Smith and Cummins 



Determination of the Coefficients 



As R. j is the response in the jth mode to the excitation e^'^'^ in the ith 

 mode, substitution in the equations of motion yields the following relations: 



•33-'^ ^33 



a.-OJ^R,, + ib„<i;R,, + c,,R 



2 p* 

 33 "^"33 ' '-33"33 °53"' "^35 



-^is'^'^Ka + ib35ajR;3 + C35R*3 - a^jC^^R*^ + ibssajR*^ + CssR*^ = 

 -^33-'Rs3 + ib33a;R*3 + C33R*3 - ^ss^'Ks + ib33C.R;3 + C33R*5 = 

 -^3S-'R53 + ib33a.R*3 + C35R*3 - a^^a^^R*^ + ibss-R^^ + c^R^^ = 1. 



Separating the real and imaginary parts of the equations, we obtain the eight 

 equations: 



(8) 



f^33 - ^^'^33) R33 - ^b33R33 + (C33 - a;2a53) R^^ - o^h^^Rl^ 



= 1 



-33 "^ "33' "33 ' ^^^33^33 ' ^^53 "^ '^53'' ^^35 ^ "'"S3'^35 

 C^33- ^'^33) R53 - ^b33Rj3 + (C33 -0.2353) R53 - ^b53R5% 



33 -^ °33'' "53 " '-"'^33"S3 " ^''53 "^ ^53^ '^SS ^ "'"ss'^SS 



(^35 - ^'^35) K33 - ^b35R33 + (C35 - 0.2355) R35 - a.b55Rj5 



= 



(9) 



C'^35 - ^^'^35) R33 + ^b35R33 + (C55 - 0.2355) R35 + a;b55R35 



(^35- ^^'^35) K53 - '^b35R53 + (C55- a.2355) R55 - o;b55R; 

 ^^35 - ^' 335) R53 + ^b35 R53 + (C55 - a;2 355) RJ5 + a.b55 K 



Let 



53 "5 5 



(10) 



452 



