinate, yielding a parameter-dependent mixed-mode SSM. The SSM and its reduced dynamics are constructed directly from the finite element governing equations without using FOM trajectories as training data. This framework reduces finite element models with thousands of degrees of freedom (DOFs) to reduced-order models (ROMs) with only a few coordinates while retaining the dominant nonlinear dynamics. Furthermore, since the dynamic pressure parameter is explicitly embedded in the reduced dynamics, highly efficient simulations under varying dynamic pressure conditions can be achieved via a single offline reduction. Finally, numerical examples demonstrate the computational accuracy and efficiency of the proposed framework, and the effects of various stiffening schemes on the critical dynamic pressure and limit cycle oscillation (LCO) amplitude are investigated.