You have some long unsupported lengths, and these will tend to large deflections (per force input) at lower frequencies.

Bracing across the corners of your frame will act against the global modes of the structure (like lozenging), but the local modes (like the beams deflecting individually) won't be as strongly affected.

When you add a brace to a beam, you will tend to split modes into two higher frequency modes (with a node where the brace is attached). When you brace half-way along a beam you will disrupt the first flexural mode, but the second flexural mode will be less effected (the S-shape deflection).

It's much easier to add stiffness than effective damping. Adding stiffness reduces deflection and pushes the resonant frequencies up.

Models are helpful, but joints will always reduce their accuracy.