  In this work, we report a theoretical coupled study of the structural and
phonons properties of bundled single- and double-walled carbon nanotubes
(DWNTs), under hydrostatic compression. Our results confirm drastic changes in
volume of SWNTs in high-pressure regime as assigned by a phase transition from
circular to collapsed phase which are strictly dependent on the tube diameter.
For the DWNTs, those results show first a transformation to a polygonized shape
of the outer tube and subsequently the simultaneous collapse of the outter and
inner tube, at the onset of the inner tube ovalization. Before the DWNT
collapse, phonon calculations reproduce the experimentally observed screening
effect on the inner tube pressure induced blue shift both for RBM and
tangential G$_z$ modes . Furthermore, the collapse of CNTs bundles induces a
sudden redshift of tangential component in agreement with experimental studies.
The G$_z$ band analysis of the SWNT collapsed tubes shows that the flattened
regions of the tubes are at the origin of their G-band signal. This explains
the observed graphite type pressure evolution of the G band in the collapsed
phase and provides in addition a mean for the identification of collapsed tubes
