  We investigate mechanical mode coupling between the four fundamental flexural
modes of two doubly-clamped, 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.
