VIBRATION MEASURING DEVICES MODULE 011 VIBRATION MEASURING DEVICES

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 2

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

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

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

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

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

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

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

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

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

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