Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device

Abstract

Phase plane analysis of the nonlinear spring-mass equation arising in modeling vibrations of a lumped mass attached to a graphene sheet with a fixed end is presented. The nonlinear lumped-mass model takes into account the nonlinear behavior of the graphene by including the third-order elastic stiffness constant and the nonlinear electrostatic force. Standard pull-in voltages are computed. Graphic phase diagrams are used to demonstrate the conclusions. The nonlinear wave forms and the associated resonance frequencies are computed and presented graphically to demonstrate the effects of the nonlinear stiffness constant comparing with the corresponding linear model. The existence of periodic solutions of the model is proved analytically for physically admissible periodic solutions, and conditions for bifurcation points on a parameter associated with the third-order elastic stiffness constant are determined.

Complex Dynamics and Statistics of 1-D Hamiltonian Lattices: Long Range Interactions and Supratransmission

“…As is well-known, the field of modeling complex materials has been expanding rapidly in recent years, with the aim of understanding the dynamical response of metallic structures used in mechanical engineering applications. In this regard, I have been studying recently with Dr. Kostas Kaloudis and Dr. Thomas Oikonomou [34]1-D Hamiltonian lattices of particles interacting via 1) graphene type interactions [28][29][30], 2) Hollomon's power-law of materials exhibiting "work hardening" [31][32][33]. Earlier studies have focused on the dynamics of single oscillators governed by suitable nonanalytic potentials describing the motion in the above two cases.…”

On the application of Sturm's theorem to analysis of dynamic pull-in for a graphene-based MEMS model

“…We consider the graphene-based MEMS model for a parallel plate capacitor. The equation for the motion of the capacitor plate proposed by [12] reads as follows…”

“…In general, the dynamic pull-in requires a lower voltage to be triggered compared to the static pull-in threshold, see [2,15]. The preliminary results for the static pull-in voltage have been stated in [12] by considering the quadratic stress-strain equation which is validated to be important for graphene with applications in MEMS. Exact conditions for the dynamic pull-in were discussed in [11].…”

Periodic oscillations for a graphene-based electrostatic micro actuator

“…A recent lumped-mass model for a graphenebased microelectromechanical system is established in [21], taking into account the third order elastic-stiffness constant of the material. Furthermore, authors in [21] determine analytically the existence of periodic solutions, determine the static pull-in voltage, and then present a bifurcation analysis for this novel graphene-based MEMS model when a constant voltage is applied. For more related results about this model with constant voltage see [18,17,2].…”

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We study the mechanical oscillations for a novel model of a graphene-based electrostatic parallel plates micro actuator introduced by Wei et al(2017), considering damping effects when a periodic voltage with alternating current is applied. Our analysis starts from recent results about this MEMS model with constant voltage, and provides new insights on the periodic mechanical responses for a variable input voltage.

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