Size dependent pull-in instability of functionally graded microbeams using a finite element formulation

The size dependent static pull-in instability of functionally graded (FG) microbeams in micro-electromechanical systems (MEMS) is studied, considering the influence of the axial force. The material properties of the microbeams are varied in the beam thickness by a power-law function, and they are calculated by the rule of mixture. To account for the microsize effect, the classical Euler-Bernoulli beam theory is employed in combination with the modified couple stress theory to describe the microbeams deformation. Based on Von Kármán nonlinear relationship, a beam element is derived and employed to establish the discretized governing equation for the microbeams. Newton-Raphson iterative procedure is adopted to compute frequencies and pull-in voltages for the microbeam with clamped ends. Numerical result reveals that the pull-in voltage is increased by the increase of the power-law exponent and the microscale parameter. The effects of the material distribution, the axial force as well as the microstructural parameter on the pull-in instability of the FG microbeams are investigated in detail.