Theoretical modeling and mechanism analysis of nonlinear metastructure for supersonic aeroelastic suppression

Nonlinear metastructures with unique mechanical properties provide potential application in broadband suppression of aeroelastic vibration; however, it is challenging to reveal the intrinsic correlation mechanism between nonlinear bandgap and aeroelastic vibration. In this study, a nonlinear metastructure with net-type nonlinear resonators (NNR) is proposed for both vibration suppression and aeroelastic performance enhancement of the wing-plate in the supersonic flow. The net-type nonlinear metastructure wing-plate is composed of a cantilever stiffened plate and multiple net-type mass-spring systems. The nonlinear stiffness of NNRs can be designed by tuning four pre-tension springs for realizing significant nonlinear effect. The cantilevered wing-like plate with various arrangements of stiffeners is modeled based on the first-order shear deformation theory. The governing equations of the nonlinear metastructure wing-plate in the supersonic flow are derived through Hamilton's principle, and the aerodynamic model are obtained by using supersonic piston aerodynamic theory. The energy transfer mechanism is firstly explored by a simplified 2-DOF nonlinear system and contributes to the design of three-dimensional (3D) nonlinear metastructure. Numerical simulations show that the present nonlinear metastructure wing-plate can be effectively used for low-frequency broadband vibration attenuation by recurrent transient resonance capture. The prototype is fabricated and the experiments are carried out to show excellent broadband vibration suppression. The supersonic aeroelastic analysis shows that the designed nonlinear metastructure wing-plate with low-additional-mass NNRs can significantly enhance the flutter boundary and suppress the post-flutter aeroelastic vibration, with an improvement of over 14% in aeroelastic stability. Especially, the flutter coupling mechanism of nonlinear metastructure and the suppression mechanism of post-flutter aeroelastic response caused by nonlinear effect of NNRs are clarified in detail. The present work demonstrates that the net-type nonlinear metastructure can provide a novel and effective approach for aeroelastic vibration suppression of supersonic wing.