The exact problem is how do I measure vibration in a moving object like a rollercoaster vehicle. Because it accelerates and decelerates the G-forces measured by a vibration sensor using an accelerometer are off since they also include the acceleration of the vehicle. This in contrast to a stationary machine which does not move
To do this, you do in fact want an accelerometer, and then you want to add to it a thing called a "high pass filter".
The reason this will work is that the "rigid body acceleration" you refer to is at a fairly low frequency compared to the vibration you want to measure. Consider your basic roller coaster ride. Going up the first your accelerometer is going to measure 1g in the vertical direction. Then going down the hill, you measure much less than one g in vertical direction, say 0.2g for a few seconds (this is assuming that your accelerometer always stays in vertical direction and doesn't change with the direction of the car). Then at the bottom of the hill, you are measuring more than 1g, say 2.0g, again for a few seconds. So our signal will have a 1 -> 0.2 -> 2.0 g waveform lasting maybe 5 seconds, or effectively 0.2 Hz. Superimposed on top of that is the vibration you want to measure. That will be at a higher frequency, perhaps 10 - 1000 Hz. So if you apply a high pass filter with a 1 Hz cutoff frequency, you'll get rid of the 0.2 Hz rigid body acceleration and keep the 10 - 1000 Hz vibration. The filtering could be done before the recording is made, or you could just record the whole thing and then filter it out later.
Another entirely different option, would be to use a displacement sensor that measures the distance between the car and the track, which will change very slightly as the car vibrates. These types of sensors can be made with a resolution of better than 0.001", so should be able capture to the vibration of interest.
