Getting non smooth spectrum after performing fft on numerically obtained acceleration data
Most of the time, a non-parametric PSD estimation based on FFT alone (called a Periodogram) will provide a random looking spectrum of the numerical data.

To reduce those random variations, or to get a smoother looking estimate, you can do one of the two things:


Use Periodogram averaging such as Welch's method.
Use a model based parametric PSD estimate instead.  


Note that the first approach will trade-off spectral resolution for reduced variance, whereas the second method will be high resolution but requires a consistent knowledge of the associated physical model of the process.