Vibration Monitoring Quantities

## Question:

Dear Sir,

My name is *******, a Civil Engineer, part of my job is Monitoring the Vibration on the structures using sensors. I have some query on the relation between the "peak particle velocity" and "amplitude". I am just wondering is there any relation or formulae to find out the amplitude from the Peak Particle Velocity measurement? I would greatly appreciate, if you could advise me.

Structural vibration monitors typically measure instantaneous acceleration by means of some sort of inertial sensor and integrate that data over time to produce a velocity signal. Integrating the velocity signal over time produces a displacement signal. One half the difference between the maximum and minimum displacement is taken to be the amplitude.

I am a bit confused by your "particle velocity" terminology. The velocity measured as I described above is not the velocity of the individual atoms or molecules of the structure but the velocity of the center of mass of that part of the structure to which the vibration sensor is attached.

Assuming that we are talking about the sort of vibration monitoring I described, the relationship between peak velocity and amplitude is not given by a simple formula. Even if the motion of the structure was simple harmonic motion, we would have to know the magnitude of the restoring force to make the connection between peak velocity and displacement. In that case you could equate the kinetic energy at the peak velocity to a potential energy as the peak displacement and solve for amplitude. In real structures, the motion is much more complex than simple harmonic motion and restoring forces tend to be non-linear. This real world complexity defeats any attempt at simple mathematical analysis.

Some vibration monitors offer the option of reading out amplitude, as well as velocity and acceleration, using the integrating technique I described above. The Bently Nevada corporation issues a little publication called "Orbit" in which they include bits of theory in their commercial message. Perhaps you would find more information there.

If you can get a graphical printout of velocity vs time from your monitoring equipment, you can do the integration yourself in a crude way by dividing the plot up into time slices and physically measuring the area under the curve. A plot of the area vs time will approximate the displacement function, revealing the peaks which are the amplitude.