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The coupling between a two-dimensional, supersonic, laminar boundary layer and a flexible surface is studied using direct numerical computations of the Navier-Stokes equations coupled with the plate equation. The flexible surface is forced to vibrate by plane acoustic waves at normal incidence emanated by a sound source located on the side of the flexible surface opposite to the boundary layer. The effect of the source excitation frequency on the surface vibration and boundary layer stability is analyzed. We find that, for frequencies near the fifth natural frequency of the surface or lower, large disturbances are introduced in the boundary layer which may alter its stability characteristics. The interaction between a stable two-dimensional disturbance of Tollmien-Schlichting (TS) type with the vibrating surface is also studied. We find that the disturbance level is higher over the vibrating flexible surface than that obtained when the surface is rigid, which indicates a strong coupling between flow and structure. However, in the absence of the sound source the disturbance level over the rigid and flexible surfaces are identical. This result is due to the high frequency of the TS disturbance which does not couple with the flexible surface.

The coupling between a two-dimensional, supersonic, laminar boundary layer and a flexible surface is studied using direct numerical computations of the Navier-Stokes equations coupled with the plate equation. The flexible surface is forced to vibrate by plane acoustic waves at normal incidence emanated by a sound source located on the side of the flexible surface opposite to the boundary layer. The effect of the source excitation frequency on the surface vibration and boundary layer stability is analyzed. The results show that, for frequencies near the fifth natural frequency of the surface or lower, large disturbances are introduced in the boundary layer that may alter its stability characteristics. The interaction between a stable two-dimensional disturbance of Tollmien-Schlichting (TS) type with the vibrating surface also is studied. The results show that the disturbance level is higher over the vibrating flexible surface than that obtained when the surface is rigid, which indicates a strong coupling between flow and structure. However, in the absence of the sound source the disturbance levels over the rigid and flexible surfaces are identical. This result is due to the high frequency of the TS disturbance, which does not couple with the flexible surface.