Finite Element Analysis of Silica Ribbons and Dumbbell Fibres

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Finite Element Analysis of Silica Ribbons and
Dumbbell Fibres

• Iain Martin
• Summer Student IGR

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Overview

• Ribbons
• Comparison between violin and torsional modes in
  Advanced LIGO ribbons
• Effect of tension
• Dumbbell fibres
• Violin modes in Advanced LIGO dumbbell fibres
• Flexing in ribbons and dumbbells
• Future work

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Advanced LIGO Ribbon - Violin Modes

• 60cm by 1.13mm by 113mm ribbon, supporting 10kg
  mass
• Violin modes in both dimensions, occur at similar
  frequencies (when under tension)
• First violin mode 493 Hz
• Frequencies in thin dimension agree with those
  predicted by treating ribbon as string

493 Hz
986 Hz
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Advanced LIGO RibbonTorsional Modes

• Torsional Modes twisting of ribbon, viewed thin
  end on
• Occur at 1.59 multiples of fundamental violin
  mode for this ribbon under this tension
• First torsional mode at 786Hz

786 Hz
1563 Hz
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Relationship of Tension and Torsional/Violin Mode
Frequencies

• Relationship of torsional and violin modes is a
  function of tension on ribbon
• Mode frequencies converge as tension increases.

Adv LIGO Tension
Breaking point
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Advanced LIGO Dumbbell

• End section
• L 10cm, r 190mm
• Middle section
• L 40cm, r 359mm
• Higher frequency modes than Advanced LIGO ribbon
• First violin mode at 630Hz
• First non-violin mode is torsion at 6kHz

630Hz
1060Hz
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Point of Flexure

• FE analysis
• Ribbon/fibre modelled under tension, fixed at top
• Transverse force applied at base of ribbon
• Theoretical flexing point given by
• 0.32mm for ribbon
• 3.1mm for dumbbell
• FE shows dumbbell flexing point further from
  attachment than for ribbon in agreement with
  theory

Adv LIGO Ribbon
Adv LIGO Dumbbell
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Conclusion

• Violin and torsion mode separation decreases with
  increasing tension at high tension, tend to
  same frequency.
• For Advanced LIGO parameters, dumbbells have
  higher frequencies than ribbons
• Flexing which is better?

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Future Work

• Experimental verification of the
  tension-torsion/violin frequency relationship
• Calculate torsional modes in ribbons analytically
  compare to experiment and FE
• Extend FE modelling to more complex cases e.g.
  ribbon-ear system

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