  The relatively large-amplitude decaying regime of transverse oscillations of
coronal loops has been known for two decades and interpreted in terms of MHD
kink modes of cylindrical plasma waveguides. Recent observational analysis has
revealed the so-called decay-less small-amplitude oscillations, with a
multi-harmonic structure being detected. Several models have been proposed to
explain them. In particular, decay-less oscillations have been described in
terms of standing kink waves driven with continuous monoperiodic motions of
loop footpoints, in terms of a simple oscillator model of forced oscillations
due to harmonic external force, and as a self-oscillatory process due to the
interaction of a loop with quasi-steady flows. However, an alternative
mechanism is needed to explain the simultaneous excitation of several
longitudinal harmonics of the oscillation. We study the mechanism of random
excitation of decay-less transverse oscillations of coronal loops. With a
spatially one-dimensional and time-dependent analytical model taking into
account effects of the wave damping and kink speed variation along the loop, we
consider transverse loop oscillations driven by random motions of footpoints.
The footpoint motions are modelled by broad-band coloured noise. We have found
the excitation of loop eigenmodes and analysed their frequency ratios as well
as the spatial structure of the oscillations along the loop. The obtained
results successfully reproduce the observed properties of decay-less
oscillations. In particular, excitation of eigenmodes of a loop as a resonator
can explain the observed quasi-monochromatic nature of decay-less oscillations
and generation of multiple harmonics detected recently. We propose the
mechanism that can interpret decay-less transverse oscillations of coronal
loops in terms of kink waves randomly driven at the loop footpoints.
