Estimating the Torsional Stiffness of a 3D Elastic Support

[gs00350]

Homework Statement

Hi,

I am trying to model the configuration seen below analytically in order to determine the natural frequency of the upright post.
The post is made from Aluminium (E=73e9) and the surrounding interface layer is made from an acrylic (0.5e9).

To model the elastic support of the interface layer I am considering using a torsional spring support, but I have no idea how to approximate the torsional spring stiffness of the 3D interface layer. I have tried multiplying the surface area of the interface by the Young's Modulus to get a quantity in N/m (i.e. stiffness) , but this still seems to give me natural frequencies that lie far away from my experimental data.

Is this a legitimate approach? Or is there a better way of estimating stiffness of such a structure?

Relevant Equations

Interface Thickness = 0.38mm
Interface Minor Diameter = 4mm
Interface Major Diameter = 4.76mm
Height of Interface Layer = 9mm
Interface Modulus = 0.5e9
Post Modulus = 73e9

 

[Lnewqban]

I would say, being wrong perhaps, that it will be easier for the post to tilt than to move sideways while remaining vertical.
Think of CM (center of mass) of post times lever respect to ring, if the schematic is proportional to the actual thing.
If that assumption is true, then the acrylic ring or bushing would be weaker to resist the tilting oscillation, as only mainly top and bottom sections would be working hard.

 

[Chestermiller]

Well, the first thing to do is neglect the deformation of the aluminum. Assume it is rigid.