Dynamic stability of a lossy locally resonant metamaterial panel in supersonic flow

Abstract

In this paper, aimed at a lossy locally resonant metamaterial panel (LLRMP) in supersonic flow, the impact of changing bandgap and metadamping properties on dynamic stability considering the fluid-structure interaction (FSI) is studied for the first time. The analytical model for studying the transmission coefficient and dynamic stability is established by using the Galerkin method, while the complex energy band is obtained based on the Bloch theorem. The bandgap properties mainly affect the instability frequency, which is attributed to the change of coupling modes that dominate the dynamic instability. The metadamping properties play an important role in affecting the critical instability dynamic pressure, which can be increased/decreased by positive/negative metadamping. The mechanism of metadamping properties changing the critical instability dynamic pressure is that the influences of damping of the host panel and locally resonant unit on the root loci are different. Besides, the ability of LLRMP in changing the critical instability dynamic pressure is investigated, which demonstrates that the critical instability dynamic pressure can be increased by 16.13 % even though the mass ratio is only 0.1. Our work broadens the potential applications of locally resonant metamaterials and provides a fresh perspective on anti-flutter design of panels in supersonic flow.