A simple model for coupled acoustic-structure resonance in Stratospheric Observatory for Infrared Astronomy

Abstract

The Stratospheric Observatory For Infrared Astronomy (SOFIA) is a joint project of NASA and the Deutsches Zentrum fur Luft- und Raumfahrt that has mounted a 2.5 m, 20 000 kg infrared telescope on a bulkhead of a specially modified Boeing 747-SP. A large sliding door will expose the observation bay to the exterior flow field at Mach 0.85 and 13 km altitude. In the open configuration the interaction of turbulence vortices generated at the leading and trailing edges of the opening has the possibility of inducing a strong acoustic signal. A concern has been raised that the peak frequencies of such a signal might coincide with the cavity resonances. The present work examines the transfer function for a known source in order to identify the cavity resonances. Simplistic reasoning argues that the worst case would occur if the cavity resonant frequencies are close to structural resonances. However, the structure’s impedance is very low at its resonances, which means that the cavity resonant frequencies are shifted from their nominal values. The present work uses a simple one-dimensional waveguide model, in which one end is terminated by a damped single-degree-of-freedom oscillator, to explain the coupled-fluid structure resonance. The characteristic equation and formulas for the pressure and displacement transfer functions are derived. Analysis of these results leads to some surprising insights regarding the role of a structure’s stiffness and mass. [Work supported by the NASA.]