You say the beam is “resting” on a nonlinear spring.  Is the beam fastened to the nonlinear spring or is there also nonlinear contact so that the beam can lift off the nonlinear spring?

Is there a static preload such as gravity?

If the beam is fastened to the nonlinear spring, you could linearize the spring and obtain preliminary results using a MSUP Harmonic Response analysis.  The results may be helpful in the next analysis.

To accommodate all nonlinearities in the model, you will have to run Transient Structural multiple times. This will be tedious because you will have to edit the load to create a sinusoidal acceleration vs time input at the correct frequency and amplitude for each point on the frequency plot. Some rules are you need at least 20 values per cycle to represent the input and you will need hundreds of cycles to allow the transient response to die out so that all that you are left at the end time is the harmonic response. To ensure the transient response dies out, you must have damping defined in the model.