The first thing you need to specify is the range of the accelerometer. A beam fixed on one end and excited will vibrate in only one axis, so a tri-axis is not required. Why waste sampling time on sensors that don't report useful data? You will need fast sampling to reproduce the motion of the beam. The maximum sample rate for a Uno is,ideally, about 9KHz for one channel (you can go faster with some degradation of accuracy). That puts the Nyquist frequency about 4.5KHz (one channel, 1.5KHz for 3) . Will the beam vibrate at a lower frequency than 4KHz?
If so then the Arduino could be fast enough, one channel only, if there is very little that has to happen between samples. Where is the data going to be stored? The Uno has 2K of SRAM. With out any overhead from the controlling program that's 1000 samples (300 per channel for 3).
Can you specify the properties of the beam and how it will be excited? Like material, dimensions, etc. You going to whack it with a hammer or stress and release, or...? You also need to look at the frequency response of the accelerometer to make sure it will be accurate at the frequency of the vibrating beam. The MMA7260 mentioned in a prior post is 3dB down at 350Hz.