converting damping

[rob768]

Is there anyone who knows how to convert the damping for, for instance a rubber coupling, specified as a magnifying value, to damping in NMs as specified in a FEM model?

 

[gio1]

The definition of Dynamic Magnifier is

DM=1/(2z)

where z is the damping ratio, z=(C/Ccrit)
with
C: damping coefficient
Ccrit: Critical damping coefficient for the system

Since Ccrit= 2*SQRT(k*m)

(k being stiffness and m mass)

One can write:

C=SQRT(k*m)/DM

 

[rob768]

Gio,

Thanks for the reply. The next question is of course:
how do I define or determine the stiffness of the total system

 

[EricZhao]

Gio1 gave us fomulars in single DOF system. For multi-DOF, K and M are matrices. So it is not going to work directly.

Do a modal analysis without damping, and get the first several natural frequency (modes).

Your DM should come with a frequency range (xHz-xxxxHz). You have to assume that the curve is flat throughout the frequency range.
z_n = 1/(2*DM) ............. z_n is the damping ratio for the n-th natural frequency(mode). Since the DM curve is assumed to be flate. z_n's have the same value for all natural frequencies (in the range xHz-xxxxHz)

Depends on your FEA software and your type of dynamic analysis, you might be able to specify damping ratio z_n for each natural frequency(mode) directly. If yes, problem solved.

If not, maybe your FEA damping model is like C = a*M+b*K. In this situation, let a = 0, b = 2*z_n / (omega_n), where omega_n is the n-th undamped natural frequency(mode). Since you just have one input "b", it means that you can only consider the damping effects on one mode. It is upto you to deside which one is your "best interest".

 

[gio1]

It all depends on how you need to apply your damping to your FE model.

If you need to define the properties of a damping element then the formulas above should help you. In that case the stiffness is the one existing bewteen the 2 sides of the dashpot.

If you need "distributed" damping then use Eric's approach.
Note that in this case you could have 2 different types of damping:

- Mass damping (tuned by the coefficient "a") Which is acting on the body as a whole, i.e. it would affect rigid body modes. You can use this to simulate the effect of a viscous medium surrounding the body while this is moving.

- Stiffness damping ("b") only acts if the body is deforming, therefore will only affect non-rigid body modes. You can use this model to simulate dissipation related to material hysteretic damping.