  The cavity electromechanical devices with radiation-pressure-interaction
induced Kerr-like nonlinearity are promising candidates to generate microwave
frequency combs. We construct a silicon-nitride-membrane-based superconducting
cavity electromechanical device and study two mechanical modes mediated
synergistic frequency combs. Around the threshold of intracavity field
instability, we firstly show independent frequency combs with tooth spacing
equalling to each mechanical mode frequency. At the overlap boundaries of these
two individual mechanical mode mediated instability thresholds, we observe
hybridization of frequency combs based on the cavity field mediated indirect
coupling between these two mechanical modes. The spectrum lines turn to be
unequally spaced but can be recognized into combinations of the coexisting
frequency combs. Beyond the boundary, the comb reverts to the single-mode case,
and which mechanical mode frequency will the tooth spacing depend on the mode
competition. Our work demonstrates mechanical mode competition enabled
switchability of frequency comb tooth spacing and can be extended to other
devices with multiple nonlinearities.
