Periodicities in O and Fe galactic cosmic particles at different energies as observed by the ACE satellite between 1997 and 2019 have been analyzed using various spectral analysis techniques. Daily mean energetic particle measurements are used to identify how several harmonics of the ~ 27-day synodic rotation period change during each individual year. Lomb-Scargle and Morlet wavelet spectral analysis of galactic cosmic particle data at different energies revealed in particular that the fourth harmonic (~7-day) of the solar rotation period occurs exceptionally strong during the minimum of solar cycle 23 (2008, 2009) when A< 0 (solar dipole pointing South) in comparison to the minimum of cycle 24 (2018,2019) when A> 0 (solar dipole pointing North). We report the presence of both the Rieger (~ 156 days) as well as the ~ 1.3-year periodicity in O and Fe GCR particles at various energies ranging from ~ 80 MeV/n to ~ 500 MeV/n.