  The dynamics of nanomechanical resonators driven by both low- and
high-frequency signals is studied. Considering, as an example, resonators made
of a doubly-clamped beam with magnetomotive driving, it is shown that
three-frequency resonances arise due to the interaction of the above
frequencies. Properties and characteristics of these resonances are determined
analytically for linear and nonlinear modes of the resonator excitation. It is
shown that in opposite to the conventional two-frequency resonance, the central
frequency of these resonances, their linear dynamic range, and the critical
value for the bistability onset are easily controlled by changing the frequency
and the amplitude of the low-frequency driving current. The obtained results
can be used when developing NMRs for sensors, filters, memory elements, and
other applications.
