Theoretical modelling and design of metamaterial stiffened plate for vibration suppression and supersonic flutter

In the study, we propose a theoretical model of a metamaterial stiffened plate with multiple cantilever beam resonators (CBRs) for the vibration suppression and supersonic flutter analysis. Based on the first-order shear deformation theory and supersonic piston aerodynamic theory, the governing equations of metamaterial stiffened plate with various arrangements of stiffeners are derived through Hamilton principle. The vibration and supersonic flutter behaviors are carried out, which are validated well by comparing with the finite element results. It is shown that the multiple-resonant CBRs can be utilized to suppress the broadband vibration of multiple modes, and improve the aeroelastic behaviors of the metamaterial stiffened plate, since the existence of multiple CBRs can affect the coupled modes of the system flutter. In particular, the flutter boundary of the system can be significantly enhanced when the designed frequencies of CBRs are near the flutter frequency of the original aeroelastic system, which reveals the flutter suppression mechanism of the present metamaterial stiffened plate. The present work demonstrates that the proposed multiple-CBRs-stiffened-based design with excellent mechanical properties (including load-bearing capacity, broadband vibration suppression and aeroelastic stability) can provide some insights and potential application of metamaterial structures for vibration and flutter controls of the supersonic plate.