Relationship between Damping Coefficient and Tan Delta
Relationship between Damping Coefficient and Tan Delta
(OP)
I am trying to determine if there is a simple empirical relationship between two methods of quantifying the amount of damping in a system - the damping coefficient (or damping ratio) and the tangent of delta.
Does anyone have any thoughts?
Does anyone have any thoughts?





RE: Relationship between Damping Coefficient and Tan Delta
Cheers
Greg Locock
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RE: Relationship between Damping Coefficient and Tan Delta
n= no cycles to decay e, (=2.718...)
The first order damped system amplitude multiplier is
e^-zetaWnt
So when this exponent =-1 it has the same decay
and
zeta Wnt=1
zeta=1/Wnt
tan delta=1/nPi
n=Wnt/2Pi
Therefore
tan delta=2/Wnt=2 zeta
FYI
zeta derives from
2zeta Wn=c/M
for the free linear 1st order spring mass damper
Mx"+cx'+kx=0
RE: Relationship between Damping Coefficient and Tan Delta
Thanks so much.