  Whilst there are observational indications that transverse MHD waves carry
enough energy to maintain the thermal structure of the solar corona, it is not
clear whether such energy can be efficiently and effectively converted into
heating. Phase-mixing of Alfv\'en waves is considered a candidate mechanism, as
it can develop transverse gradient where magnetic energy can be converted into
thermal energy. However, phase-mixing is a process that crucially depends on
the amplitude and period of the transverse oscillations, and only recently have
we obtained a complete measurement of the power spectrum for transverse
oscillations in the corona. We aim to investigate the heating generated by
phase-mixing of transverse oscillations triggered by buffeting of a coronal
loop that follows from the observed coronal power spectrum as well as the
impact of these persistent oscillations on the structure of coronal loops. We
consider a 3D MHD model of an active region coronal loop and we perturb its
footpoints with a 2D horizontal driver that represents a random buffeting
motion of the loop footpoints. Our driver is composed of 1000 pulses
superimposed to generate the observed power spectrum. We find that the heating
supply from the observed power spectrum in the solar corona through phase
mixing is not sufficient to maintain the million degree active region solar
corona. We also find that the development of Kelvin-Helmholtz instabilities
could be a common phenomenon in coronal loops that could affect their apparent
life time. This study concludes that is unlikely that phase-mixing of Alfv\'en
waves resulting from an observed power spectrum of transverse coronal loop
oscillations can heat the active region solar corona. However, transverse waves
could play an important role in the development of small scale structures.
