We study the nonlinear dynamics induced in suspended nanomembranes by their clampings. The nonlocal character of the nonlinearity is demonstrated via intermode couplings. We also monitor the resonator phase-space trajectory and characterize its mechanical response in the presence of a strong pump excitation. We observe a shift in the oscillation frequency and phase conjugation of the mechanical mode. Such nonlinear effects are inherent to any submicron-scale mechanical resonator and are expected to play a role in their quantum dynamics as well.
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