MODULE 011
VIBRATION MEASURING DEVICES
1
DISPLACEMENT TRANSMISSIBILITY
FROM BASE TO MASS IN BASE EXCITATION
Z
X
Y
Relative / base
Absolute / base
Amplification of displacement amplitude (transmissibility of displacement amplitude)
2
VIBRATION MEASURING DEVICES - SEISMOMETER
6
5

4
0.1
0.2
0.3
0.4
0.5
0.6
3
When r →
lim
r
∞
relative displacem ent Z
2
1
1
base displacem entY
0
0
1
2
3
4
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
5
r
VIBRATION MEASURING DEVICES - SEISMOMETER
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
ζ = 0.25
Frequency of base excitation:
b
Natural frequency of device:
n
b
For seismometer:
ζ = 0.5
Seismometer range
b
n
Inman p. 146
n
3
VIBRATION MEASURING DEVICES - SEISMOMETER
k = 500N/m
c = 39.7 Ns/m
m = 4.38kg
k = 500N/m
Base excitation:
x =10cos(50*t)
seismometer.SLDASM
Half amplitude = 10mm
Circular excitation frequency 50 rad/s
Period 0.126s
VIBRATION MEASURING DEVICES - SEISMOMETER
Steady state
half amplitude:
12mm
Transient
response
Steady state
response
6
Results of time response
analysis
VIBRATION MEASURING DEVICES - SEISMOMETER
(50rad/s, 12.4mm)
Results of frequency response analysis
VIBRATION MEASURING DEVICES - SEISMOMETER
Seismometer Measures base displacement
8
VIBRATION MEASURING DEVICES - ACCELEROMETER
?
What happens when r → 0
Solution of the relative displacement
can be presented as
Inman p. 146
lim
r0
1
(1  r )  (2  r )
2
2
1
2
therefore
is proportional to base acceleration
VIBRATION MEASURING DEVICES - ACCELEROMETER
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
b
Frequency of base excitation
n
Natural frequency of device
0
Accelerometer range
ζ = 0.5
b
n
 0.2
0   b  0.2  n
ζ = 0.7
b
n
10
VIBRATION MEASURING DEVICES - ACCELEROMETER
Accelerometer measures base acceleration
VIBRATION MEASURING DEVICES - ACCELEROMETER
Displacement amplitude of mass is proportional to base acceleration.
 n z(t )  y (t )
2
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   b  0.2 n
m=10kg
m=10kg
k=100000N/m
k=100000N/m
ζ=0.7
ζ=0.7
5m/s2
accelerometer.SLDASM
10m/s2
VIBRATION MEASURING DEVICES - ACCELEROMETER
Frequency range 0-10 rad/s
Frequency range 0-10 rad/s
Base acceleration 5m/s2
Base acceleration 10m/s2
VIBRATION MEASURING DEVICES - ACCELEROMETER
Frequency range 0-300 rad/s
Frequency range 0-300 rad/s
Base acceleration 5m/s2
Base acceleration 10m/s2