# Thread: Rayleigh Damping, tand, Prony-Parameters

1. Junior Member
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2005-08
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## Rayleigh Damping, tand, Prony-Parameters

Hi

I'm trying to simulate the rolling resistance of a thermoplastic polymer wheel.
Because of less material information (only mechanical loss angle=tand) i tried at first to implement the materialdamping with the rayleigh-law. I used just the stifness-matrix multiplier. The analysis works so far. But when i use two different damping parameters (two-component-wheel) then result a negative rolling resistance. That makes no sense to me. Do you have a logical answer?

I'm also interestet about using the viscoelastic properties by Prony. Therefore i need to determine the prony parameters. Exist a mathematical coherence between the prony parameters and the machanical loss angle tand?

Thanks a lot for every answer!
:?

2. Interesting project. Are you using FE software to simulate the rolling? Can you elaborate on what you mean with the "Rayleigh-law"? What approach are you taking to determine the rolling resistance of the wheel?

In general, my understanding is that the rolling resistance is strongly dependent on the energy loss (hysteresis) of the material in the wheel. If you get negative rolling resistance that suggests that perhaps the Rayleigh-law is not accurate enough to capture the hysteresis of the thermoplastic material(s) that you are working with.

Instead of using the Rayleigh-law I would first try linear viscoelasticity specified by a Prony series. Yes, if you know the dynamic properties of your material (i.e. the storage modulus and the tan delta) then you can use that information to determine the tan delta response. Some FE software can do this automatically for you, or you can also do it rather easily using Matlab or some other math software.

Best of luck,
Jorgen

3. Junior Member
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Dear Jorgen,

I'm working with Marc 2005. The Rayleigh-law is a velocitiy-dependent damping where the damping-matrix: c=sum{a*[m]+b*[k]} is. To compare the simulated rolling resistance i have some values from literature.

What i know is the tan(delta) and the youngs'modulus, which by less damping is close to the storage modulus. Can you give me a short description of determining the prony parameter with the data i have?

Thanks a lot and sorry about some misspellings!

Mario

4. Hi Mario,

You can find a short description of how to determine the Prony series in this pdf-file.

- Jorgen

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6. AXS
Junior Member
Join Date
2006-06
Posts
5

## Re: Rayleigh Damping, tand, Prony-Parameters

hello

i am a french researcher, and i see on polymerfem.com your question about modelisation of rubber using Marc

From you experimental data, how do you implement it in Marc?

I have the shear modulus vs. frequenci
With it, i am able to calculate the Prony coefficent

but in Msc Marc, i have to imput the prony parameters of the STRAIN ENERGY (and not shear modulus) in large strain

may you help me???

Pierre Perrot
pperrot@estia.fr

7. Since I don't use MSC.Marc very often, can you specify exactly what format the Prony series parameters need to be specified in?

It is likely a simply conversion between the two formats.

- Jorgen

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