The Consistent Couple Stress Theory-Based Vibration and Post-Buckling Analysis of Bi-directional Functionally Graded Microbeam

Abstract

The present work aims to study the free vibration, buckling and post-buckling behaviors of bidirectional functionally graded (BDFG) microbeams. The material properties of a BDFG microbeam were varied continuously in both thickness and axial directions. Furthermore, four different kinds of material distribution function were taken into consideration, two of which were symmetrical in the thickness direction, and the remaining two were asymmetrical. Employing the Timoshenko beam theory and the consistent couple stress theory (CCST), the governing equations and associated boundary conditions of BDFG microbeams were formulated by Hamilton’s principle. The differential quadrature method (DQM) and Newton’s method were applied to solve the eigenvalue problems and buckling path, respectively. Finally, several parametric investigations were carried out to probe the influence of material distribution functions, length to thickness ratio, gradient indexes and size effect on the vibration and buckling behaviors of BDFG microbeam under different boundary conditions.

Keywords

• bidirectional functionally graded (BDFG) microbeam
• symmetrical and asymmetrical material distribution
• consistent couple stress theory (CCST)
• free vibration
• post-buckling