Vibration analysis of functionally graded microbeams with a moving mass based on Timoshenko beam theory

Abstract

Vibration analysis of functionally graded (FG) microbeams carrying a moving mass is carried out in the framework of Timoshenko beam theory. The beam material properties are considered to be graded in the thickness by a power-law function, and they are estimated by Mori-Tanaka scheme. The influence of the microsize effect is captured with the aid of the modified couple stress theory (MCST). A finite beam element is formulated and used to establish the discretized equation of motion for the beams. Vibration characteristics, including the natural frequencies, the time histories for mid-span deflection, the dynamic magnification factor and the stress distribution, are computed for a simply supported beam. The obtained result reveals that both the dynamic deflection and dynamic magnification factor are overestimated by ignoring the microsize effect. The effects of the material distribution, the moving mass velocity and the length scale parameter are studied in detail and highlighted.