WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

Relations to recent work 15
Amplitude (last mass)
1.0
0.8
0.6
0.4
0.2
0
0.8 1.2
Frequency
1.6 2.0
Figure 2.9 Relative amplitude of the last mass for non-homogeneous nonlinearity (solid
line) for a structure with 400 attached oscillators. The circular dots and the two dashed
lines show the amplitude for fixed nonlinearities of 0.3, 0.12 and 0.88 corresponding to
the average, lowest and the highest value used for the chain with varying non-linearities.
From paper [3].
2D lattices with defects, and by Yan et al. (2009) on localized modes for 1D elastic
waves. Recently, experimental work has been carried out by Hladky-Hennionne and
de Billy (2007) who investigated bandgaps in 1D diatomic structures and by Yao
et al. (2008) who examined a structure with local resonators.
A large amount of recent papers concentrate on the creation of low-frequency
bandgapsusing local oscillators–oftenreferredtoaslocallyresonant materials. The
research has focused on the use of local oscillators in different types of mechanical
structures such as beams, plates and rotating shafts (Wang et al., 2006; Yu et al.,
2006a,b; Liu et al., 2007). The connection between locally resonant materials and
multiple added mass-dampers was recently investigated in a conference paper by
the author and Boyan Lazarov (Jensen and Lazarov, 2007). Furthermore, the link
between locally resonant materials and electromagnetic metamaterials was pointed
out recently by Huang et al. (2009) and Zhou and Hu (2009).