Nonlinear flutter suppression and performance evaluation of periodically embedded nonlinear vibration absorbers in a supersonic FGM plate

Abstract

To break the limitation of the conventional passive flutter and nonlinear aeroelastic suppressions, a supersonic functionally graded material (FGM) plate featuring periodically embedded nonlinear vibration absorbers (NVAs) is proposed based on the metamaterial concept. Using the von Karman large deformation theory and supersonic piston aerodynamic theory, the motion equations of a supersonic FGM plate coupled with NVAs are derived by using the Hamilton principle. Linear flutter analysis shows that the multiple-NVA design can change the flutter coupling mechanism of the original aeroelastic system and significantly enhance its aerothermoelastic stability. Subsequently, the nonlinear aeroelastic behaviors of the plate and the energy transfer mechanism between it and the NVAs are examined using an energy-based analysis approach. The comparison of bifurcation diagrams indicates that the attachment of periodic NVAs realizes a superior suppression of vibration absorption than a single NVA. Numerical results show that the nonlinear dynamic responses of the plate can be substantially reduced via the targeted energy transfer of NVAs in the post-flutter regime. In particular, the passive control performance of the periodic NVAs does not degrade under an increase in the dynamic pressure and it can also be applicable to different airflow directions. Furthermore, a significant reduction of more than 95% in the response amplitude of the plate can be achieved by properly tuning the NVA nonlinear parameters. The present work demonstrates that the design of periodic array of NVAs is effective at enhancing the flutter stability and mitigating nonlinear aeroelastic responses of the supersonic plate.