Biomedical Engineering Reference
In-Depth Information
frequency forced response tool dynamics was obtained by using acoustic
emission sensors.
The response of the substructures has been defined as:
X
H
H
F
1
11
12
1
X
H
H
F
2
21
22
2
X
H
F
3
33
33
Xx
,
F
f
,
M
where: Hij - transfer function of the substructures, subscripts indicate the
location of the displacement and force, X - represented by translational
displacement x as well as rotation θ and F -represented by force f and moment
M.
The matrices of the assembled structures are defined as:
X
G
G
G
F
11
12
13
X
G
G
G
F
2
21
22
23
2
X
G
G
G
F
31
32
33
where: Gij are the transfer functions of the assembly. The TF matrices are
obtained either using EMA (experimental modal analysis) or FEA. The
responses at the beginning and end of the substructure 1 can be predicted
mathematically taking both translational and rotational degrees of freedom
into account. The rotational dynamics at the end of substructure 2 are
identified using the technique covered in [40] giving the result:
(
b G
h
b h
G
b h
h
b h
h
h
h
h
h
h
h
ff
11,
ff
22,
mf
ff
21,
mf
12,
ff
ff
11,
ff
22,
mf
ff
h
21,
mf
12,
ff
21,
mf
22,
ff
12,
ff
21,
ff
12,
ff
22,
mf
b
mf
h
h
G
h
h
h
h
G
11,
ff
22,
ff
11,
ff
22,
ff
21,
ff
12,
ff
21,
ff
12,
ff
1
2
2
2
b
b h
G
(2
b h
h
h
h
h
h
mm
ff
21,
mf
ff
11,
f f
22,
mf
21,
mf
12,
f f
21,
mf
22,
ff
h
h
G
h
h
h
hG
12,
ff
11,
ff
22,
ff
11,
ff
22,
ff
21,
ff
12,
ff
21,
ff
12,
ff
- 2
b G
h
h
-
h
h
h
h
h
h
h
- 2
h
b h
-
h
h
h
h
)
G
ff
11,
ff
22,
mf
21,
mf
12,
mf
22,
mf
22,
ff
21,
ff
21,
mf
21,
ff
12,
ff
ff
21,
mf
12,
ff
21,
mf
21,
ff
22,
mf
12,
ff
21,
ff
2
2
2
2
-
h
h
h
G
h
h
h
h
h
b h
h
h
h
h
h
h
h
h
h
G
22,
ff
12,
mf
21,
mf
11,
f f
22,
ff
12,
mf
21,
mf
11,
ff
22,
mf
ff
11,
ff
22,
ff
12,
mf
21,
ff
22,
mf
11,
ff
22,
ff
12,
mf
21,
ff
22,
mf
11,
ff
h
b G
h
h
h
h
h
-
2
h
b G
h
h
h
h
h
-
h
h
h
h
G
22
mf
ff
11,
ff
12,
ff
22,
ff
22,
mf
21,
mf
11,
ff
22,
mf
ff
11,
ff
11,
ff
12,
ff
12.
mf
21,
ff
22,
mf
12,
ff
22,
ff
22,
mf
21,
mf
11,
ff
2
-
h
h
h
h
h
2
h
b G
h
h
h
b h
- 2
h
b h
h
h
h
h
hG
12,
ff
22,
ff
12,
mf
21,
mf
21,
ff
12,
ff
ff
11,
ff
22,
mf
21,
mf
12,
ff
ff
21,
mf
12,
ff
ff
11,
ff
22,
mf
21,
mf
12,
ff
22
,
mf
21,
ff
11,
ff
2
2
2
2
h
h
h
h
-
h
h
h
-
h
h
h
h
12,
ff
21,
mf
21,
ff
22,
mf
12,
ff
21,
mf
22,
ff
12,
ff
22,
mf
21,
ff
11,
ff
