Relationship between Damping Coefficient and Tan Delta 1

[gandersen70]

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?

 

[GregLocock]

Yup, it is a standard solution. Harris "Shock and Vibration" should have it, as would many modal analysis theory books.



Cheers

Greg Locock


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[zekeman]

tan delta =1/nPi
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

 

[gandersen70]

Ah yes. Makes sense to me.

Thanks so much.