convert damping values in frequency domain to transient damping (generalized maxwell model)

[engsea]

I have the individual damping values ( kN.s/mm ) / frequency for an isolator pad used in a vibro-hammer.
For the steady state solutions the isolator is modeled as a spring in parallel with a dashpot with the correct damping for the frequency under consideration.

The non-linear damping in the initial startup of the system ( transient case ) can not be specified per frequency.
After going through some theory about viscoelasticity the idea is now to model the time domain damping as a generalized maxwell model.

However most of the papers are dealing with FEM viscoelastic material models ( storage modulus , loss modulus prony series ).
I'm not using FEM and just need the ( time domain equivalent ) generalized maxwell model parameters based on the given frequency damping values of the isolator pad.

Is it a good idea trying to implement non linear damping in the time domain by means of a generalized maxwell model of springs and dashpots, or am I on the wrong track ?
I would appreciate some help or links to websites, papers .. anything what can help me to estimate the parameters of the springs/dashpots based on the provided damping/freq values.

 

[GregLocock]

I haven't done it exactly like that but I'd just build the Maxwell model and fine tune it iteratively to give the right frequency domain behaviour, rather than trying to calculate values directly.

https://en.wikipedia.org/wiki/Standard_linear_solid_model#Maxwell_representation

is a good intro.

Cheers

Greg Locock


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[GregLocock]

https://en.wikipedia.org/wiki/Maxwell_material

is better

Cheers

Greg Locock


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[engsea]

Indeed new here.

I'm not a student writing a thesis or so, I have 35+ years experience in pressure vessel and structural calculations and knew this forum from my past as a pressure vessel designer.
This is the first time that I have a vibrohammer hanging in a structure and need to find a way to derive equivalent 'static' design loads for use in my expertise domain, structural design.

After some googling/studying, viscoelasticity and generalized maxwell model seemed the best option for the frequency dependent damping in the time domain.
Searching for viscoelasticity on eng-tips lead me to this forum.

I'm not a specialist in vibration or acoustics and apologies if this post does not belong here and will try to close or delete it.

( BTW thanks for your answer, it's the same as what I was trying to do but then for an N-order maxwell model. )

 

[GregLocock]

There's nothing wrong with the thread, that's just my sig

I'm not sure a simple Maxwell model is appropriate for a typical impact hammer, the tips I used were rubber, nylon or steel, or whatever else came to hand (I have used plasticene or black duct tape if I couldn't find the extra mass that screwed on the hammer head). With the usual setup for a modal analysis you don't need to model the tip.

For rubber and foam and probably nylon I'd use a multi Maxwell type model, with an undamped spring as one of the parallel elements being the main stiffness. ie 2 branches, one is a spring, one is a spring and damper in series. This is similar to a vehicle suspension, in layout.

There are more complex models, but I haven't used them. I think we used a Hammerstein model for foam as in jounce bumpers, but I never set one up.



Cheers

Greg Locock


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[GregLocock]

https://au.mathworks.com/matlabcentral/fileexchange/68710-dma2prony_opt

may be useful

Cheers

Greg Locock


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