Abstract
We propose a general one-dimensional {\em continuous} formulation to analyzethe vibrational modes of antenna-like nanomechanical resonators consisting oftwo symmetric arrays of cantilevers affixed to a central nano-beam. Thecantilever arrays can have arbitrary density and length profile along the beam.We obtain the secular equation that allows for the determination of theirfrequency spectrum and illustrate the results on the particular examples ofstructures with constant or alternating cantilever length profiles. We showthat our analytical results capture the vibration spectrum of such resonatorsand elucidate key relationships that could prove advantageous for experimentaldevice performance. Furthermore, using a perturbative approach to treat thenonlinear and dissipative dynamics of driven structures, we analyze theanharmonic coupling between two specific widely spaced modes of thecoupled-element device, with direct application to experiments.