# Viscoelastic Modeling (Transmissibility) - ANSYS

hello, first post here. I seen all the great responses, coupled with the slow responses I usually get from ANSYS support made me register.

Anyways, heres what Im trying to do. I am trying to model a very soft Silicone, which will be used as a vibration damper. I was doing a simple analysis using just the shear modulus, damping ratio, and a completely guessed youngs modulus. It got me a little ways, but not far enough. I would like to model this as a viscoelastic material.

I have read: Prony_Series_Conversion.pdf and am just a little confused. I can get the Transmissibility, T, of the material, which is the ratio of dynamic to loss modulus (G/G) as a function of frequency. Based on that, I took the two relations and divided them. I then created a function F, which is a function of variables g, tau, and constant T.

This eliminates G0 from the equations, giving me 1 equation, 2 unknowns. Initially, I just assumed N = 1, and tried using a Conjugate Graident Method, which tries to minimize the function, I wrote years ago to get the values for tau_1 and g_1. Since I moved everything from one side, the function should have a minimum at 0. From this, I figured I could go back to the G equation, and back substitute for G0.

However, this does not work at all for some reason. I am wondering, how does one choose N? Can we go into a little more detail in the optimization of these constants? I can get G, and G as a function of freq, but like a few other posts Ive read, I cant figure out how to get the Prony constants.

Thanks a lot,

Lets see, when you say N I assume that you are referring to the number of Prony series terms. Is that right? If so, then I would start with N=1, and increase N until I get a reasonable good fit to the experimental data. I would stick with N<10 or so, however.

If you know G and G as a function of frequency, then Abaqus has a built-in tool for determining the Prony series. Based on your post I assume that ANSYS does not 🙁

In that case the document [URL= https://www.polymerfem.com/forums/showthread.php?t=37 ]Prony_Series_Conversion.pdf[/URL] outlines a method for determining the necessary Prony parameters.

Can you explain more why it did not work for you?

-Jorgen

Im not saying that it didnt work, Im just not familiar with the method to solve it. I pulled out my Numerical Recipes to read about the Simplex method. It needs the equations in a linear combination form. It then kind of subtracts the constraints from the domain to obtain a minimzing solution. The equation that were trying to solve is nonlinear.

Im just not sure how to solve both equations, simultaneously for several different frequencies, all at the same time. Is there a reference anywhere to the routines that Abaqus uses?

As you noticed, the term Simplex Algorithm is also used to describe an method to solve a linear programing problem. Here I was refering to the Nelder-Mead Simplex algorithm that can be used to solve non-linear optimization problems.

I dont think it is necessary to write a code from scratch (unless you like that), instead I recommend that you use your favorite math software, e.g. Matlab, Mathematica, MathCAD, python w. scipy, etc.

I dont know if Abaqus gives a reference to the algorithm that they use. I suspect not.

-Jorgen

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