  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.
