Please provide more details on the geometry and insert an image into your reply.
A Modal analysis must have all the mass in the model, so you should not remove the bolts from the simulation unless you replace their mass with a point mass.
A Modal analysis is a Linear analysis so you must use linear connections between the thin plate and the larger plate. You can use four Fixed Joints to connect a hole in the thin plate with a hole in the larger plate. Create a Remote Point at each hole center that you can use for the Fixed Joint and the Point Mass.
Instead of meshing the thin plate with SOLSH190 elements, I recommend you edit the Geometry and create a midsurface and mesh the surface with shell elements.
If you must use a SOLSH190 element, you must apply a mesh method called Sweep and set it up as shown below.
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