Biomedical Engineering Reference
In-Depth Information
τ
d
is time constant or relaxation time
β(0 < β ≤ 1) is a stretching exponent
In the experiment presented in Hou et al. [4], the first stage of the loading
process
F
(
t
) was given as
t
t
()
=
(9.2)
Ft
F
(
tt
≤
)
0
o
0
Equation (9.1) indicates that the piezovoltage is generated in proportion to
the load
F
(
t
) and it decays in the stretched exponential law simultaneously.
When the loading remains constant, the fitted piezovoltage function is
t
c
−
τ
()
=
Vt
Ve
o
(9.3)
where τ
c
is a time constant and
V
o
is the peak voltage when the first stage of
the loading process ends. Letting
t
=
t
o
and substituting Equation (9.2) into
Equation (9.1) yields
β
t
o
d
−
τ
(9.4)
VKFe
o
=⋅
⋅
o
Equation (9.3) represents that the piezovoltage decays in a typical expo-
nential law. The fitted functions for the piezovoltage of sample 1 are then
written as
0.2993
t
−
t
t
−
0.271
F
e
11.79
(
tt
≤
)
o
o
o
()
=
Vt
(9.5)
0.2993
t
o
−
−
t
−
0.271
Fe
11.79
⋅
e
94
(
tt
>
)
o
o
In Figure 9.12(a)-(e) the curves represent the fitting function (9.5) with
different
F
o
and
t
o
and the curves are the corresponding measured piezo-
voltages. Figure 9.12(a)-(c) shows three fitting curves with
F
o
= 150 N and
t
o
= 250, 500, and 1000 ms, respectively. Figure 9.12(d) and (e) shows two fit-
ting curves with
t
o
= 250 ms and
F
o
= 50,100 N, respectively. It is evident that
the fitted functions coincide well with the measured curves. The values of
K,
τ
d
,
β, and τ
c
are listed in Table 9.3.
The fitted functions for sample 2 are as follows [4]:
0.302
t
−
t
t
−
0.295
F
e
12.74
(
tt
≤
)
o
o
()
=
o
Vt
(9.6)
0.302
t
o
t
−
−
−
0.295
Fe
12.74
⋅
e
93
(
tt
>
)
o
o
