Abstract:
In this work, we construct and analyze a mathematical model of coupled longitudinal-transverse vibrations of a rectangular pretensioned strip under conditions of internal combinational resonance between two transverse modes and one longitudinal vibration mode of the
structure in view of advanced nanosystems made of two-dimensional materials. The issues of
generating frequency combs based on the proposed nanoresonator design are investigated in the
context of the development of nondestructive methods of laser optothermal excitation of vibrations of atomically thin nanostructures. Conditions have been analytically found for the amount
of deformation of the initial tension of the layer required to realize resonance between eigenmodes with given indices of variability along the length. The necessary relationships between
the indices of vibration modes involved in nonlinear interaction are determined. It is shown that,
under conditions of internal resonance, beats are excited in the system, the spectrum of which
has the form of a frequency comb. Two qualitatively different types of beats are identified —
those caused by the initial excitation in the working longitudinal form of vibrations 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 along three
interacting modal coordinates and on the value of the internal frequency detuning parameter of
the system is shown.
Keywords:2D material resonators, nanomechanical systems, suspended nanolayers, nonlinear modal coupling, perturbation methods, phononic frequency comb
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