Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory

In this paper, a nonlinear continuum model is developed for the large amplitude vibration of nanoelectromechanical resonators using piezoelectric nanofilms (PNFs) under external electric voltage. Hamilton’s principle in conjunction with von Karman’s theory is employed to derive the differential equations of motion. Size effects are incorporated into both the governing equations and in-plane boundary conditions using nonlocal continuum mechanics. Explicit expressions are presented for the nonlinear natural frequencies and critical electric voltages of PNFs. In comparison to the available experimental data and molecular dynamics simulation results, the present nonlocal model with reasonable small scale parameters results in more accurate estimation of natural frequencies than the classical theory of plates. It is anticipated that the results of the present work would be helpful in experimental characterization of the mechanical properties of piezoelectric nanoresonators.