  Aims. We studied the manifestation of decayless oscillations in 3D
simulations of coronal loops, driven by random motions. Methods. Using the
PLUTO code, we ran magnetohydrodynamic (MHD) simulations of a straight
gravitationally stratified flux tube, with its footpoints embedded in
chromospheric plasma. We consider transverse waves drivers with a horizontally
polarised red noise power-law spectrum. Results. Our broadband drivers lead to
the excitation of standing waves with frequencies equal to the fundamental
standing kink mode and its harmonics. These standing kink oscillations have
non-decaying amplitudes, and spectra that depend on the characteristics of the
loops, with the latter amplifying the resonant frequencies from the drivers. We
thus report for the first time in 3D simulations the manifestation of decayless
oscillations from broadband drivers. The spatial and temporal evolution of our
oscillation spectra reveals the manifestation of a half harmonic, which
exhibits half the frequency of the identified fundamental mode with a similar
spatial profile. Our results suggest that this mode is related to the presence
of the transition region in our model and could be interpreted as being the
equivalent to the fundamental mode of standing sound waves driven on pipes
closed at one end. Conclusions. The potential existence of this half harmonic
has important implications for coronal seismology, since misinterpreting it for
the fundamental mode of the system can lead to false estimations of the average
kink speed profile along oscillating loops. Finally, its detection could
potentially give us a tool for distinguishing between different excitation and
driving mechanisms of decayless oscillations in observations.
