Differences between FFT from acceleration, velocity and displacement data of a dynamic system
I have the same problem and I made some simulation and calculations to understand this phenomenon.

Facts:


velocity is an integral of acceleration
displacement is an integral of velocity
sine wave having frequency f is sin( 2*pi * f * t ) where t is time in seconds
integral of sin( n*t ) is -1/n * cos( n*t ) 
double integral of sin( n*t ) is -1/n^2 * sin( n*t )
To make equations cleaner, I'll use k = 2*pi


Calculations:

If you have hypothetical acceleration measurement signal having frequencies 1Hz, 10Hz, 100Hz with equal amplitudes, then:


acceleration: sin(k*t) + sin(k*10*t) + sin(k*100*t)
velocity: -1/(k) * cos(k*t) - 1/(k*10) * cos(k*10*t) - 1/(k*100) * cos(k*100*t)
displacement: -1/(k^2) * sin(k*t) - 1/(k^2*10*10) * sin(k*10*t) - 1/(k^2*100*100) * sin(k*100*t)


So, it seems that:


Both acceleration, velocity and displacement signals have the peaks at the same place: 1Hz, 10Hz, 100Hz
the 10Hz and 100Hz peaks of velocity are lower and the peaks of displacement are MUCH lower that the peaks of acceleration
the 100Hz peak of displacement is 10,000 times lower that 100Hz peak of acceleration


Simulations:

I made short R script which created the acceleration signal above. Then I integrated it (cumulative sum) to get velocity and displacement signals and finally took fft of them. The results verified the calculations