on the stability of an electrostatically-actuated functionally graded magneto-electro-elastic micro-beams under magneto-electric conditions

in this paper, the stability of a functionally graded magneto-electro-elastic (fg-mee) micro-beam under actuation of electrostatic pressure is studied. for this purpose euler-bernoulli beam theory and constitutive relations for magneto-electro-elastic (mee) materials have been used. we have supposed that material properties vary exponentially along the thickness direction of the micro-beam. governing motion equations of the micro-beam are derived by using of hamilton’s principle. maxwell’s equation and magneto-electric boundary conditions are used in order to determine and formulate magnetic and electric potentials distribution along the thickness direction of the micro-beam. by using of magneto-electric potential distribution, effective axial forces induced by external magneto-electric potential are formulated and then the governing motion equation of the micro-beam under electrostatic actuation is obtained. a galerkin-based step by step linearization method (sslm) has been used for static analysis. for dynamic analysis, the galerkin reduced order model has been used. static pull-in instability for 5 types of mee micro-beam with different gradient indexes has been investigated. furthermore, the effects of external magneto-electric potential on the static and dynamic stability of the micro-beam are discussed in    detail.