WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

FRF (dB) FRF (dB)
150
100
50
0
ARTICLE IN PRESS
J.S. Jensen / Journal of Sound and Vibration 266 (2003) 1053–1078 1067
-50
-100
=0.0%
=0.1%
=1.0%
=5.0%
0
4 8 12 16
(a) Frequency, (kHz)
150
100
50
0
-50
-100
0
(b)
no disorder
1% disorder
5% disorder
20% disorder
4 8
Frequency, (kHz)
12 16
Fig. 8. (a) The influence on the response of the last mass of added viscous damping characterized by the actual to
critical damping ratio z of the individual masses, and (b) the influence of random disorder of the sizes of the individual
masses. For all curves M ¼ 10:
The imperfections are simulated by adding a random variation to each mass size. The variation is
indicated by a disorder percentage representing the maximum variation of the mass relative to its
nominal value.
Fig. 8b shows that the response is insensitive to the presence of small imperfections. Only if the
structure deviates significantly from the perfect periodic (20% disorder) is the response inside the
band gap noticeably changed by e.g., the presence of local resonances. But even with this high
level of imperfection the band gap is still clearly seen in the response.