Fig 1. Basic Upper structure with first mode at 204 Hz, mesh contains 62000 nodes and 26000 elements, Constrained in 14 places around the top face.

Fig 2. Above view shows raised pads for fixed supports around the top face.

Fig 3. Addition of ring (ledge) around the top of the structure for the purposes of clamping, above view shows raised pads for fixed supports surrounding the top ring.

Fig 4. Addition of ring (ledge) around the top of the structure for the purposes of clamping, above view shows close up view of raised pads for fixed supports at the corner of the top ring.

Fig 5. Structure with the addition of a 10mm ring (ledge) around the top face. 1st mode 140Hz. Constrained in 14 places around the ring as shown in figure 3.

Fig 6. Structure with the addition of a 10mm ring (ledge) around the top face, 2nd mode 200Hz characterised by removable truss and channel beam on the lower ring, shown in red, as panting in the z direction. Constrained in 14 places around the ring as shown in figure 3.

Fig 7. Structure with the addition of a 25mm ring (ledge) around the top face. 1st mode 153Hz. Constrained in 14 places around the ring as shown in figure 3.

Fig 8. Structure with the addition of a 25mm ring (ledge) around the top face, 2nd mode 212Hz characterised by removable truss and channel beam on the lower ring, shown in red, as panting in the z direction. Constrained in 14 places around the ring as shown in figure 3.

Fig 9. Structure with increased cross sectional area of non removable truss from 6mm to 8mm. 1st mode 209Hz. Constrained in 14 places as shown in figure 2.

Fig 10. Structure with increased cross sectional area of non removable truss from 6mm to 8mm and the addition of a 25mm ring (ledge) around the top face, 2nd mode 213Hz. Constrained in 14 places around the ring as shown in Fig 3.

Fig 11. Structure with increased footprint of gussets on the fixed truss with mass removed (something like a triangulated I beam). Constrained in 14 places around the top face (no ring) as shown in figure 2, 1st frequency 208Hz.

Fig 12. Structure with increased footprint of gussets on the fixed truss with mass removed (something like a triangulated I beam) and an additional ring (ledge) constrained in 14 places around the ring as shown in figure 3, 1st frequency 214.5Hz.

Fig 13. Structure with additional plates on the fixed trusses and reduced footprint of gussets, 1st frequency 214Hz.

Fig 14. Structure with the addition of the top ring (ledge) without the implementation ring, 1st mode 223.2 Hz.

Fig 15. Structure with the addition of the top ring (ledge) and extra plates on the fixed trusses, with the implementation ring and tablecloth removed, 1st mode 266 Hz.