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MODULE 011
VIBRATION MEASURING DEVICES
2Amplification of displacement amplitude (transmissibility of displacement amplitude)
DISPLACEMENT TRANSMISSIBILITY
FROM BASE TO MASS IN BASE EXCITATION
Relative / base
Absolute / base
X
Z
Y
r
For larger values of r the relative displacement and the displacement of the base have the same amplitude.
Hence the device can be used to measure base displacement if the frequency of base displacement is at least
three time the device natural frequency
VIBRATION MEASURING DEVICES - SEISMOMETER
relative displacement Zlim 1
base displacementYr
When r → ∞
Seismometer
For large r (r>3) the relative displacement and the displacement of the base have the same magnitude.
Therefore, a device with a low natural frequency can be used to measure base displacement if the frequency of the
base displacement is at least three times higher than the natural frequency of the device. This device is called
seismometer.
Seismometer measures amplitude of displacement
Inman p. 146
ζ = 0.25
ζ = 0.5
Seismometer range
b
n
Natural frequency of device:
Frequency of base excitation:
b
n
3b
n
For seismometer:
VIBRATION MEASURING DEVICES - SEISMOMETER
k = 500N/mc = 39.7 Ns/m
m = 4.38kg
Base excitation:
x =10cos(50*t)
Half amplitude = 10mmCircular excitation frequency 50 rad/sPeriod 0.126s
seismometer.SLDASM
k = 500N/m
VIBRATION MEASURING DEVICES - SEISMOMETER
6
Steady statehalf amplitude: 12mm
Transient response
Steady state response
Results of time response analysis
VIBRATION MEASURING DEVICES - SEISMOMETER
Results of frequency response analysis
(50rad/s, 12.4mm)
VIBRATION MEASURING DEVICES - SEISMOMETER
8Seismometer Measures base displacement
VIBRATION MEASURING DEVICES - SEISMOMETER
Inman p. 146
can be presented as
2 2 20
1lim 1
(1 ) (2 )r r r
therefore is proportional to base acceleration
What happens when r → 0 ?Solution of the relative displacement
VIBRATION MEASURING DEVICES - ACCELEROMETER
10
Accelerometer
For small r (r< 0.5) the relative displacement is approximately proportional to the base acceleration. This proportionality is best for ζ = 0.7
Therefore, a device with a high natural frequency can be used to measure acceleration. This device is called accelerometer.
Accelerometer measures acceleration
ζ = 0.25
ζ = 0.5
ζ = 0.7
0 0.2
0 0.2
b
n
b n
Accelerometer range
b
n
Natural frequency of device
Frequency of base excitation
b
n
VIBRATION MEASURING DEVICES - ACCELEROMETER
Accelerometer measures base acceleration
VIBRATION MEASURING DEVICES - ACCELEROMETER
Displacement amplitude of mass is proportional to base acceleration.
To prove it we subject a SDOF with natural frequency 100rad/s to base acceleration 5m/s2
and then 10m/s2 with frequency range 0-10Hz. This frequency range satisfies the
requirement: 0 0.2 b n
m=10kg
k=100000N/m
ζ=0.7
m=10kg
k=100000N/m
ζ=0.7
5m/s2 10m/s2
accelerometer.SLDASM
2 ( ) ( )nz t y t
VIBRATION MEASURING DEVICES - ACCELEROMETER
Frequency range 0-10 rad/s
Base acceleration 5m/s2
Frequency range 0-10 rad/s
Base acceleration 10m/s2
VIBRATION MEASURING DEVICES - ACCELEROMETER
Frequency range 0-300 rad/s
Base acceleration 5m/s2
Frequency range 0-300 rad/s
Base acceleration 10m/s2
VIBRATION MEASURING DEVICES - ACCELEROMETER
