STUDY OF THE RESPONSE OF A VIBRATING 

 PLATE IMMERSED IN A FLUID 



L. Maestrello 



NASA Langley Research Center 

 Hampton ^ Virginia 

 and 

 T. L. J. Linden 

 European Space Operations Center 

 Darmstadt i Germany 



I. INTRODUCTION 



A large aircraft in supersonic flight undergoes large variations 

 in flow field over its surface. This paper is concerned with studying 

 the response of a structure excited by convected turbulence at nearly 

 zero pressure gradient and by shock-boundary layer interaction, 

 with the inclusion of the coupling due to the acoustic field on each 

 side of a panel. Shock waves on thin-walled structures can innpose 

 severe loading problems, the most common of which is the self- 

 induced oscillation which is generated by an oscillating shock. The 

 shock wave can easily couple with the forcing frequency present in 

 the environment, including panel resonances. 



From interior noise point of view, the upper region of the 

 airplane fuselage is considered the principal noise radiator. The 

 aerodynamics in this region are known from the Prandtl-Mayer 

 relation, and further downstream by shock-boundary interaction. In 

 addition, the fuselage skin experiences traveling shock waves which 

 run up and down the skin during the acceleration period, which might 

 last twenty miinutes for a Mach 3 airplane. 



In supersonic flight, the vibration of the surface is influenced 

 by the back pressure resulting from the radiation of sound on both 

 sides of the surface, so that, the surface motion and radiation are 

 coupled phenomena. The interior noise level is determined by skin 

 panel vibrations. For radiation below the critical frequency, the 

 major source of sound arises from the interaction of the bending wave 

 with the discontinuity of the boundary. Above the critical frequency. 



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