Nonlinear Vibration of Functionally Graded Electrostatically Actuated Microbeams Considering the Influence of Intermolecular Forces with Zero Initial Conditions

Within the framework of the nonlocal strain gradient and the Euler–Bernoulli beam theories, a model of electrostatically actuated functionally graded (FG) microbeams is developed taking into account the intermolecular interaction forces in it. In addition to the electrostatic forces resulting from the applied DC voltage between a fixed substrate and the FG microbeam, the Casimir and van der Waals forces were also considered. The governing equation of motion of FG microbeams was derived by employing the Hamilton principle. Utilizing the Galerkin and the equivalent linearization methods, an analytical solution was obtained for the nonlinear vibration problem with zero initial conditions. To validate the accuracy of the results obtained, our solution was compared with the numerical and analytic solutions published in the literature.