We investigate mechanical mode coupling between the four fundamental flexural modes of two doublyclamped, high-Q silicon-nitride nanomechanical string resonators. Strong mechanical coupling between the strings is induced by the strain mediated via a shared clamping point, engineered to increase the exchange of oscillatory energy. One of the resonators is controlled dielectrically, which results in strong coupling between its out-of-plane and in-plane flexural modes. We show both, inter-string out-of-plane-in-plane and 3-mode resonance of the four coupled fundamental vibrational modes of a resonator pair, giving rise to a simple and a multimode avoided crossing, respectively.

We investigate the influence of gold thin-films subsequently deposited on a set of initially bare, doubly clamped, high-stress silicon nitride string resonators at room temperature. Analytical expressions for resonance frequency, quality factor and damping for both in- and out-of-plane flexural modes of the bilayer system are presented, which allows for the determination of effective elastic parameters of the composite structure from our experimental data. We find the inverse quality factor to scale linearly with the gold film thickness, indicating that the overall damping is governed by losses in the metal. Correspondingly, the mechanical linewidth increases by more than one order of magnitude compared to the bare silicon nitride string resonator. Furthermore, we extract mechanical quality factors of the gold film for both flexural modes and show that they can be enhanced by complete deposition of the metal in a single step, suggesting that surface and interface losses play a vital role in metal thin-films.

We investigate nonlinear dispersive mode coupling between the flexural in-and out-of-plane modes of two doubly clamped, nanomechanical silicon nitride string resonators. As the amplitude of one mode transitions from the linear response regime into the nonlinear regime, we find a frequency shift of the two other modes. The resonators are strongly elastically coupled via a shared clamping point and can be tuned in and out of resonance dielectrically, giving rise to multimode avoided crossings. When the modes start to hybridize, the modes' polarization changes. This affects the nonlinear dispersive coupling in a non-trivial way. We propose a theoretical model to describe the dependence of the dispersive coupling on the mode hybridization.