Two-Stage Assumed Mode Method for Flutter Analysis of Supersonic Panels with Elastic Supports and Attached Masses

During the service life of a supersonic aircraft, panels are susceptible to damaged boundary supports and unexpected attached masses, which can critically alter their flutter characteristics. This paper proposes a novel two-stage assumed mode method to efficiently analyze the modal properties and expanded flutter envelopes of such compromised structures. In the first stage, the bending modes of a Euler–Bernoulli beam under elastic supports in two orthogonal directions are combined to construct the assumed modes of the intact panel, forming a modal matrix that satisfies geometric boundary conditions and establishing the baseline dynamic model. In the second stage, the method is reapplied to derive the generalized eigenvalue problem for the panel with attached masses, accurately capturing the modified mode shapes and frequencies. Subsequently, based on the principle of virtual work and first-order piston theory, the generalized aerodynamic forces are formulated. These are then incorporated into the flutter equations, which are solved in the frequency domain using the p-k method. The results demonstrate that elastic supports generally lower flutter velocities and frequencies. However, an interesting finding is that a centrally attached mass of 0.03 kg (≈10% of the panel mass) can increase the flutter speed by about 10%, whereas the same mass placed off-center may reduce it by roughly 2%. Furthermore, the proposed 9-point damper layout is shown to raise the flutter speed of an elastically supported panel with an off-center mass by up to 18% and the flutter frequency by over 13%, thereby recovering and even exceeding the design flutter boundary.