We theoretically investigate the nonlinear dynamics of an optomechanical system, where the system consists of N identical mechanical oscillators individually coupled to a common cavity field. We find that the optomechanical nonlinearity can be enhanced N times through theoretical analysis and numerical simulation in such a system. This leads to the power thresholds to observe the nonlinear behaviors (bistable, period-doubling, and chaotic dynamics) being reduced to 1/N. In addition, we find that changing the sign (positive or negative) of the coupling strength partly does not affect the threshold of driving power for generating corresponding nonlinear phenomena. Our work may provide a way to engineer optomechanical devices with a lower threshold, which has potential applications in implementing secret information processing and optical sensing.