Analytical solution for nonlinear dynamic response of the viscoelastic microbeam under electrical actuation based upon micropolar theory of elasticity

In this paper, the dynamic response of electro actuated viscoelastic microbeam is investigated and micropolar theory of elasticity has been used to consider the effects of size in microstructure. Euler-Bernoulli beam theory and Hamilton’s principle with considering viscoelastic integral constitutive equations, the midplane stretching effect, the axial residual stress and electrostatic force has been used to obtain the equation of motion and the boundary condition of fixed-fixed viscoelastic microbeam. Therefore, the nonlinear integro-differential equation in Volterra integral equation form is obtained. Galerkin method will be used, in order to solve the nonlinear partial integro-differential governing equation and then it converted to the ordinary integro-differential equation. By using the fourth order Runge - Kutta method, we can obtain the response (transverse displacement) of the electro actuated viscoelastic microbeam. In the following, the effect of initial gap value and material length scale parameter on the viscoelastic microbeam behavior are investigated. In the end, the viscoelastic microbeam is simulated in the FE software and the problem is analyzed in quasi-static form. In order to validate, the simulation result is compared with the result obtained from the quasi-static solution of the viscoelastic microbeam.