Agilent Technologies Nano Indenter G200 User Manual page 339

Agilent Nano Indenter G200 User's Guide
You must allow for damping in both the indentation head and in the
sample, so D is an equivalent dashpot:
For a forcing function of the form:
Assume a particular solution for the resulting displacement that looks
like:
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
yields:
F
o
----- -
z
o
and
These two equations may be solved simultaneously for K and D.
Finally, the stiffness and damping of the contact are given by:
Continuous Stiffness Measurement A
D = D + D
i s
it
F t  
= F e
o
i t   
–
z t  
= z e
o
into Equation 34 and equating magnitudes
2
2
  
= K m – +
D

tan = -------------------- -
2
K m –
(36)
(37)
(38)
2
D 
(39)
(40)
A-10