Effect of grazing flow on structural-acoustic response of an elastic plate with sound in a duct

The design of supersonic and hypersonic vehicles involves the challenging task of designing thin panels that can withstand severe unsteady pressure and thermal loads. A good understanding and accurate prediction of the coupled structural-acoustic response of thin panels subjected to sound waves are key elements of this design process. Due to the cost of in-flight testing, the experimental assessment of the structural-acoustic response of skin panels is usually conducted in ground-based facilities consisting of a duct in which acoustic waves propagate at grazing incidence with skin panels mounted along the duct walls. A key limitation of such facility is the absence of flow, the impact of which on the structural-acoustic response of the skin panel is still poorly understood. To shed some insight on this key contribution, this analytical and numerical study focuses on the structural-acoustic interaction of sound with a thin elastic plate mounted flush on a wall in a rectangular duct in the presence of a uniform mean subsonic and supersonic flow. A linear, time-harmonic theory based on modal descriptions of the plate velocity and duct acoustic fields is first developed. The theory includes the effect of uniform mean flow in the duct and clamped and simply-supported boundary conditions for the plate. The sound radiated by the plate is calculated using Doak's theory [22], extended in this work to account for subsonic and supersonic uniform mean flow in the duct, and verified using the numerical solver. The theoretical model provides important insight on the effect of flow in the duct on the coupled response of the plate. Four metrics characterizing the coupled response are considered: the deviation of the peak response frequency from the in vacuo natural frequency of plate, the amplitude of the peak response, the effective acoustic damping of the plate, and the plate modal coupling through the duct acoustic field. The theory is extended to estimate the onset of instability in the structural response of a duct-mounted clamped-plate with grazing flow for estimating its range of applicability. Numerical simulations of the coupled response of a duct-mounted clamped plate are performed using a 3D coupled numerical solver, which includes a high-fidelity finite difference fluid solver and an implicit finite element structural solver in a fully coupled framework. The 3D solver is used to predict the response of duct-mounted thin plates to plane waves with a broadband frequency content and in the presence of a uniform mean flow. The spectral response of the integral average of the rms plate velocity is computed for two plate thicknesses at various Mach numbers, and is compared with that computed using linear theory. The predictions provided by the theoretical model compare well with the numerical models except in the presence of an instability. For a typical aerospace structure, the plate-fluid coupling does little to change the fundamental vibration frequencies from their in vacuo values but significantly alters the amplitudes of the plate vibration. The effect of flow on the structural-acoustic coupling is mainly by modifying the acoustic source structure of the vibrating plate and by modifying the radiation pattern. Further, the inter-modal coupling through the acoustic field is also a strong function of M!. The effect of flow in most cases is to reduce the amplitude of the plate response until panel instability sets in.