Random aeroelastic vibration of nonlinear metamaterial supersonic plates

High-speed aircraft generally endure complex and random vibration environments, thus mitigating random vibrations in the wing is critical to ensuring flight safety. Nonlinear acoustic metamaterials (NAM) provide efficient ways for structural vibration reduction. This paper investigates the random aeroelastic vibration of a supersonic NAM wing plate, which has never been studied. Based on a theoretical model combining mode superposition and modified third-order piston theory, extensive numerical simulations and statistical analyses are performed to show the aeroelastic properties of pure plate, linear and nonlinear metamaterial plates. The results indicate that, under broadband random excitation, the mean value, standard deviation, and maximum peak value of the time-domain displacement and velocity responses of the NAM plate are significantly reduced by >50 %, demonstrating superior vibration reduction capabilities compared to the linear metamaterial plate. The parameter analysis reveals the influence regularities of aerodynamic and structural parameters on the random vibration reduction properties of the NAM plate. Furthermore, we design the NAM plate composed of double frequency resonators, which exhibits superior reduction effects on broadband random vibration under low damping condition. This research provides valuable insight into the aeroelastic vibration control of supersonic wings in complex aerodynamic environments, and promotes the application of strongly nonlinear metamaterials.