Thank you for the photos, that really helps to explain what you are trying to model. I agree that the single stud is going to create a cantilever beam support to your test specimen.
It is often the case in simulation where perfect geometry and perfectly aligned loads don't create a result that matches an experimental result. An example is a column under a compressive load in a nonlinear static structural analysis. The column just compresses, but experimentally, it buckles. In order to simulate reality, imperfection in the geometry is introduced and/or the load is applied off-center. You may need to introduce some small amount of imperfection to see Mode 8 appear in the harmonic response results.
The vibration exciter appears to be an electrodynamic shaker and when you put in a sine wave, it will vibrate at that frequency. It's good that you are using it in the vertical orientation. You don't need to include the exciter in your model.
You said you are not using MSUP because you want to model a damped system. MSUP Harmonic Response analysis is always used with damping. The damping controls are in the same place under the analysis settings. The limitation is you can't use Structural Damping and simply provide one input like you did with the full Harmonic Response, but you can insert damping as two values for Mass and Stiffness damping, or a table of values versus frequency.
I recommend you switch to MSUP Harmonic Response, because then you can make the face of the rod a Fixed Support and use Base Excitation as the Harmonic Load. This will more accurately represent the connection of the stud to the shaker.