Agilent Technologies Nano Indenter G200 - Page 339

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
Equation 38 into Equation 34 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:
DD
i
D
s
+=
Ft F
o
e
it
=
zt z
o
e
i t –
=
F
o
z
o
------
Km
2
–
2
D
2
+=
tan
D
Km
2
–
---------------------=