Free vibration and buckling characteristics of porous functionally graded materials (FGMs) micro‐beams based on the modified couple stress theory

Abstract

AbstractBased on the modified couple stress theory (MCST), the free vibration and buckling characteristics of porous functionally graded materials micro‐beams (P‐FGMs and E‐FGMs) are studied. Firstly, two types of pore distribution are considered for functionally graded materials (FGMs) micro‐beams. The governing differential equations of free vibration and buckling of FGMs micro‐beams are derived by Hamilton's principle and dimensionless. Then, the dimensionless governing differential equations and their boundary conditions are transformed by differential transformation method (DTM), then the equivalent algebraic characteristic equations with natural frequencies are obtained. Finally, the dimensionless fundamental frequency and critical buckling load of the free vibration of the porous FGMs micro‐beam under four different boundary conditions of clamped‐clamped (C‐C), clamped‐simply supported (C‐S), simply supported‐simply supported (S‐S) and clamped‐free (C‐F) are calculated. The results are compared with the existing literature data, and the correctness is verified. The effects of porosity, scale parameter, stiffness ratio, axial load and gradient index on the dimensionless natural frequency and critical buckling load of FGMs micro‐beams are discussed.