Nonlinear Vibration and Dynamic Stability Analysis of a Nanocomposite Viscoelastic Microplate Under an Electrostatic Actuation

In this paper, nonlinear vibration and dynamic stability analysis of a CNT- reinforced nanocomposite viscoelastic microplate under an electrostatic actuation are investigated. The microplate is assumed as a square immovable simply supported microplate and an electrostatic actuation is applied on it. In order to obtain material properties of the nanocomposite microplate, the Eshelby–Mori–Tanaka method is implemented. The nonlinear equations of motion of the microplate are derived and, using the Galerkin method and multiple scale method, these equations are solved. It is shown that nanocomposite viscoelastic microplate increases the natural frequency and deflection of the microplate simultaneously, but, there are some limitations because of high values of viscoelastic damping of the nanocomposite materials. Furthermore, the damping of the nanocomposite microplate is changed, as the electrostatic voltage is changed. This situation is an unfavorable phenomenon. Also nonlinear behavior of the microplate is quite variable as nanotube volume fraction varies and, for a given voltage, it can show softening or hardening behavior as CNT volume fraction changes. This matter should be considered in designing of the microdevices, especially microresonators.