On the generation of frequency combs based on mechanical vibrations of 2D material nanosheets

We study the nonlinear dynamics of a rectangular atomically thin nanostrip under conditions of internal combinational resonance between two transverse and one longitudinal modes of mechanical vibrations. Conditions have been analytically found for the initial pretension of the layer required to realize resonance between eigenforms with given indices of variability along the length. It is shown that under conditions of internal resonance, a nonlinear mode of free oscillations is excited in the system, the spectrum of which has the form of a frequency comb. Two qualitatively different types of oscillations of this kind are identified – those caused by the initial excitation in the working longitudinal form of oscillations and in two transverse forms. A significant dependence of the spectral composition of the generated frequency combs on the relationships between the amplitudes of the initial disturbance for the three interacting modes and on the value of the internal frequency detuning parameter of the system is shown.