Response of a Vibrating Plate in a Fluid 

 \ a ag / ^ 



\ a ac / 



miT , 



+ — T#S ^^L sinrnn(£iC^)"| _ sinrHH(^)l (sh/c +c. ch/c )i 



/K^N^ ^/mTT\2 j r L^c ^ 2 /J L ac V 2 /J ^ r r rY 



where 



_ cos /Cr- Ch /Cr 



•" ~ sin /Cp + sh /Cp 



and the normalization Np is given by [ Dzygadlo 1967] 



-2 1 1 



Nr = -^— (sh 2/Cr - sin 2ACr) "^ T~^^^ '^r ^°^ '^r ~ ^^^ '^r ^^ '^r^ 



+ ^-^ (ch 2ACp - cos 2/Cj. - 4 sin k^ sh AC^) 



2 r 1 



■*" Q'r Ll ■'"4 (sin 2/Cp + sh 2/c^) 



- — (sin /Cp ch /Cp + sh K^. cos /c^)J 



and the eigenvalues K^ are the roots of the equation 



cos /Cp cosh Kj = i 



513 



