Aero-acoustic-elastic flutter of plates

Abstract

The linear stability of an elastic plate with supersonic freestream flow on one side and a cavity on the other is investigated for the special case when the first acoustic frequency of the cavity is close to the natural frequencies of the plate. To illustrate the effect of aero-acoustic-elastic coupling on flutter onset, a simplified three degrees-of-freedom model is derived including two structural and one dynamic acoustic pressure modes. The model is nondimensionalized to obtain three parameters that describe the acoustic-elastic coupling and one for the aerodynamic stiffness as modeled using Piston Theory aerodynamics. The role of the nondimensional parameters on flutter onset and frequency is investigated. A test case from a recent wind tunnel experiment is analyzed using the full computational model to validate the findings from the illustrative model and quantify the effect of acoustic coupling on flutter onset. A linear stability analysis predicts that the plate used in the experiments is stable at the wind tunnel conditions for cavity depth greater than 60% chordlength. For smaller cavity depth, the plate is expected to flutter as the first and second structural modes coalesce. Wall impedance is included in the analysis to investigate the effect of acoustic damping. Higher-order acoustic-elastic mode crossings are stabilized when acoustic damping is included however the two-mode flutter instability is not affected. These results suggest that the full aero-acoustic-elastic coupling must be considered for accurate prediction of flutter onset and aeroelastic behavior of elastic plates in supersonic flow. Moreover, this phenomenon can be leveraged in wind tunnel experiments to measure post-flutter responses at reduced dynamic pressures by appropriate design of the acoustic cavity.