Dynamic Stiffness and static stiffness in metals 1

[caemagic]

Hello ,

I would like to know whether it is safe to assume that static and dynamic stiffness in metals can be assumed to be the same. Metals , in general have very little damping ,hence both static and dynamic stiffness should not differ am I correct ?
Thank you
caemagic

 

[GregLocock]

Yes, that is a reasonable assumption for steel. Typically in a steel structure most of the damping comes from joints, press fits and impedance mismatch, none of which can be modelled with any great accuracy in a typical model.



Cheers

Greg Locock


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[caemagic]

Thnx greg

 

[electricpete]

I think Greg nailed it in terms of material properties.

I just wanted to mention the term "dynamic stiffness" sometimes has a different meaning. For example in your other post thread384-350920

Certainly dynamic stiffness if we define it similar to a transfer function is a function of frequency (and is different than static stiffness except when we consider dynamic stiffness at zero frequency).

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(2B)+(2B)' ?

 

[caemagic]

Dear electricpete ,

Thank you so much for your reply , I would like to ask whether dynamic stiffness term may have a different meaning , I thought that the dynamic stiffness obtained from the FRF (as greg said) is the theoretical dynamic stiffness? what is the difference between dynamic stiffness obtained from FRF and dynamic stiffness as a material property ?

Thank you so much

 

[electricpete]

E = Young’s modulus is a material property. It depends primarily on the material (the type of steel). It does not depend on the shape built out of the steel. E does not vary with frequency.

k = stiffness
k = F / x = Force over displacement
Depends on the material (E) as well as the shape.
For uniaxial tensile specimen, k = E*A /L
k does not vary with frequency

DS = dynamic stiffness.
According to Harris’ Shock and Vib Handbook, 6th ed:
“Dynamic stiffness is the ratio of the change of force to the change of displacement under dynamic conditions”
DS(w) = F(w) / X(w)
We can see this is an extension of the idea of stiffness.
It depends not only on E and shape, but also on mass present in the system (rho).
Let's look at a discrete version. For undamped SDOF system, the DS might have the form
DS(w) = k – m*w^2
Note it does depends on frequency. It would equal the [static] stiffness k only if we substitute w = 0.


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(2B)+(2B)' ?

 

[electricpete]

It depends not only on E and shape, but also on mass present in the system (rho).

It also could depend on damping in some situations.

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(2B)+(2B)' ?

 

[amanuensis]

Electricpete's explanation is quite correct at first approach, but things are actually more complicated.

The Young's modulus of a material varies with frequency. Its value depends on the temperature and frequency.
But temperature has more influence than frequency.
E always increases with frequency and always decreases with temperature.

 

[GregLocock]

"E always increases with frequency and always decreases with temperature."

Always? For every solid material?

Well, not according to these guys

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=AD0662716

figure 37

But hey what would they know.



Cheers

Greg Locock


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[electricpete]

Sea ice.. you got him there.

I was thinking of responding to point out the op seems to be seeking a basic understanding, not looking for small effects. Nevertheless, I'm sure I should have said Esteel does not vary significantly with frequency, rather than flat out saying it doesn't.

Out of curiosity, how much can Esteel (pick your alloy) vary with frequency?

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(2B)+(2B)' ?

 

[GregLocock]

Quick answer to the non-question on temperature - the properties of a metal will change when the crystal structure changes with temp, and could go either way. That is very closely related to the ice example.

I'm more used to considering dynamic moduli of elastomers as a function of frequency, I can't think of an example where the effective of frequency on dynamic modulus of an engineering metal has made a ha'p'orth of difference.



Cheers

Greg Locock


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[MikeHalloran]

It should be noted that all of the discussion above applies only when the material is below the elastic limit, or yield point stress. Think of it as an upper bound of applicability for the equations given.

Between that limit and the material's ultimate stress, strain rate sensitivity and work hardening, and other nonlinear mechanisms, make analysis more interesting.

Caemagic, if you are modeling a forming operation, explosive forming, or plastic design, your equations will need some adjusting.

Mike Halloran
Pembroke Pines, FL, USA

 

[amanuensis]

It's precisely because E increases with frequency that it is necessary to separate static and dynamic Young's modulus.


Secondly, damping has nothing to do with that.
Damping can be seen in some way as the imaginary part of the complex E.

Greg answered to the non-question of damping in assembled structure whereas the question was to ask if the difference was due to the internal damping of the material.

 

[hacksaw]

just a foot note, some materials properties handbooks will show both a dynamic and a static elastic modulus.

in resolving the critical frequencies of simple structures used simplified elastic modulus estimates we found that the difference between vibrational tests and tensile testing were due to the use of simplified estimates of the natural frequencies and/or imprecise assumptions of the support conditions used in vibration testing.

this was resolved for both ceramics, where simply supported prisms are used ASTM E1876, and metals where "clamped" cantilevers are commonly used for checks of the material properties.

when the material properties and the limitations of the beam equations are taken into account, the modulus developed by tensite testing is the number to use.