Two successive frequency-locking intervals and pressure-induced jump readout via 1:1:1 internal resonance in electrically coupled molybdenum disulfide nanodrums

Amplitude-dependent frequency drift limits readout stability in nonlinear nanoelectromechanical resonators. We study two successive frequency-locking intervals in a reduced model of three electrically coupled molybdenum disulfide nanodrums near 1:1:1 internal resonance. The model includes directional coupling about the dc-biased equilibria and pressure-dependent frequency and damping. Stationary multiple-scale solutions are continued numerically and compared with a separately computed harmonic-balance response. The selected unlocking boundary sinφ1 = 1 is a limit of real stationary phase and does not imply vanishing intermodal energy transfer. For a no-jump operating point, a synthetic-drive-plus-300 K thermomechanical noise budget predicts a 76.9050% reduction in minimum Allan deviation relative to the uncoupled reference. Pressure continuation at fixed normalized drive resolves two successive downward jumps in the active-drum peak frequency. Joint adjustment of gate voltage and drive keeps the first jump near 10 Pa while tuning the second jump over a wider pressure range. An independent coupled-field finite-element calculation supports the electrical transfer pathway through a controlled comparison of connected and open ac branches. The finite-element assessment concerns small-signal transfer, while nonlinear locking is examined within the reduced-order model.