The stiffness of a structure is best increased by changing the shape of the parts from shapes that allow bending to occur in the part, such as the long flat parts I can see inside the cube, to parts that don't allow bending to occur, such as truss links that form triangle and tetrahedral structures.
Optical mounting should be designed so as to not transfer stress to the mount. There is a design methodology called Exact Constraint design that provides this benefit. If the connection between the cube structure and the optical mount is over constrained, that allows high stress to occur in the optical mount. Change the design to Exact Constraint, and the stress in the optical mount will be reduced.
If you want me to look at this design and offer suggestions, please use File > Archive to create a .wbpz file and attach that after you reply with the version of ANSYS you are using. Also say what CAD system created the geometry. If you imported a Geometry file into SpaceClaim or DesignModeler, put that file in a zip archive and attach that also.
The goal would be to move the modal frequencies above 1400 Hz because after 800 Hz, the PSD magnitude drops rapidly until 2000 Hz.