WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

2.1 Band diagram and forced vibrations 9
Frequency (kHz)
a) b)
80
60
40
20
0
M Γ X M
Reduced wavevector
Figure 2.1 a) A 2D unit cell consisting of an inclusion with 3×3 masses and connecting
springs (in bold) surrounded by a matrix material with additional masses and springs, b)
The corresponding band diagram showing the frequency of propagating modes versus the
reduced wavevector (indicating wavelength and direction of propagation). From paper [1].
B
unit cell
My
Mx
f cosΩt
Response in A (log-scale)
200
150
100
50
-50
A
0
a) b)
0
Mx = My = 3
Mx = My = 7
Mx = My = 15
Mx = My = 21
20 40
Frequency, Ω (kHz)
60 80
Figure 2.2 a) A simply supported structure with Mx × My unit cells subjected to a
periodic load f cosΩt, b) The acceleration response in point A with different numbers of
unit cells in the structure. From paper [1].