nonlinear vibration of an electrostatically actuated ‎functionally graded microbeam under longitudinal magnetic ‎field

in this work, we develop a model of an electrostatically actuated functionally graded (fg) microbeam under a longitudinal magnetic field based on the euler-bernoulli beam and nonlocal strain gradient theories to investigate the nonlinear vibration problem. the fg microbeam is placed between two electrodes, a dc voltage applied between the two fixed electrodes causes an electrostatic force to be exerted on the fg microbeam. the fg microbeam is composed of metal and ceramic in which the properties of these materials are assumed to change in the thickness direction according to the simple power-law distribution. the galerkin method and the hamiltonian approach are employed to find the approximate frequency of the fg microbeam. the accuracy of the present solution is verified by comparing the obtained results with the numerical results and the published results in the literature. effects of the power-law index, the material length scale parameter, the nonlocal parameter, the applied voltage and the magnetic force on the nonlinear vibration behaviour of the fg microbeam are studied and discussed.