Nonlinear finite-element analysis of a two-dimensional panel oscillating in supersonic flow

In this study, the total Lagrangian formulation (TLF) is implemented in a finite-element structural solver to analyze the panel flutter problem, which involves large structural deformations. To accurately compute the aerodynamic loads acting on the panel while considering the panel’s deformations, the structural solver is coupled with a finite-element computational fluid dynamics (CFD) solver, which adopts the arbitrary Lagrangian–Eulerian (ALE) formulation to solve the unsteady Euler equations. The coupled solver is then applied to analyze the flutter behavior of a panel in the supersonic flow regime. Finally, the results are compared with those reported in the literature, which rely on the von Karman nonlinear theory based on the small strain assumption, as well as other studies using the TLF within a finite-volume framework. This study demonstrates that the panel undergoes limit-cycle oscillations (LCOs), with generally good agreement between the findings of this study and the existing literature in predicting the amplitude and frequency of the LCOs. However, discrepancies in amplitude are observed between the current results and those obtained using von Kármán theory, with increasing divergence as the amplitudes approach the panel thickness. In addition, for the case of a free-stream Mach number of 1.8, results obtained using the TLF method within a finite-volume framework indicate that the panel oscillates in higher modes (seventh mode). In contrast, both this study, employing TLF within a finite-element framework, and those employing von Kármán theory predict oscillation as a combination of the first and second modes. These findings highlight the need for further investigation, particularly with experimental results, which could provide valuable insights into the actual behavior of the panel under such conditions.