1. VIBRATION MEASURING DEVICES
MODULE 011
VIBRATION MEASURING DEVICES

2. DISPLACEMENT TRANSMISSIBILITY FROM BASE TO MASS IN BASE EXCITATIONZ X Y
Relative / base
Absolute / base
Amplification of displacement amplitude (transmissibility of displacement amplitude) 2 2

3. VIBRATION MEASURING DEVICES - SEISMOMETER
When r → ∞ 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

4. VIBRATION MEASURING DEVICES - 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
Frequency of base excitation:
ζ = 0.25
Natural frequency of device:
For seismometer:
ζ = 0.5
Seismometer range
Inman p. 146

5. VIBRATION MEASURING DEVICES - SEISMOMETER
m = 4.38kg
k = 500N/m
c = 39.7 Ns/m
k = 500N/m
Base excitation:
x =10cos(50*t)
Half amplitude = 10mm
Circular excitation frequency 50 rad/s
Period 0.126s
seismometer.SLDASM

6. Results of time response analysis
VIBRATION MEASURING DEVICES - SEISMOMETER
Steady state
half amplitude:
12mm
Transient response
Steady state response
Results of time response analysis

7. Results of frequency response analysis
VIBRATION MEASURING DEVICES - SEISMOMETER
(50rad/s, 12.4mm)
Results of frequency response analysis

8. Seismometer Measures base displacement
VIBRATION MEASURING DEVICES - SEISMOMETER
Seismometer Measures base displacement 8 8

9. VIBRATION MEASURING DEVICES - ACCELEROMETER
What happens when r → 0 ?
Solution of the relative displacement
can be presented as
Inman p. 146
therefore
is proportional to base acceleration

10. VIBRATION MEASURING DEVICES - 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
Frequency of base excitation
ζ = 0.25
Natural frequency of device
Accelerometer range
ζ = 0.5
ζ = 0.7

11. VIBRATION MEASURING DEVICES - ACCELEROMETER
Accelerometer measures base acceleration

12. 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:
m=10kg
k=100000N/m
ζ=0.7
m=10kg
k=100000N/m
ζ=0.7
5m/s2
10m/s2
accelerometer.SLDASM

13. VIBRATION MEASURING DEVICES - ACCELEROMETER
Frequency range 0-10 rad/s
Base acceleration 5m/s2
Frequency range 0-10 rad/s
Base acceleration 10m/s2

14. VIBRATION MEASURING DEVICES - ACCELEROMETER
Frequency range rad/s
Base acceleration 5m/s2
Frequency range rad/s
Base acceleration 10m/s2