Supersonic meta-plate with tunable-stiffness nonlinear oscillators for nonlinear flutter suppression

A meta-plate structure featuring periodic tunable-stiffness nonlinear oscillators (NLOs) are proposed for nonlinear vibration and flutter suppressions. The tunable nonlinear stiffness of NLOs can be realized through a pair of linear tension or compression springs. Using the first-order shear deformation theory and supersonic piston aerodynamic theory, the governing equations of a supersonic meta-plate integrated with NLOs are derived by using the Hamilton principle, in which the geometrical nonlinearity of the plate is considered based on von Karman large deformation theory. The semi-analytical solutions of the amplitude-dependent bandgap are developed by modal analysis approach for assessing the bandgap behavior of the meta-plate. The numerical simulations show that the present meta-plate exhibits the tunable-bandgap characteristic by adjusting the pre-compression/-tension ratio of the NLO springs, which can be effectively used for low-frequency broadband vibration attenuation. In particular, the vibration energy of the primary plate is continuously transferred to the NLOs by internal resonant capture in the bandgap range and then dissipated. Furthermore, the comparison of bifurcation diagrams shows that the meta-plate behaves excellent suppression performance with a substantial amplitude reduction of up to 96.1% in the entire post-flutter region. It is found that the broadband energy transmission of the meta-plate for performance enhancement of nonlinear flutter suppression can be achieved by properly tailoring the NLO parameters, i.e., spring stiffness, pre-compression/-tension ratio and mass ratio. The complex nonlinear responses including chaotic motion with extremely small amplitude are also induced. The present work demonstrates that the tunable-stiffness-NLOs-based metamaterial design can provide a novel and effective approach for nonlinear vibration and flutter suppression of supersonic plate.