Mechanical behavior of a FGM micro-beam subjected to a nonlinear electrostatic pressure

The present article studies the mechanical behavior of a FGM micro-beam subjected to a nonlinear electrostatic pressure. The FGM micro-beam is made of metal and ceramic and material properties vary continuously along the beam thickness according to a power-law. The nonlinear equation of dynamic motion of the FGM micro-beam is derived. By solving the equation of the static deflection, equilibrium positions of the micro-beam are determined and shown in the state control space. To study the stability of the fixed points, the trajectories of the beam motion are illustrated in the phase plane for different initial conditions. In order to find the response of the micro-beam to a step DC applied voltage, the nonlinear equation of motion is solved using a Galerkin based reduced order model. Moreover, time histories and phase portraits for different applied voltages are illustrated. The effect of different power law exponent on the stability of the micro-beam is studied.