Modeling and Numerical Analysis for MEMS Graphene Resonator

Ji-Huan He¹Qingmei Bai²Ye-Cheng Luo³Dilyara Kuangaliyeva⁴Grant Ellis⁴Yerkebulan Yessetov⁴Piotr Skrzypacz^4*

• ¹School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, China
• ²School of Mathematics and Big Data, Hohhot Minzu College, Hohhot, Inner Mongolia Autonomous Region, China
• ³School of Jia Yang, Zhejiang Shuren University, Hangzhou, Jiangsu Province, China
• ⁴Nazarbayev University, Nur-Sultan, Akmola, Kazakhstan

This paper 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 is performed. The constitutive nonlinear equation of the system is derived using the energy method and Hamilton's principle. An analytical solution to the nonlinear static problem is obtained. The generalized stiffness coefficient for the lumped model of the cantilever graphene beam under load at its tip is calculated, enabling a comprehensive analysis of its dynamic behavior. A key focus is on investigating the dynamic pull-in conditions of the system under both constant and harmonic excitation. Analytical predictions are validated through numerical simulations. The system exhibits periodic solutions when the excitation parameters are below a certain threshold described by a separatrix curve, leading to sustained oscillations. On the other hand, if the excitation parameters exceed this threshold, the system experienced pull-in instability, causing the beam to touch down. Furthermore, we explore the impact of excitation frequency on the dynamic response of the graphene cantilever beam under harmonic load. The simulations reveal that choosing the excitation frequency near the beam's resonance frequency can lead to structural collapse under certain parameter conditions.