Investigation of nonlinear pull-in phenomena in functionally graded micro-beams under electrostatic excitation

In this research, the behavior of functionally graded micro-beams under electrostatic excitation is investigated. The system model is developed based on Euler-Bernoulli beam theory. In the developed model, the effects of electrostatic excitation and mid-layer stretching are considered. In order to solve the nonlinear governing equation, Generalized Differential Quadrature method and the Newton-Raphson method are used. To develop the pull-in voltage through the numerical results, a novel algorithm is developed. For numerical integration, Generalized Integral Quadrature is also used. Finally, the major problem of this method that prevent it from being used more frequently is discussed and a solution of that problem is suggested. In numerical results of this research, the pull-in voltage variation with respect to the functionally graded micro-beam stiffness distribution and initial gap of micro-beam is studied. Results show that increasing the micro-beam equivalent stiffness or beams initial gap, will increase the pull-in voltage. The boundary conditions effect on the micro-beam pull-in voltage is also studid in the numerical results.