Continuous Stiffness Measurement A
Agilent Nano Indenter G200 User’s Guide
A-10
You must allow for damping in both the indentation head and in the
sample, so
D
is an equivalent dashpot:
(36)
For a forcing function of the form:
(37)
Assume a particular solution for the resulting displacement that looks
like:
(38)
In other words, the displacement oscillates at the same frequency as the
force (w), but lags by a phase angle, f. Substituting the particular
solution of
into
and equating magnitudes
yields:
(39)
and
(40)
These two equations may be solved simultaneously for
K
and
D
.
Finally, the stiffness and damping of the contact are given by:
D
D
i
D
s
+
=
F t
F
o
e
i
t
=
z t
z
o
e
i
t
–
=
F
o
z
o
------
K
m
2
–
2
D
2
+
=
tan
D
K
m
2
–
---------------------
=
