Vibration and isolation

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Vibration and isolation
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Seismic isolation

• Use very low spring constant (soft) springs
• Tripod arrangement used for mounting early AFMs
• Had long period (rigid body) vibration but
  isolated above resonance
• Large supported mass also lowers resonance
• Measure with accelerometers, one for each
  direction

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Optical table legs

• Same basic idea low spring constant support
• Table will tilt as a whole but not transmit floor
• (seismic) vibration
• Table will couple through electric wires, etc.
• Equipment on table sensitive to acoustic vib.
• Suspension becomes unstable if CG too high
• Must use three active legs and one slave
  otherwise unstable

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Coupled vibration

• Good and bad electric cables bad
• Coupling interferometer to mirror under test is
  good
• Both vibrate together (in phase) so fringes still
• Nice animation in references of coupled masses
• Gives idea of multiple modes in solids
• This is a one D model but can see effect in other
  D
• Simulate in lab with sample of different springs
  and masses

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Acoustic vibration

• Sound (acoustic vibration) is air pressure waves
• Transmitters (vibrating plates - speaker cones)
  are also good receivers
• Decrease coupling by putting holes in plates
• Making plates of damped materials (lead sheet)
• Acoustic coupling often not recognized for what
  it is
• Need a sound pressure sensor (microphone not
  accelerometer)

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Resonances and stiffness

• Cantilever wire (rod) off speaker cone
• Note fundamental and higher modes
• Note how sharp the resonance is, high Q
• Use resonance, length and diameter to find E
• Also, clamp wire as cantilever, add small weight
  measure deflection and calculate E
• Do two methods give about the same value for E

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Torsional rigidity

• For solid of uniform circular cross-section, the
  torsion relations are
• T/J GF/l
• where
• F is the angle of twist in radians.
• T is the torque (Nm or ftlbf).
• l is the length of the object the torque is being
  applied to or over.
• G is the shear modulus or more commonly the
  modulus of rigidity and is usually given in
  gigapascals (GPa), lbf/in2 (psi), or lbf/ft2.
• J is the torsion constant for the section .
• the product GJ is called the torsional rigidity.
• Applying small torque difficult so measure
  frequency and find G

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Kinematic stackups

• Problem illustrated by convex test plate
• Measure frequency of vibration (rocking)
• From geometry of part is this reasonable?
• Would frequency be higher or lower if longer
  radius?
• Nothing is flat so need to make flat to flat
  connections kinematic
• One thing that helps is acoustic damping thin
  air film

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Measurement Schema

• Measurement tools 10x more accurate (or
  sensitive) than tolerance implies confidence in
  measurement
• In optics, measuring accuracy about same as
  tolerance need error separation methods
• Quantum optics act of measuring changes result

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Symmetry and reversal
Assume f(x) over -1 to 1 To find fe(x) 1/2f(x)
f(-x) fo(x) 1/2f(x) f(-x) Works for
surfaces too fee ¼f(x,y) f(-x,y) f(x,-y)
f(-x,-y), etc
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Centroid and remove rotationally symmetric error
Relative pseudo aberration value 9.51 9.38 1.
56
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Pseudo astigmatism and coma
.75
1.02
.71
.57
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