Random vibration with rubber parts

[Anonymous]

I have a cylindrical container that is support by rubber (hyperelastic) o-rings inside a pipe. The pipe is under going random vibration. The rubber o-rings serve as a vibration isolator (dampener) for the cylindrical container. I was able to determine the first 10 natural frequency modes using Mechanical Simulation non-linear natural frequency analysis. Now I want to do a non-linear random vibration analysis but there is no such choice under non-linear. There is such a choice under linear but as expected the analysis failed do to improper material usage (i.e. rubber is non-linear).

1. Is there a way to do this in Mechanical Simulation?

2. There is a large industry dependent upon rubber vibration isolators. How do they do their non-linear random vibration simulations?

Regards, Dan

[AstroJohnPE]

Hi Dan,

I recall reading a white paper many years ago that described how to transform the random vibration input into a series of displacements for an MES analysis. Or it might have been a response spectrum. You might be able to find it by searching the internet for the key words. I believe this paper was written prior to Autodesk's acquisition of Algor, and I do not know if the paper was revised to the Autodesk letterhead, so you might want to include Algor in the search.

Otherwise, you should look at the stress-strain curve for the material to determine how linear or nonlinear the material may be over the range of stresses to which you will subject it. Even if the material is "nonlinear" over a wide range, it can be analyzed as linear if the material is operating in a "linear" portion of its stress-strain curve.

Also, keep in mind that the "nonlinear" natural frequency is not a nonlinear analysis. Since the natural frequency analysis has no loads, the displacements are "not real". Without displacement, there is no strain. Without strain, there is no way to know where the material is operating at on the stress-strain curve. "Nonlinear" natural frequency only uses the stiffness of the material under 0 load. The capability is provided only for the convenience of calculating some frequencies without needing to change the analysis type, material model, and material properties from nonlinear to linear. Or another way to think of it is that the software "converts" the nonlinear properties to linear properties for you, and then runs the linear modal analysis.

[Anonymous]

John,

I understand the natural frequency calculation is independent of loads (thus strain) but isn't the natural frequency based on the "stiffness matrix" (and mass) and since rubber has a non-linear stiffness isn't the "stiffness matrix" non-linear?

I googled for the white paper but I couldn't find it. Your idea of transforming the random vibration input into a series of displacements and analyzing as linear if the rubber is operating in a "linear" portion of its stress-strain curve seems like it could work. I'm not that adept at FEA vibration so the above sounds somewhat involved, time consuming, and prone to errors. I would have to do some simple simulations to validate this procedure but I just don't have the time at the moment. Building a prototype and testing it on a shake table seems quicker.

Thanks for your reply, Dan

[AstroJohnPE]

No. The stiffness matrix has to be linear for the natural frequency analysis. It is based on the stiffness in the no load condition.

[Anonymous]

Hi John,

Thanks for the clarification, Dan