Finite element analysis of fluttering plates reinforced by flexible beams: An energy-based approach

Aircraft and spacecraft skin can undergo potentially destructive aeroelastic motions in high-speed flight. Reliable mathematical modelling is crucial for understanding such phenomena and aiding aerospace structural design. The panels of real skin structures are normally thin-walled elements riveted to beams and frames that act as stiffeners. In panel flutter literature, however, such stiffening components are normally idealised as perfectly immovable supports or, at best, as linear springs, which restricts the level of information to be obtained from the analyses. Aiming to better understand how the flexibility and mobility of stiffeners affect the aeroelastic behaviour of reinforced panels, the present work employs a more realistic model for skin structures. The Mindlin theory is used for the panel, and the stiffener is modelled as an eccentric Timoshenko beam. Geometrical non-linearity is added to both models, and the supersonic aerodynamic loads are calculated via linear piston theory. The Finite Element Method is employed for spatial discretisation, and an iterative Newmark-type scheme is used for time marching. Differently from what is typically done in the literature, the results are discussed not only from the standpoint of oscillation amplitudes, but also using energy distribution assessment. Solutions have been generated for several flow conditions and stiffener cross-sections. Comparison between the present results and those from a structurally-idealised model has demonstrated that modelling stiffeners as immovable boundaries overestimates flutter onset conditions and underestimates post-flutter amplitudes, thus being an unconservative simplification. Energy distribution analysis has shown that, for reasonably flexible stiffeners, the aeroelastic system can bifurcate and move between two stable limit cycles, one of which displays larger energy levels. Furthermore, it has been shown that the total energy can be unevenly distributed along the structure during flutter, which can be used to determine suitable locations for control devices or energy sinks.