Nonlinear vibration analysis of circular multilayer graphene-based NEMS sensors using harmonic balance and pseudo-arclength continuation methods

Abstract

In this study, the partial differential equation (PDE) for a circular multilayer graphene-based nano-electro-mechanical (NEMS) capacitive sensor was formulated in polar coordinates, considering electrostatic effects with fringing field correction, intermolecular Casimir force, and harmonic external pressure. The continuum model incorporates a nonlocal parameter based on Eringen's theory and interlayer shear effects. Using 8th order polynomial trial functions in the Galerkin reduced order method (ROM) for clamped boundary conditions, the equation for the first mode shape was derived. The natural frequencies in different graphene layers were compared with similar studies on rectangular multilayer graphene sheets (MLGSs). Voltage-frequency graphs highlighted the importance of Casimir force in small scenarios. After validating the mathematical model, nonlinear vibration analysis was performed using the harmonic balance method and pseudo-arclength continuation. The frequency-response (F–R) curves revealed softening behavior even at small deflections and superharmonic resonance under high pressures. Excellent agreement was observed between the direct numerical integration and the third order harmonic balance method. Finally, the influence of applied voltage on the nonlinear dynamics of the MLGS-based NEMS sensor was presented. © 2025 Elsevier Ltd