Page 471 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)
P. 471
458 Random Vibrations Chap. 13
13-37 An SDF system with viscous damping ( = 0.03 is excited by white-noise excitation
Fit) having a constant power spectral density of 5 X 10^ N^/Hz. The system has a
natural frequency of = 30 rad/s and a mass of 1500 kg. Determine a. Assuming
Rayleigh distribution for peaks, determine the probability that the maximum peak
response will exceed 0.037 m.
13-38 Starting with the relationship
f
x(t) = j fit - )hi f )df
•'n
and using the FT technique, show that
X{io)) = F{i(o)H{i(o)
and
r ^ 'y
= f Sp{(i))\ H(i(o)\ d(i)
where
Sf(o)) = lim —7f;F(ia))F*(ia))
7_,oo i
13-39 Starting with the relationship
show that
H(io)) _ i24>ioj)
H%iw)
13-40 Find the frequency spectrum of the rectangular pulse shown in Fig. P13-40.
fit)
- L n L ^
2 ^ 2 Figure P13-40.
13-41 Show that the unit step function has no Fourier transform. Ffint: Examine
oo
/ _ \f i ‘)\dt
