It sounds like a low pass filter is all that is needed. There are several considerations in selecting low-pass cutoff frequencies. Given that you know something about the input (shaker table motion) and the structure, you can select the filter type and bandwidth.
Considering that I don't know anything about your setup, I will quote from Mechanical Vibrations and Shock Measurments, "It is not possible to give generally valid rules for selection of bandwidth".
That being said, here are two potentially invalid rules to consider
- Don't let your filter remove the real thing...the mechanical reasonance of the instrumented structure. You want to capture the strain/deflection of the structure, so the bandwidth must be greater than the -3dB frequency of the structure. If possible, you want seperate the filter and natural frequncy by as much as possible while still achieving the goal of removing noise. This is a balancing act which is custom to each application.
- If digitally filtering, always be mindful of aliasing. Aliasing is when high frequncy content appears as low frequency folded/ghost content due to sampling frequency being below 2*signalFrequency.
There are other guidlines, but start here and return with more questions.