  We study the dynamical regime of wave turbulence of a vibrated thin elastic
plate based on experimental and numerical observations. We focus our study to
the strongly non linear regime described in a previous letter by N. Yokoyama &
M. Takaoka. At small forcing, a weakly non linear regime is compatible with the
Weak Turbulence Theory when the dissipation is localized at high wavenumber.
When the forcing intensity is increased, a strongly non linear regime emerges:
singular structures dominate the dynamics at large scale whereas at small
scales the weak turbulence is still present. A turbulence of singular
structures, with folds and D-cones, develops that alters significantly the
energy spectra and causes the emergence of intermittency.
