I am happy to help, but it will take time to get to a model that reproduces this paper. There is a lot you can show the professor even today, all the issues you have learned about.
I think the fastest path to success is the 3D shell model. You need to have some basic skill in SpaceClaim to do that, such as using the Mirror button to reflect surfaces about the center of the unit cell and using the Move tool, holding the Ctrl key to make a copy to stack up 3 layers.
I was thinking about the 4 columns in the array. It seems to me that those are just springs in parallel. Since you are constraining the left and right edges with an X=0 support (frictionless), what is added by having 4 columns? The original paper had 5 columns and 4 layers. If you have no left and right edge support, then there is a difference between 1 column and 5 columns. But with a left and right edge support, there should be no difference between 1 and 4 columns, except the mass will be 4 times larger on the 4 column model than the 1 column model. However the 1 column model will solve 4 times faster!
I recommend you build a 1 column 3D shell model. You could even build a 1/2 cell model, and cut the mass in half again, but it would not look as nice as the full cell.
Use a Fixed Joint, Behavior = Rigid, to hold the 5 edges that come together at the top of the unit cell. The five edges are the left/right flat flexures, the left/right curved flexures and the horizontal thick frame, which is also a shell model with an edge at the center. Do the same at the bottom where 3 edges come together. Use a Fixed Joint at sides of the frame to hold the outer end of the flat flexures.
The top bar on the frame should have no extra elements. Simply add a Distributed mass on those elements to apply the needed mass.