1. Advanced LIGO UK G040060-00-K 1 Blade transmissibility by FEA Justin Greenhalgh, Rutherford Appleton Lab LSC, March 2004 LIGO-G040058-00-K

2. Advanced LIGO UK G040060-00-K 2 Contents Report –Motivation –Background –Results –Next steps Discussion –Is this the right way to go? –Any caveats etc?

3. Advanced LIGO UK G040060-00-K 3 Background Norna (ALUKGLA0010) showed that the isolation in the quads (and triples?) will be OK provided that the internal modes of the different blades are high enough and do not coincide. Ken went on to assert (ALUKGLA0007) that high enough meant about 40 Hz. Picture from Norna. Will the blades give adequate isolation? In particular, will the peaks in transmissibility caused by the internal modes overlap? And what is the effect of the mass of the wire clamps?

4. Advanced LIGO UK G040060-00-K 4 From Norna’s paper:

5. Advanced LIGO UK G040060-00-K 5

6. Advanced LIGO UK G040060-00-K 6 So – find the actual transmissibility of the blades and multiply by the curves above (updated). (Even better, reproduce the curves above PLUS blade internal modes).

7. Advanced LIGO UK G040060-00-K 7 Run through T040024 Modal analysis of reference blade Modal analysis of blade from Conceptual design Harmonic –No damping (cf Norna’s plot) –With damping, various damping ratios Test effect of changing alpha on internal modes Prestress Add wire Effect of wire clamp mass

8. Advanced LIGO UK G040060-00-K 8 T040024 Pretty simple stuff over Christmas Uses ANSYS macro language for ease of “what if” scenarios Simple to write macros so that a command of the form – bf1,.48,.0045,.096,.01,20,1,1000,.050,11 Will find the eigenvalues of a blade 0.48m long, 0.0045 thick,.096 root width, 0.01m tip width, find up to 20 eigenmodes in the range 1 to 1000 Hz, with.05kg wire clamp and 11kg mass.

9. Advanced LIGO UK G040060-00-K 9 T040024 ANSYS will find –Eigenvalues and normal mode shapes –Transmissibility in a given frequency range and linear frequency step

10. Advanced LIGO UK G040060-00-K 10 What equations is the FE solving? Modal analysis Harmonic analysis Damping

11. Advanced LIGO UK G040060-00-K 11 FE equations So, use 1/(2Q) as the damping value in the ANSYS DMPRAT command.

12. Advanced LIGO UK G040060-00-K 12 Modal analysis of reference blade Modal analysis of “reference” blade Frequency has been measured at 55 Hz

13. Advanced LIGO UK G040060-00-K 13

14. Advanced LIGO UK G040060-00-K 14 Modal analysis of blade from Conceptual design

15. Advanced LIGO UK G040060-00-K 15 Effect of adding mass at blade tip 11 kg mass at blade tip

16. Advanced LIGO UK G040060-00-K 16 Harmonic No damping With damping, various damping ratios

17. Advanced LIGO UK G040060-00-K 17 Harmonic – with damping “Zoom in” on peak by specifying restricted frequency range

18. Advanced LIGO UK G040060-00-K 18 Extended frequency range

19. Advanced LIGO UK G040060-00-K 19 Varying damping ratios

20. Advanced LIGO UK G040060-00-K 20 Test effect of changing shape on internal modes

21. Advanced LIGO UK G040060-00-K 21 Varying length and root width - 1

22. Advanced LIGO UK G040060-00-K 22 Varying length and root width - 2

23. Advanced LIGO UK G040060-00-K 23 Prestress With Without Little/no effect, as expected

24. Advanced LIGO UK G040060-00-K 24 Add wire Wire constrained laterally

25. Advanced LIGO UK G040060-00-K 25 Mode shapes Do any of these tie up with this peak?

26. Advanced LIGO UK G040060-00-K 26

27. Advanced LIGO UK G040060-00-K 27

28. Advanced LIGO UK G040060-00-K 28 Effect of wire clamp mass

29. Advanced LIGO UK G040060-00-K 29 Note T040025 Revised dimensions Easy changes allows look at a set of blades NB resolution of peak Results so far

30. Advanced LIGO UK G040060-00-K 30 T040025 - Model

31. Advanced LIGO UK G040060-00-K 31 Resolving the peaks… All three blades are analysed at a background range plus an “zoom” range for each one:

32. Advanced LIGO UK G040060-00-K 32 T040025 – typical results

33. Advanced LIGO UK G040060-00-K 33 Next So far – simply testing out the methods + tools Next – get more detailed/serious –Reference to this group – am I doing anything silly? –Check this method can reproduce Husman results –Get latest blade/wire dimensions –Check transmissibility vs measurements Calum’s thesis? Elsewhere? –Cross check with more detailed FE models (RAJ, MPL, others?) –Explore effect of clamp mass again –Model sloping wires –What other effects to bear in mind?

34. Advanced LIGO UK G040060-00-K 34 Discussion points Reference to this group – am I doing anything silly? Check transmissibility vs measurements –Calum’s thesis? –Elsewhere? Cross check with more detailed FE models (RAJ, MPL, others?) Explore effect of clamp mass again Does this include “Norna’s curves” or do those need to be added in to the results? What other effects to bear in mind?