  In this work we theoretically investigate the stochastic resonance (SR)
effect in an optomechanical membrane system subject to two weak signals (one
optical field and one mechanical force). The quadratic optomechanical coupling
allows us to find a region with tristability where the noise activated
stochastic switching among three stable states occurs and SR phenomena are
observed at the cooperation of input signals and noises. We show that the
mechanical force and the optical field respectively serve as an additive signal
and a multiplicative signal to the membrane position and they induce completely
different SR behaviors. Moreover, when two signals coexist the SR effect can be
enhanced and the beating effect appears in the SR synchronization process with
unsynchronized signals.
