ENG 0310 Design Contest: Base Isolation System

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ENG 0310 Design Contest Base Isolation System
Goal design a spring/dashpot suspension system
to hold a laser as steady as possible on a
vibrating base.
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Important Dates

• Friday, November 14 Submit names of group
  members and team name on paper before 4pm.
  Maximum of 5 students per group.
• Friday, November 21 Submit design and drawings.
• Fabrication can start as soon as the design is
  submitted.
• Monday, December 8 Final demonstration/contest,
  Final reports due.

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Vibration Control Base Isolation
Soft, Springy Mount
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(No Transcript)
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The Christchurch Arts CenterWith and Without
Base Isolation
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Other Suspension Systems (same idea) Keeps
equipment steady while the supports vibrate!
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Cars
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Printed Circuit Board Manufacture
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Everyday examples
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Free vibrations
C

• Vibration occurs at the system-dependent natural
  freqency.
• The oscillations decay exponentially (if
  )
• Initial condidtions x0x(0) and v0 v(0)
  determine the amplitude and phase

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Forced Vibrations Periodic forcing
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Typical Response
Displacement
Time
Transient vibrations xh(t) at the natural
frequency. Depend on I.C. These decay
exponentially with time.
Steady-state Vibrations xp(t) at the forcing
frequency Independent of I.C. These do not decay.
Total response x(t)xh(t)xp(t)
Amplitude of the steady-state vibrations is
(very) large if the forcing frequency is at or
near the system natural frequency.
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The Steady State Response Damped
C
Amplitude X/(F0/k)
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Vibration under base excitation
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Base Excitation
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Base Excitation
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Steady state response
Displacement
Time
Transient vibrations xh(t) at the natural
frequency. Depend on I.C. These decay
exponentially with time.
Steady-state vibrations xh(t) at the forcing
frequency Independent of I.C. These do not decay.
Steady state response
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Amplitude of the steady state response
Isolation
Amplitude X/Y
Amplification
w/wn
Pick a (soft) spring so that (wn)2k/mlt w2/2. Use
light damping
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• Design parameters
• The laser is the Apollo MP2703B Classic Comfort
  Laser Pointer (Figure 2). Its mass is 49 g is
  13 cm long and has a diameter of 1.4 cm.
• The table will vibrate over a range of
  frequencies fw/2p from 0 to 7 Hz, or 0ltwlt14p
  radians/sec. The peak-to-peak amplitude of motion
  for the table is 2Y0.6 cm.
• You must be able to affix your isolation system
  to the square surface of the shake table, which
  has side length 0.3 meters.
• Your laser will project its beam onto a screen
  b1 meter from the table edge.
• When the table is shaken at frequencies of 5 Hz
  or higher, the peak-to-peak amplitude A2X of the
  lasers projection on the screen must be less
  than 0.3 cm. The best designs will hold the laser
  beam to an even smaller displacement
• When the table is shaken at frequencies below 5
  Hz, the peak-to-peak displacement of the lasers
  projection must be less than 2.4 cm.
• Minimize the weight.

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Note on the Spring-Mass Frequency
mg
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Works for any spring system!
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Car Suspension

• Wheel Motion
• Isolation when (wn)2k/mlt w2/2(2pv/L)2/2
• Typical car fn1 Hz wn2p radians/sec
• Isolates for bump-spacing Lltv/ meters. (v in
  meters per second)
• If v25mph10m/sec maximum bump spacing is 7
  meters