The Basic Physics of a Shake The Basic Physics of a Shake yyTableTable
Patrick N. Laplace, Ph.D.Research Assistant Professor
UNR LSSL Laboratory Manager
NEES@UNevada‐Reno NEES@UBuffalo NEES@UC San Diego
Shake Table Training Workshop 2010 – San Diego, CA
The classic springThe classic spring--massmass--damperdamperThe classic springThe classic spring massmass damperdamper
Input (ui) Output (uo)
C
MInput (ui) p ( o)
K
M
1. Apply a constant amplitude input (uiopen loop) at varying frequencies.
2 Measure the output (u ) at each2. Measure the output (uo) at each input frequency
3. Plot (uo/ui versus frequency)
Shake Table Training Workshop 2010– San Diego, CA
Replace spring/damper with an Replace spring/damper with an actuatoractuator
Input (ui)
Output (uo)M
1. K is the “oil column stiffness”
2. C is the actuator dampingp g
3. M is the table mass
4. Plot (uo/ui versus frequency)
Shake Table Training Workshop 2010– San Diego, CA
What can we infer from this plot?What can we infer from this plot?What can we infer from this plot?What can we infer from this plot?
Output = Input Output >> Input Output << InputGood!
p p
Not Good!
p p
Not Good!
But I’m running Open Loop
Shake Table Training Workshop 2010– San Diego, CA
g p p
Let’s run in Closed LoopLet’s run in Closed LoopLet s run in Closed LoopLet s run in Closed LoopInput (ui)
+
Output (uo)M
+-error
But I still get this responseresponse
Why?
Shake Table Training Workshop 2010– San Diego, CA
One reason: look at Act. LVDTOne reason: look at Act. LVDTLVDT
M
1. Apply a constant “0.5 g” sine wave at various frequenciesq
2. Measure table displacement
3. Remember, we are still closing the loop with displacementthe loop with displacement
4. Conclusion: LVDT feedback is very small at higher frequencies Other reasons dela phase elocit feedback
Shake Table Training Workshop 2010– San Diego, CA
frequencies. Other reasons: delay, phase, velocity feedback
Now add a specimen on the tableNow add a specimen on the tableNow add a specimen on the tableNow add a specimen on the table
M
SpecimenOil Column
Shake Table Training Workshop 2010– San Diego, CA
Oil Column
What about delay (phase)?What about delay (phase)?What about delay (phase)?What about delay (phase)?
Open loop Closed loop phase Closed loop phase
with specimen
Shake Table Training Workshop 2010– San Diego, CA
What can we do?What can we do?What can we do?What can we do?
Displacement (D)
Velocity (V) = dt(D)
Acceleration (A) = dt(V)
Jerk (J) = dt(A)
Shake Table Training Workshop 2010– San Diego, CA
Feed Forward (Lead Terms)Feed Forward (Lead Terms)Feed Forward (Lead Terms)…Feed Forward (Lead Terms)…
VelocityAcceleration
Displacement
AccelerationJerk
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ResultsResultsResults…Results…
No forward terms
With forward termsterms
Shake Table Training Workshop 2010– San Diego, CA
ButButBut…But…1. Forward Terms are NOT feedback terms
2. Phase and Gain problems still exist for specimens above and below oil-column frequency and the oil column itself
•We can adequately deal with specimens ybelow oil column using notch filters (beware non-linear specimens) and compensation.
•Specimens above oil column are difficult due to phase matching and low system gain
•Oil column can be dealt with using delta-p stabilization
•Why are they called Seismic Tables and
Shake Table Training Workshop 2010– San Diego, CA
not Vibration Tables?
So how do we get D, V, A, and So how do we get D, V, A, and J?J?
Seismologist
1. Records A from accelerometer
2 Pre-filter padding
Shake Table (reference generator)
1. Gets A from student
2 High pass filter2. Pre-filter padding
3. Filtering
4. Integration
2. High-pass filter
3. Integrate for V and D and differentiate for J
5. Baseline correction
6. Post filtering
“E i ”7. “Experience”
8. Repeat?
Shake Table Training Workshop 2010– San Diego, CA
High Pass FilterHigh Pass FilterC l l t Di l t f A l tiC l l t Di l t f A l tiCalulate Displacement from AccelerationCalulate Displacement from Acceleration
Filter cut-in = 1Hz
Filter cut-in = 0.1Hz
Shake Table Training Workshop 2010– San Diego, CA
Differentiate Displacement to get Differentiate Displacement to get A l iA l iAccelerationAcceleration
Conditioned
Unconditioned
Shake Table Training Workshop 2010– San Diego, CA
Conclusions:Conclusions:1. Shake tables and specimens can at a minimum be described by spring-
mass dampers
2 Delay (phase) is partly from the shake table and partly from the controller-2. Delay (phase) is partly from the shake table and partly from the controller-actuator-instrument control loop.
3. Delay (phase) can be dealt with up to a point
4. We haven’t talked about
1. Dealing with specimen resonance
2 Shake table non-linearities2. Shake table non linearities
3. External disturbances (coherence)
4. Friction
5. Mechanical resonances (bowstring)
6. Multiple Tables (Multiple Tables with Actuators)
Shake Table Training Workshop 2010– San Diego, CA
Please rememberPlease remember1. Every Shake Table performs differently
2 Every system has its limitations2. Every system has its limitations
3. We have a set of tools, and each test requires a different combination of these toolsdifferent combination of these tools
4. There is no magic control algorithm that will solve all these challenges (MRAC, MCS, MFAC each work on athese challenges (MRAC, MCS, MFAC each work on a small subset of control problems)
Shake Table Training Workshop 2010– San Diego, CA
3 UNR 43 UNR 4--span bridgesspan bridges3 different control strategies3 different control strategies
MTS Shake table controller Command Generator LabVIEWNational InstrumentsNational InstrumentsMTS STS
Tcp/ip
scramnet
Data AcquisitionSCXI chassis
Multi Core PCChassis
SCXI Tcp/ipTcp/ip
scramnet
Data AcquisitionSCXI chassis Chassis
SCXI Tcp/ip
Realtime HostTcp/ip Host
Tcp/ipTcp/ipTarget
scramnetscramnet
Fiber optic cable
Instrument cables
scramnetscramnet
Control cablesFiber optic cable
scramnetscramnet
Shake TableShake TableShake TableAbutmentActuators
Shake Table Training Workshop 2010– San Diego, CA
Thank you!Thank you!yy
Shake Table Training Workshop 2010– San Diego, CA
