MODELING AND NUMERICAL ANALYSIS OF MAGMEMS FABRICATED USING GRAPHENE

Abstract

Microelectromechanical systems (MEMS) are widely used in applications requiring high sensitivity, rapid response, and miniaturization. Among such devices, clampedclamped microbeams are of particular interest due to their robustness under external loads and their versatile vibration characteristics. This thesis explores the integration of graphene into clamped-clamped microbeams to enhance mechanical properties and increase resistance to instability. Wepresent a comprehensive analytical and numerical study of a clamped–clamped microbeam enhanced with graphene and actuated magnetically via the Lorentz force. Starting from Hamilton’s principle and the Euler–Bernoulli beam theory, we derive the full nonlinear partial differential equation governing the transverse motion, incorporating both linear bending stiffness and a graphene-induced nonlinear stiffness term. Electromagnetic forcing is modeled by both scalar and vector formulations of the Lorentz force, and the scalar form is adopted to capture geometric nonlinearity. A one-mode Galerkin reduction yields a single-degree-of-freedom lumped-mass model, which is rendered dimensionless to identify key parameters: the nonlinearity coefficient andtheactuation intensity K. We then analyze dynamic pull-in using energy–balance and phase-plane methods, deriving an exact criterion for the existence of periodic orbits versus pull-in collapse. The Galerkin approach provides explicit approximate expressions for the pull-in threshold, small-oscillation frequency, and periodic solutions. Extensive numerical simulations confirm the analytical findings. Finally, we demonstrate resonance behavior via frequency sweeps and time-domain studies, revealing amplification near the natural frequency and assessing the increased pull-in risk under resonant excitation. Our results demonstrate that the proposed magMEMS model accurately captures both qualitative and quantitative behaviors of graphene-reinforced microbeams under magnetic actuation, offering a tractable framework for design and stability analysis of next-generation MEMS devices.