Interpreting the FFT results of a structural vibration problem
If the beam is under the excitation of a sweeping wave, then the peak(s) in the FFT of the response is not necessarily the natural frequency of the beam. As an extreme, if you are exciting the beam with a constant frequency omega, your FFT of the acceleration time history will have a dominant peak at omega.

However, if the beam is under random excitation, or an impulse, the first peak in you FFT will be your natural frequency. And there is a method named "peak-picking method" to find out the natural frequency. Here is a reference for that: Google books