Dynamic instability analysis of piezoelectric nanoplates under combined AC/DC voltages

Abstract

This work is devoted to the severe and still unsolved problem of a complete study of the instability of piezoelectric nanoplates under the combined impact of direct current (DC) and alternating current (AC) voltages, nonlocal piezoelastic dependencies, and interaction with an elastic foundation. These combined investigations are rarely discussed in the literature, although they are crucial to the successful functioning of nanoelectromechanical systems (NEMS), such as sensors, actuators, and energy harvesters. To address this research gap, we build a unified theoretical model, founded on Hamilton's principle, Mindlin plate theory, and Eringen nonlocal elasticity theory. Discretization of the governing equations is performed using the Galerkin method, with Floquet theory employed to rigorously identify parametric resonance effects and determine the stability and unstable regions of the voltage-frequency parameter space. The impact of controlling physical parameters, such as nonlocal scale factors, geometric dimensions, magnitude of DC voltage, and elastic foundation stiffness, is systematically studied to explain their collective contributions to instabilities. Our findings indicate that a nonlocal effect, combined with large lateral dimensions, tends to cause instability, whereas a stiff substrate and negative DC voltage enhance stability. Numerical simulations confirm the theory by showing uninhibited transverse displacement in vicinity of resonance regions. This detailed investigation not only contributes to the basic knowledge of electromechanical coupling and dynamics in piezoelectric nanoplates but also provides practical design guidelines to maximize the robustness and efficiency of NEMS devices in the future. © 2025 Elsevier B.V., All rights reserved.