4 ——y = Tr T 
So stan AAA ANA A WINE f Hh Re Mh Nae ye i MAM tcl i APA WAARATH Aw! N ant 
z i ait ey 
-—4 _1 ys 5 mn 
70 80 90 100 110 120 
6 ~— = — 
= 0 Ate , Ay apf H pa A Ui 0 AAA | aA \ | af | M an fy NAA An af\ | tial | ff\_ 
4 
70 80 1 1 
90 TIME 10 20 
Fig. 11.12. Simulated time histories of linear random excitation X(f and nonlinear 
response Y(t), and its components Y4(t), Yo(t), and Y(t) o, = 1.0. 
(From Daizell.17) 
Here, Y;(t), Y2(t), and Y3(t) show the first, second, and third terms of the Voltera 
expansion of Y(t) as Eq. 11.67. 
Figures 11.13 and 11.14 show the first and second order impulse response functions 
h,(t) and ho(t), t2) in the form of the weighting functions 8}. Sit and Fig. 11.15 shows a 
portion of the third order impulse response function h3(t), tz, t3) at the sequence of f3 val- 
ues in the form Set: It is interesting that impulse responses are obtained quite beautifully 
by this analysis. 
Fig. 11.13. Truncated linear discrete kernel g}. 
(From Dalzell.17) 
321 
