MODELING AND NUMERICAL ANALYSIS OF GRAPHENE MICROBEAM RESONATOR

Abstract

Microelectromechanical systems (MEMS) have emerged as a revolutionary technology, enabling the development of miniaturized devices with diverse functionalities and superior performance. Among the essential components of MEMS, microresonators hold significant importance as they find applications in various fields, including mass and force sensing, molecular detection, and nanoscale imaging. The quest to improve the sensitivity and performance of microresonators has led researchers to explore novel materials and innovative designs. This thesis delves into the static and dynamic behavior of graphene cantilever beam resonators under electrostatic actuation at their free tips. A rigorous analysis of the system’s response was performed. The constitutive nonlinear equation of the system was derived using the Energy method and Hamilton’s principle. An analytical solution to the nonlinear static problem was obtained. A lumped mass model was developed to study the essential dynamics of the graphene cantilever beam. The generalized stiffness coefficient for the beam under load at its tip was calculated, enabling a comprehensive analysis of its dynamic behavior. A key focus was on investigating the dynamic pull-in conditions of the system under both constant and harmonic excitation. Analytical predictions were validated through numerical simulations. We observed that the system exhibited periodic solutions when the excitation parameters 𝛼 and 𝜆 were below a certain separatix curve, leading to sustained oscillations. On the other hand, if these parameters exceeded the separatix curve, the system experienced pull-in instability, causing the beam to collapse. Furthermore, we explored the impact of excitation frequency on the dynamic response of the graphene cantilever beam under harmonic load. The simulations revealed that choosing the excitation frequency near the beam’s resonant frequency could lead to structural collapse under certain parameter conditions.