On the Vibration Analysis of Micropolar Beams Based on the Finite Element Method

Presented in this paper is the analysis of free vibration characteristics of micropolar beams based on the finite element method (FEM). To do so, a new and general three-dimensional formulation is developed for the micropolar elasticity theory. To derive the FE formulation of beam-type structures, the obtained general relations are reduced on the basis of the Timoshenko beam theory. In this regard, quadratic shape functions are utilized to interpolate the displacements and micro-rotations of micropolar beam element. Selected numerical results are provided on the free vibration responses of micropolar beams with different boundary conditions and geometries and thus, the microstructural effects are successfully investigated.