  High quality factor mechanical resonators have shown great promise in
developing classical or quantum technologies. Simultaneously, progress has been
made in developing controlled mechanical nonlinearity. Here we combine these
two directions of progress in a single platform consisting of coupled Silicon
Nitride (SiNx) and graphene mechanical resonators. We show that nonlinear
response can be induced on a large area SiNx resonator mode and can be
efficiently controlled by coupling it to a gate-tunable, freely suspended
graphene mode. The induced nonlinear response of the hybrid modes, as measured
on the SiNx resonator surface is giant, with one of the highest measured
Duffing constants. We observe a novel phononic frequency comb which we use as
an alternate validation of the measured values, along with numerical
simulations which are in overall agreement with measurements.
