0.25 
(a E R “OBSERVED” EXCITATION 4 
0.20 5 
z 
a \ E 
QO 0.15 
4 j 
< 1 
= 0.10 
mn 
a. 0.05 
oO 
z — LINEAR ESTIMATE 
E ---- Ul . NONLINEAR 
(09) 
z 
io 
Q 
| 
<x 
rea 
ke 
oO 
uw 
ao. 
o 
= 0.8 — U2 . NONLINEAR i 
= ---- U3 , NONLINEAR 
7) ie =| 
vs 
ni 
a 
1 
< 
oc 
Ee 
oO 
Ww 
oa. 
7) 
SPECTRAL DENSITY 
0 5 10 15 20 
FREQUENCY, rad/sec 
Fig. 11.16. Observed and predicted spectra and the components of spectrum of 
nonlinear response of the simulated system, nominal o, = 1.0. 
(From Dalzell.17) 
7. Expansion to higher order nonlinear process. 
By the same procedure as previously used for quadratic and cubic nonlinear pro- 
cesses, we can go on to higher order nonlinearities. For example, from Brillinger,® 
Syxx. ..x(@1,@2° * *@m) 
pescewinas 0.0. Cuey Qe (11.88) 
m!Sxx(@1) Sxx(@2)* + - Sxx(@m) 
Ay (@1,@2,° - *®m) = 
324 
