Dynamic finite element modeling of axially functionally graded Timoshenko microbeams under a moving mass

This paper presents a finite element model for dynamic analysis of axial functionally graded (AFG) microbeams subjected to amovingmass. Thematerial properties of themicrobeams are considered to vary in the axial direction by a power-law function, and they are evaluated byMori-Tanaka scheme. The first-order shear deformation theory is employed in conjunction with the modified couple stress theory to establish the differential equations of motion for the AFG microbeams. A two-node beam element with six degrees of freedom was derived and used in combination with Newmark method to solve the equations of motion and to compute the dynamic response of the microbeams. Numerical investigations are carried out on AFG microbeam with simply supported ends. The proposed method is validated by comparing with results in previous work. The effects of dimension-less material length scale parameters, the material distribution and the moving mass parameters on the dynamic characteristics of the AFG microbeams are studied and discussed in detail.