Size-dependent free vibrations of electrostatically predeformed functionally graded micro-cantilevers

Size-dependent free vibration analysis of cantilever-type resonant micro-sensors made of non-homogeneous functionally graded materials with two material phases is the objective of the present paper. For this aim, the modified couple stress theory together with the Euler-Bernoulli beam model is considered, and the size-dependent equation of motion which accounts for the non-linear and distributed electrostatic force is derived using the Hamilton's principle. The natural frequencies of the system are extracted using the Galerkin weighted residual method. It is found that the fundamental frequency of the system is decreased with an increase of applied voltage and becomes zero when the input voltage reaches the pull-in voltage of the system. The findings of the present paper are compared and validated by available results in the literature and excellent agreements between them are observed.