  We study the excitation and damping of transverse oscillations in a
multi-stranded model of a straight line-tied coronal loop. The transverse
geometry of our equilibrium configuration is quite irregular and more realistic
than the usual cylindrical loop model. By numerically solving the
time-dependent ideal magnetohydrodynamic equations in two dimensions we show
how the global motion of the whole bundle of strands, excited by an external
disturbance, is converted into localized Alfv\'enic motions due to the process
of resonant absorption. This process produces the attenuation of the transverse
oscillations. At any location in the structure two dominant frequencies are
found, the frequency of the global mode, or quasi-mode, and the local Alfv\'en
frequency. We find that the mechanism of mode conversion, due to the coupling
between fast and Alfv\'en waves, is not compromised by the complicated geometry
of the model. We also show that it is possible to have energy conversion not
only at the external edge of the composite loop but also inside the structure.
The implications of these results and their relationship with the observations
are discussed.
