Nonlinear frequency shift behavior of graphene–elastic–piezoelectric laminated films as a nano-mass detector

•Nonlinear frequency shift of graphene–elastic–piezoelectric laminated mass detectors.•Adjusting voltage applied on the piezoelectric layer in mass detector can enhance its sensitivity.•Frequency shift at the center of GEP laminated mass detectors presents maximum.•The small scale effect decreases the effect of attached mass on the frequency shift.

This paper presents an analytical method to investigate the nonlinear frequency shift of graphene–elastic–piezoelectric (GEP) laminated films as a resonant mass detector. Based on the nonlocal elastic theory and nonlinear geometrical relation, the nonlinear dynamic governing equations containing deflection function, stress function and electric potential function are constructed by Hamilton's principles, then are solved by Galerkin method and the iterative homotopy harmonic balance method. The effects of some key parameters on the nonlinear frequency shift are described. Results show that both nonlinearity and nonlocal parameter appear in significant influences on the frequency shift of GEP laminated nano-mass detector, and the frequency shift can be controlled by adjusting the external voltage acted on the piezoelectric layer when different mass particles attach to the detector surface. The present work can serve as a guideline for the design of a nanoscale resonant mass detector or other GEP-films based electromechanical resonator sensors.

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