Why Fourier Transform doesn't show obvious periodicity?
An FFT doesn't necessarily show a fundamental periodicity, but instead spectral periodicities, which might be higher harmonics (or overtones) of the periodicity that you might perceive visually.

Also, some spectral peaks can be hidden under (the windowing artifacts of) a relatively  large enough DC offset.  If you subtract the mean of the data before doing the FFT, these frequency peaks might show up more clearly.