Page 463 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

450 Random Vibrations Chap. 13

Figure 13.8-1. S(f) and //( /)
leading to y ^ of Equation 13.7-9.

For a single-DOF system, we have
1/k
H{ f ) (13.8-10)
i - ( / / / „ ) 1 +i [ 2 a f / L ) ]
If the system is lightly damped, the response function H(f ) is peaked steeply at
resonance, and the system acts like a narrow-band filter. If the spectral density of
the excitation is broad, as in Fig. 13.8-1, the mean square response for the
single-DOF system can be approximated by the equation

2 _ c / ^ \ ^
(13.8-11)
where

= / " •'n
1 - ( / / / j 1 + { 2 a f / L ï
and S^{f^) is the spectral density of the excitation at frequency /^.
Example 13.8-1
The response of any structure to a single-point random excitation can be computed by
a simple numerical procedure, provided the spectral density of the excitation and the
frequency response curve of the structure are known. For example, consider the
structure of Fig. 13.8-2(a), whose base is subjected to a random acceleration input
with the power spectral density function shown in Fig. 13.8-2(b). It is desired to

m

H _ o
(a) Figure 13.8-2.