244
APPLICATIONS OF MULTI-DEGREE OF FREEDOM ANALYSIS
= (1.24G(pi,w) - 5.44G(p2,w)] x 1(F4 kg1/2s“2
(9.90)
The squares of the moduli of these last two results are, respectively,
|x[G(p,w)|2 = (4.45P + 1.52Q)2
(9.91)
|xiG(p,w)|2 = (1.24P - 5.44Q)2
(9.92)
in which the quantities P and Q are defined by
(yov 1 A
P = - ----- , ‘
(sinh 61k — sinh 38k)
(9.93)
k sinh 61k
Q = —------------- (sinh 38k + 0k cosh 38k)
(9.94)
ksinh 61k
Note that a and 0 are constants given by équations (9.84). Also, the wave
number k is related to the wave frequency w by dispersion équation (3.16),
which in this exarnple is
a;2 - 9.81k tanh 61k
With équations (9.86)-(9.88) and (9.91)-(9.94), the spectral densities of the
horizonal deflections based on équation (9.80) then hâve the following forms:
Ç(,
.... (4.45 x 10~4)2(4.45P + 1.52Q)2
“ (2.7062 — w2)2 + 0.01(2.706)2w2
+ „ , ? (1.24 x 10~4)(1.24F - 5.44Q)2
v ~ ’ (11.092 -a>2)2 + 0.01(11.09)2w2
S(G.w) = S,(u>)
(1.52 x 1Q-4)2(4.45P + 1.52Q)2
(2.7062 - w2)2 + 0.01(2.706)2üj2
+s f (-5.44 x 10-4)(1.24P - 5.44Q)2
’ (11.092 — w2)2 + 0 01(11.09)2a;2
(9.96)
(9.97)