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.

## Answer:

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.