Non-Hermitian aeroelastic dynamics of locally-resonant piezoelectric metastructures subjected to supersonic flows

Piezoelectric metastructures offer high adaptability for vibration control in aerospace engineering. Under supersonic flow conditions, aeroelastic effects significantly impact elastic wave properties and thus the vibration suppression performance of piezoelectric metastructures. Nevertheless, comprehensive investigations of their aeroelastic dynamics remain absent. To fill this gap, we develop an analytical framework for an aero-elasto-electric coupled metastructure in this study, and investigate its elastic wave propagation and vibration suppression properties. A non-Hermitian effect is observed through analyzing the dispersion relations of cells and the frequency response functions of finite metastructures. It leads to the amplification of vibration transmission in the flow direction (forward direction), while causing attenuation in the direction against the flow (backward direction), with the phenomenon particularly evident at low frequencies. Nevertheless, the non-Hermitian effect could not enhance the backward vibration attenuation within the local-resonance bandgap. With bandgaps located in low-frequency ranges, the backward attenuation performance may even vanish. In contrast, the forward bandgap attenuation is consistently maintained under supersonic flows with varying dynamic pressure. Distinct nonreciprocal patterns may emerge within and outside the low-frequency bandgap. If the bandgap is designed to lie in a relatively high-frequency range, it can still prohibit vibration transmission effectively in all directions. These findings on the aeroelastic dynamics of piezoelectric metastructures provide useful design guidelines for their applications in supersonic aircraft.