Graphene-based mass sensors: Chaotic dynamics analysis using the nonlocal strain gradient model

Abstract

Nonlinear oscillations of graphene resonators are unavoidable due to enhancing the mass sensitivity of graphene-based mass sensors and the nonlinear behavior of the systems provides the route to chaos. In this paper, the nonlinear and chaotic behavior of the graphene-based mass sensor is investigated. The nano-mechanical sensor includes an electrostatically actuated fully clamped single-graphene sheet as a nano-resonator with an attached concentrated mass. By neglecting the rotary inertia, the equation of motion of the nano- resonator and the attached mass is derived using the nonlocal strain gradient theory of elasticity. The nano-resonator is modeled as a Kirchhoff nano-plate with the von Kármán-type geometric nonlinearity. Applying the Galerkin decomposition method to the partial differential equation of motion leads to the ordinary differential equation. Based on the Melnikov's integral method two analytical criteria are derived which provide necessary conditions that determine the chaotic region of the system. The chaotic dynamics of the system are also scrutinized and verified through plotting the Lyapunov exponent diagram, phase plane trajectories and Poincaré maps.