  A phenomenological model describing the time-frequency dependence of the
power spectrum of thin plates vibrating in a wave turbulence regime, is
introduced. The model equation contains as basic solutions the Rayleigh-Jeans
equipartition of energy, as well as the Kolmogorov-Zakharov spectrum of wave
turbulence. In the Wave Turbulence Theory framework, the model is used to
investigate the self-similar, non-stationary solutions of forced and free
turbulent vibrations. Frequency-dependent damping laws can easily be accounted
for. Their effects on the characteristics of the stationary spectra of
turbulence are then investigated. Thanks to this analysis, self-similar
universal solutions are given, relating the power spectrum to both the injected
power and the damping law.
