Uaestvelto and Linden 



Analogous to (28), the expression for the CPSD of P, can be written 

 in terms of EWmnWrt from (29). The same can also be done for the 

 radiation. 



b) One Dimensional Model 



To simplify the computations we assume that the transverse 

 plate dimension is very large and that no flexural waves propagate 

 in the transverse direction. With these simplifications Eq. (22) 

 may be written 



where 



Wn + / r„„W^ = $„ (30) 



>oo 



4.*(Ka)A[<,,(^)] 



r„ = r dK-: — . ^ ■•■^'-'^ (31) 



nm J _ x(K) 



where 



2 2 

 T(K) = K - 7 



Vk^ + (M^ - i)K^ - 2kKM 



and 



" J _ T(K 



The circumvention of the branch points in the above expressions will 

 be described shortly. 



If Gfnn denotes the inverse matrix to S^n ■*" ^mn then the 

 solution to (30) is 



Wn = ) Gnm^m 

 m 



Now performing the ensemble averages as before gives 



<W,W*> = ^ G,,<^,4>s*>G* (33) 



r,s 



but 



498 



