Nonlinear vibration and stability of functionally graded porous microbeam under electrostatic actuation

Abstract

In this work, a microbeam model based on the Euler–Bernoulli beam theory and the nonlocal strain gradient theory was developed to study nonlinear vibration and stability of a functionally graded porous microbeam under electrostatic actuation. The electrostatic force is the driving force per unit length, resulting from electrostatic excitation. The material properties of the microbeam change continuously along thickness direction according to simple power-law distribution in terms of the fractions of constituents. Two cases of even and uneven porosity distributions are considered. The Hamilton principle is used to obtain the governing equations of the motion for the microbeam. The equation of motion for the microbeams is reduced to a nonlinear ordinary differential equation with rational restoring force by applying Galerkin method. The frequency–amplitude relationship is given in the closed form by employing He’s Hamiltonian approach. The expression of the static pull-in voltage is also derived. Effects of the material length scale parameter, the nonlocal parameter, the power-law index, the porosity distribution factor, the applied voltage and the initial amplitude on nonlinear vibration and stability of the functionally graded porous microbeam are examined and discussed.