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?
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