Fig. 3

Synchronization bandwidths of different amplitudes. To ensure consistent cubic and quintic nonlinear stiffness, the resonator was excited to have the same maximum amplitude under different driving modes by adjusting the AC excitation voltage. The DC voltage V_dc was maintained at 35 V. The AC excitation voltage was found to be 550 mV for parametric excitation and 335 mV for direct excitation. The frequency ratio Ω_s/Ω versus the amplitude of the self-sustaining oscillation is depicted using a colormap plot, where the cyan-colored region is synchronized. a Parametric excitation. b Direct excitation. The SBW with respect to the amplitude with c experimental results and d theoretical results following Eqs. (12), (13)