Biomedical Engineering Reference
In-Depth Information
(a) Zero Reference
4
150
100
50
0
2
0
2
4
6
8
10
12
Time (
µ
s)
4
4
2
2
0
0
0
2
4
6
8
10
12
FW
SW
Time (
µ
s)
4
1
0.5
0
2
0
0
2
4
6
8
10
12
Time (
µ
s)
200
4
2
100
0
0
0
2
4
6
8
10
12
Time (
µ
s)
Fig. 9.5
The four panels in this figure represent different data from the same four experiments
illustrated in Fig.
9.3
, thus the description of the experiment and the small cartoons for each panel
have the same significance. The difference is the plot of amplitude vs. time for a wave passing
thought different media have been replaced by the frequency spectrum of waves vs. time for the
wave passing thought the different media. The frequency spectrum for the wave in water alone,
panels 1 and 4, is seen to be the same general shape; this shape is missing from panel 3 where there
is no water, but is identified in panel 2 as the frequency spectrum representing the energy
associated with the slow wave (SW). The frequency spectrum representing the energy associated
with the fast wave (FW) is shown in panel 3 where the wave is passed through the unsaturated
porous specimen
Example 9.6.1: Wave Propagation in a Principal Direction of Symmetry
Determine the wave velocities and the polarization vectors or eigenvectors for
cancellous bone associated with a harmonic wave propagating along an axis of
material symmetry. Let the axis of material symmetry be
e
1
. The properties of the
specified cancellous bone are a porosity
f ¼
0.5, a density of the matrix material
of the porous structure of 2,000 kg/m
3
, and a density of the pore fluid of the porous
structure of 1,000 kg/m
3
.FromYangetal.(
1999
) the values of the compliance
and elasticity tensors for orthotropic elastic coefficients are approximately
given by
Search WWH ::
Custom Search