Modal Frequences

[mike0123m]

I have some questions regarding a beam with two points a and b. The acceleration in one direction is recorded at 20 samples per second for 5 minutes. How can I determine if the two points are moving in the same direction or opposite direction in a given mode? How do you determine the relative magnitude of motion at the two points and generate a mode shape? Any ideas?

 

[MiketheEngineer]

You might want to try the "Mechanical Acoustics/Vibration"
forum

 

[271828]

You'd have to use experimental modal analysis techniques to really pin that down because you said "in a given mode."

Put an accelerometer at Point A and Point B. Then apply a measured force (usually from an instrumented impulse hammer or from a shaker with a force transducer) to the beam either at A, B, or somewhere else. The point is that you don't want to apply the force at a location that the beam isn't moving--a so-called "node" in the mode shape you're interested in.

With the measured time domain signals for the force and accelerations, you can compute the FRF, which is the ratio of the output (acceleration) to the input (force). It's a complex number with a real and imaginary part at each frequency.

The magnitude of the FRF is just that, a magnitude, so it doesn't tell you anything about the direction. The real part of the FRf crosses zero at natural frequencies, so it doens't help either.

However, the imaginary part of the FRF at a natural frequency indicates mode shape amplitude and direction. Look at the imaginary parts of the FRF for Point A and Point B. If these two numbers are the same sign, then the mode shape is such that both points are going in the same direction and by how much (relative to each other).

 

[271828]

Just read my post and something needs clarification.

You'd measure two FRFs, one for the accel at Point A and one for the accel at Point B, both for the SAME input force. (Doesn't have to be the same test, but the force has to be in the same place.) View the imaginary parts at f = fn of these two FRFs to see whether they're both of the same sign.

For example, if at f = fn,
Im(FRFA) = 0.3 V/V and
Im(FRFB) = -0.6 V/V,

then you know the mode shape with frequency fn has Point B moving twice as much as Piont A, and in the opposite direction.

 

[mike0123m]

Thanks, 271828. Your explanation helped a lot!

 

[271828]

If you want to know if Point A and Point B are moving in the same direction, but don't care about this or that mode, then you can put an accelerometer at each location, excite the beam, and just look at the a vs t plots for both locations.

If the waveforms lay on top of each other or are of the same sign, then that tells you they're going in the same direction. If one's at a max while the other's at a min, then they're going the opposite directions.

This is a haphazard way to look at it, though. EMA is the only real way do get a good look at what's going on.