Maestvello and Linden 



In comparing the results of the present and previous experi- 

 ments , It Is concluded that the sign change of the convection velocity- 

 Is attributed to the presence of the shock. Furthermore, the cross - 

 correlation of the wall pressure also reflects a phase change for a 

 separation of 2.5 inches, which Is in the same location as the phase 

 change which occurs for the displacement correlation In Fig, 5. 



III. ANALYSIS OF ACOUSTICALLY COUPLED PANELS 



a) Two-dinnenslonal Finite Panel 



The vibration of the panel is induced by an arbitrary, external 

 pressure field F. It is assumed that the panel motion does not 

 Interact with the turbulent boundary layer, i.e. , the forcing field is 

 not altered by the plate motion. However, the panel is acoustically 

 coupled to the fluid on both sides of the panel. 



The equation of motion for an harmonic component of the dis- 

 placement, W, of a thin panel with a force, F, and a pressure 

 differential, pg - P| + 6p acting upon it, obeys the equation 



BA^W - ppco^w = F + P2 - Pi + 6p (1) 



where the bending stiffness, B, may include hysteretic damping, 

 and where pp is the mass per unit area of the panel, co is the 

 angular frequency, pg is the acoustic pressure on the streamslde of 

 of the panel, p, is the acoustic pressure below the panel and 6p 

 Is the static pressure differential. 



The perturbation pressures, P| and pg, are related to the 

 velocity potentials, which satisfy time- independent wave equations in 

 the appropriate regions. In solving these equations one uses a 

 boundary condition which relates the potentials to the panel displace- 

 ment. These relationships may be made more obvious through the 

 use of Green's theorem. Thus, it is required to solve a system of 

 three coupled partial differential equations, the first of which is not 

 separable for the clamped edge boundary condition. 



Pi and pg may be found directly as function of W, Thus , 

 consider first the cavity. The acoustic velocity potential, <p , satis- 

 fies the Helmholtz equation 



A^ + kV = (2) 



with boundary condition 9^/9n = on all walls except on the plate 

 where 9^/9n = - icoW. 



The Greens function, g, for a cavity with hard walls satisfies 



484 



