Nonlinear dynamic analysis of vibratory behavior of a graphene nano/microelectromechanical system

Abstract

The nano/microelectromechanical systems (N/MEMS) have gained considerable attention in the past few decades for their attractive properties such as small size, high reliability, batch fabrication, and low power consumption. Carbon‐based nanostructures such as one‐dimensional carbon nanotubes (CNTs) and two‐dimensional graphene are the key materials in many N/MEMS and very attractive due to their unique properties and ultra‐small dimensions especially the large surface area‐to‐volume ratio make them prime candidates for sensing applications in N/MEMS. Therefore, the main objective of this manuscript is to analyze the dynamic behavior of a graphene N/MEMS. The mathematical model of this system uses constitutive stress–strain law and the electrostatic Coulomb force for the restoring force of the spring and the driving force of the mass attached to the spring, respectively. The modeled system is then solved by employing the variational iteration method (VIM) accompanied by the techniques of the Laplace transform. This coupling of VIM and Laplace transform (Laplace‐based variational iteration method [LVIM]) not only suggests an easier approach to determine the Lagrange multiplier used in the VIM but also provides approximate nonlinear frequency and approximate solution of graphene N/MEMS in an efficient way. Moreover, the LVIM also approximates the pull‐in threshold, a critical phenomenon associated with N/MEMS, in terms of model parameters. Finally, to verify the obtained findings, the results are compared with those achieved numerically as well.

Fractal Pull-in Stability Theory for Microelectromechanical Systems

“…In Equation ( 7), when a and k take different values, it will correspond to different equations. It is worth noting that only in the presence of electrostatic force, that is a = 0, under steadystate conditions, our model is simplified to the well-known Nathan model or parallel plate capacitor model [6].…”

“…where σ , ε, E represent the axial stress, axial strain, Young's modulus, and elastic stiffness constant, respectively. The moving part is affected by the restoring force Frproduced by the axial displacement of the graphene belt and the electrostatic force Fe produced by the applied voltage V. According to Equation ( 1), Fr and Fe can be write as [1,6],…”

“…Many literatures have conducted a lot of analysis on the dynamic pull-in of MEMS models of linear materials [1][2][3][4][5]. There are many materials used to prepare electrostatic MEMS devices, and among many materials, graphene is considered an excellent material for these devices [6].…”

Low-frequency vibro-acoustic response of an optimized fiber-reinforced graphite truss sandwich panel filled with wood-based material

“…8, for the purpose of enhancing the devices' capacity in terms of mass, energy, and charge transfer. In order to better understand the oscillatory behavior of nano/microelectromechanical systems, Anjum and He 9 put forward an effective Laplace-based variational iteration method approach, which combined the variational iteration method and Laplace transform, to investigate the amplitude-frequency relationship. Furthermore, low-frequency noise is pervasive in urban life, produced not only by natural reasons (sea waves, wind turbulence, etc.)…”

The modified Lindstedt–Poincare method for solving quadratic nonlinear oscillators

“…However, generalization or modifications of some classical perturbation techniques overcome this limitation. In particular, modifications of the Lindstedt-Poincare (LP) method, [6][7][8][9][10] He's homotopy perturbation method, [11][12][13] iterative methods, [14][15][16] the Hamiltonian approach, 17 and linearization method 18,19 are also widely used tools to solve strongly nonlinear oscillators. Cheung et al 6 introduced a small parameter in the frequency series and solved some strong nonlinear oscillators which are the main concern of this article.…”