1. 1 FEA of Towers for Dome C JL Dournaux / JPh Amans GEPI, Pôle Instrumental - Paris Observatory jean-laurent.dournaux@obspm.fr

2. 2 FEA of Towers for Dome C  Means to increase tower’s stability  Mechanical behaviour of steels at low temperatures  Description of the models used for simulation  Results on nominal solutions  Purposed solutions to improve stability of truss tower

3. 3 How to increase tower’s stability (Hammerschlag et al., 2006)  Active methods consume power and can generate heat  Some passive methods are: Eigenfrequencies of towers > 10 Hz  Energy in the wind variations decreases quickly between 1 and 10 Hz Only plane motions of the platform parallel to the ground (i.e. no rotations x or y)  Astronomical objects are far away  But Changes in tower’s design have to keep the centre of the tower free to lift the telescope

4. 4 Aim of the study  Preliminary FEA of 2 concept towers designed by JP Amans (GEPI, Paris Observatory)  Check the stability of these concept towers  Improve performances of these 2 concept towers Truss Tower“Amans” Tabouret Tower (ATT)

5. 5 Mechanical Behaviour of Steels at low temperatures  E increases slowly when T decreases  Small differences in E values between summer (-30°C) and winter (-80°C) For a C steel: 207 / 210 GPa For a stainless steel: 168 / 174 GPa  Ductility decreases strongly when T decreases 5 Stainless Steel / 6 C Steel (Thermeau, 2004)

6. 6 Models Description  Containers and platform are not modelled  Boundary Conditions: Tower’s feet are fixed Mass applied on the top of the tower: 100 t  No rotation between tubes (joints)  No thermal gradients

7. 7 Dynamic behaviour of truss tower ModeFréquenceRxRyDescription du mode N°(Hz)Fraction 15,16 / 5,2047,7% Flexion 1er ordre / 25,16 / 5,2047,7% Flexion 1er ordre / 317,6 / 17,720,0% Torsion / 418,54 / 18,680,0% Ouverture sommet 521,16 / 21,311,7% Flexion 2e ordre / 621,16 / 21,311,7% Flexion 2e ordre / 721,57 / 21,730,0% Traction Compression /  Tube 300x5, C steel  Small differences of dynamic behaviour in summer and in winter: frequencies variations < 0,1 Hz

8. 8 Dynamic behaviour of truss tower  Tube 300x5, stainless steel  Small differences of dynamic behaviour in summer and in winter: frequencies variations < 0,1 Hz ModeFréquenceRxRyDescription du mode N°(Hz)Fraction 14,64 / 4,7347,7% Flexion 1er ordre / 24,64 / 4,7347,7% Flexion 1er ordre / 315,85 / 16,130,0% Torsion / 416,70 / 16,990,0% Ouverture sommet 519,05 / 19,391,7% Flexion 2e ordre / 619,05 / 19,391,7% Flexion 2e ordre / 719,43 / 19,780,0% Traction Compression /

9. 9 Dynamic behaviour of truss tower  The following results are for a Carbon steel @ -80°C  The 1st modes @ 5,2 Hz harm because they create a strong rotation of platform  Change tower’s design to increase these frequencies and reduce the rotation they produce

10. 10 Dynamic behaviour of truss tower  Different kind of add-ons are tested  The most efficient is obtained by reinforcing the corners of the tower in all directions  Reinforce only the 2 first floors allows to increase the frequency @ 5.3 Hz. The rate of rotation is almost not affected

11. 11 Dynamic behaviour of truss tower  Increase tube diameter of the 2 firsts floors allows to improve tower’s performances DiamètreEpaisseurSection M (t) Modes 1+2 mm cm² Fréq moy (Hz)ΣRx (%)ΣRy (%) 300523,419,85,3193,4% 508323,919,95,4293,1% 508539,722,26,3190,9% 1016579,628,17,6385,1% 10168127,234,08,3179,8%79,7%

12. 12 Dynamic behaviour of Amans Tabouret(Stool) Tower  Tubes 1016x4 & 291x3  Modes 1/2 & 4/5 harm  Eigenfrequencies are lower than for truss tower but the platform is more stable ModeFréquenceTxTyTzRxRyRz N°(Hz)Fraction 13,800,8%52,3%0,0%59,0%0,9%0,0% 23,8052,3%0,8%0,0%0,9%59,0%0,0% 36,410,0% 67,0% 46,5125,7%0,1%0,0%0,1%16,4%0,0% 56,510,1%25,7%0,0%16,4%0,1%0,0% 69,380,0% 2,3%

13. 13 Dynamic behaviour of ATT  Tower’s performances seem to be less sensitive to tube diameter than Truss Tower ǾEp.Section M (t) Modes 1+2 Modes 4+5 mm cm² f moyΣRx (%)ΣRy (%)f moyΣRxΣRy 1016463,732,43,8060,0% 6,5116,4% 10168127,262,63,6861,3% 6,3014,0% 15248191,193,14,5670,1% 8,217,3%

14. 14 Conclusions  Results: Add appropriate add-ons and increase diameters of vertical tubes of first floors may allow to obtain 1st modes of truss tower beyond 10 Hz Platform’s rotations are weaker for ATT but eigenfrequencies too  Next steps: Test other concept tower(s) Master student (Calculate transfer function to precisely determine wind effects by FEM, implement methods for vibration control, define a prototype…) in collaboration with Pr André Preumont (ULB/INSA Lyon)