Model of response spectrum and modal interaction in coupled nanomechanical resonators

We develop a simple continuum model to analyze the vibrational modes of a nanomechanical multi-element structure. In this model, arrays of sub-micron cantilevers located symmetrically on both sides of the central clamped-clamped nanobeam are replaced by a continuum. In this approach, the punctual shear forces exerted by the cantilevers on the central beam are smoothed out and the equations of motion of the structure become exactly solvable. Our analytical results capture the main features of the vibrational modes observed both numerically and experimentally. Furthermore, using a perturbative approach to treat the nonlinear dynamics of the structure, we establish its frequency-amplitude response and analyze the mechanism of anharmonic coupling between two specific widely spaced modes of the resonator.