Free vibration and buckling analyses of a size-dependent axially functionally graded beam incorporating transverse shear deformation

Abstract

A new size-dependent axially functionally graded (AFG) beam model with transverse shear deformation is proposed based on the modified couple stress theory (MCST). Besides, present new model incorporates only one material length scale parameter (MLSP) which can effectively capture the scale effects. Moreover, the first-order and third-order shear deformation theory are considered in this new model respectively, which differ from the existing micro AFG Euler-Bernoulli model. Subsequently, free vibration and buckling behaviors are investigated based on the rule of mixture. Related governing equations are derived and numerically solved by Hamilton’s principle and differential quadrature method (DQM) respectively. Afterwards, some results are compared with published literatures to demonstrate the validity and accuracy of current formulation. Finally, the effects of geometric size, shear deformation and material non-homogeneity on the critical loads and natural frequencies are discussed.