  A weakly nonlinear spectrum and a strongly nonlinear spectrum coexist in a
statistically steady state of elastic wave turbulence. The analytical
representation of the nonlinear frequency is obtained by evaluating the
extended self-nonlinear interactions. The {\em critical\/} wavenumbers at which
the nonlinear frequencies are comparable with the linear frequencies agree with
the {\em separation\/} wavenumbers between the weak and strong turbulence
spectra. We also confirm the validity of our analytical representation of the
separation wavenumbers through comparison with the results of direct numerical
simulations by changing the material parameters of a vibrating plate.
