The concept of non-Hermitian mechanics introduces new dimensions to metamaterial research, yet current studies have primarily focused on wave manipulation, neglecting the vibration transmittance characteristics of finite-size metamaterials with boundary reflections. This paper explores the asymmetric vibration transmittance characteristics of a simply supported Non-Hermitian Metamaterial Panel (NHMP) with two lossy resonators, under the impact of supersonic aerodynamic forces. By examining the non-Hermiticity of a non-aerodynamically loaded NHMP and a host panel aeroelastic system separately, we demonstrate that the NHMP subjected to supersonic aerodynamic force is a complex non-Hermitian system, exhibiting asymmetric vibration transmittance driven by both the fluid–structure interaction effect and lossy resonators. We theoretically and numerically clarify that an ideal aeroelastic system, such as a host panel aeroelastic system, functions as a non-Hermitian mechanical system due to the fluid–structure interaction effect, with the critical flutter point aligning with the Exceptional Point (EP). The results of this study indicate that at low dynamic pressures, the lossy resonators primarily govern asymmetric vibration transmittance, whereas at high dynamic pressures, the fluid–structure interaction effect becomes the dominant factor. Notably, at the EP, asymmetric vibration transmittance is unaffected by the mass ratio of lossy resonators, which is attributed to the invariance of the operational deflection shapes of the NHMP at the EP. This study offers a novel perspective on panel aeroelastic systems and non-Hermitian metamaterials, advancing the field through its comprehensive analyses.

Skin panels on supersonic vehicles are subjected to aero-thermo-acoustic loads, resulting in a well-known multi-physics dynamic problem. The high-frequency dynamic response of these panels significantly impacts the structural safety of supersonic vehicles, but it has been rarely investigated. Given that existing methods are inefficient for high-frequency dynamic analysis in multi-physics fields, the present work addresses this challenge by proposing a Stochastic Energy Finite Element Method (SEFEM). SEFEM uses energy density instead of displacement to describe the dynamic response, thereby significantly enhancing its efficiency. In SEFEM, the effects of aerodynamic and thermal loads on the energy propagation characteristics are studied analytically and incorporated into the energy density governing equation. These effects are also considered when calculating the input power generated by the acoustic load, and two effective approaches named Frequency Response Function Method (FRFM) and Mechanical Impedance Method (MIM) are developed accordingly and integrated into SEFEM. The good accuracy, applicability, and high efficiency of the proposed SEFEM are demonstrated through numerical simulations performed on a two-dimensional panel under aero-thermo-acoustic loads. Additionally, the effects and underlying mechanisms of aero-thermo-acoustic loads on the high-frequency response are explored. This work not only presents an efficient approach for predicting high-frequency dynamic response of panels subjected to aero-thermo-acoustic loads, but also provides insights into the high-frequency dynamic characteristics in multi-physics fields.