How you can see in the picture below, there are 3 signals from 3 piezo accelerometers placed on a oscillating 3D structure. The structure should vibrate only along the z axis (blue track), but there are also some other parasitic vibrations on x and y axis (green and red). The 3 axis are perpendicular to each other. You see that the green track is almost everywhere positive and this makes me think; indeed a vibration signal should be a zero-mean signal. So I'm thinking that this is due to a offset, but if so, the three signals seem to have three different offsets (the blue one will have the smallest one I guess). Is it right or I'm wrong?
Alhtough this answer should be awarded to Pete, because he has spotted it first.
The accelerometer has a sensitivity of 5%, which corresponds to 100[mV/g]. what you are measuring is 0.1[m/s^2], which is about 0.01g. So the actual signal you should be receiving from the piezoelectric accelerometer is about 1[mV], which is quite low.
Now, if you see the oscillations, -particularly for the red signal which are quite clear- if you notice its about 5 full cycles per 0.1[s] (or close). This is suspicioucly close to the 50[Hz] frequency of the electric grid (if you are in the right part of the world). Of course, it could be for other reason's also, because the blue signal also shares that frequency, although the shape is not sinusoidal.
So my guess, this is just noise in the channel from the electrical grid. You might be able to isolate it with some aluminum foil, but then again I am not certain. The reason is that the signal that you try to obtain is very very small.
You are using a piezo electric accelerometer. There are always always always offsets and low frequency noise on a piezoelectric accel. Depending on the charge amp, anything below about 3 hz is meaningless. Just high pass filter the signal to get rid of it. If you need to read below 3 hz then you shouldn't use a piezoelectric. Use mems or piezo resistive in that case.