On the effects of structural coupling on the supersonic flutter and limit cycle oscillations of transversely reinforced panels

Panel flutter is an aeroelastic phenomenon that can critically affect aircraft skin in supersonic flight. The majority of works published on this subject treat each skin panel as an isolated structural element. In reality, however, aircraft skin is usually built as large panels stiffened by stringers and frames. Thus, the multiple subpanels sitting between stiffeners are structurally coupled rather than isolated, and therefore can interact during flutter. In the present work, a reinforced panel is simulated as a rectangular plate reinforced by an elastic beam that “subdivides” the panel into two square subpanels (bays). The panel is modeled as a Mindlin-vonKarman plate, and the stiffener as a nonlinear eccentric Timoshenko beam. The problem is discretized through the Finite Element Method, and the resulting nonlinear equations of motion are solved via numerical time-marching. This approach is a higher-fidelity extension to the methodology employed by the authors in previous works, where the stiffeners were idealized as immovable simple supports - the so-called multibay model. The present results are compared to those from both the multibay model and the single-panel model. Each bay in the stiffened panel is identical to the reference single panel. Results are produced for several stiffener cross-sectional aspect ratios, r. Linear flutter boundary results show that, as r increases, the critical dynamic pressure asymptotically approaches that of a single panel. Nonlinear post-flutter analyses reveal the occurrence of jump discontinuities in the limit cycle amplitude diagrams. Similarly to what has been seen in the literature for multibay panels, the jumps are related to the nonlinear structural coupling between neighboring bays, and occur when there is a shift in the flutter mechanism. Furthermore, it is shown that reducing the cross-sectional aspect ratio postpones not only the onset of flutter but also the jumps, which can be avoided for sufficiently small r. Important engineering design guidelines can be established from the present study, as the multibay and single-panel models are shown to be generally conservative regarding linear behavior, but potentially unsafe in the post-flutter regime.