Finite element analysis of vibrating micro-beams and -plates using a three-dimensional micropolar element

The micropolar theory (MPT), through taking the rotational degrees of freedom of material particles into account, is a suitable elasticity theory for the mechanical analysis of microstructures. In this article, the vibration behavior of microscale beams and plates is studied based on MPT. To this end, first, a three-dimensional (3D) formulation is developed for the micropolar continua which can be readily used in the finite element analyses. Then, a non-classical 3D element is introduced to investigate the free vibration characteristics of micropolar beams and plates. The microstructure effect on the frequencies of microbeams and microplates under different kinds of boundary conditions is illustrated. Also, the results of MPT are compared with those of classical theory and it is indicated that there is a considerable difference between their predictions at small scales.