Dynamic finite element analysis of microbeams under a moving mass based on refined third-order shear deformation theory

Abstract

The dynamic behavior of microbeams with rectangular cross section under action of a moving mass is studied in the present paper in the framework of a refined higher-order shear deformation beam theory. The modified couple stress theory (MCST) with only one additional scale parameter is adopted to describe the influence of the microsize effect on the dynamic response of the microbeams. A finite element formulation with ten degrees of freedom is formulated and used to establish the discretized equation of motion for the microbeams. The formulation, taking into account the influence of the inertial effect, the Coriolis and centrifugal forces resulted from the mass moving, is derived from the expressions of the elastic and kinetic energies of the microbeams. The accuracy and efficiency of the derived formulation are confirmed by comparing the result obtained in the present work with the published data. The dynamic response of the microbeams with simply supported ends, such as the curves for dimensionless mid-span deflection-moving time relationship, the dynamic magnification factors (DMFs) and the thickness distribution of stresses are assessed by using an implicit Newmark method. The obtained numerical results reveal that the material length scale parameter which is introduced in the MCST has an important role on the dynamic behavior of the microbeams, and the DMF obtained from the theory incoporating the MCST is considerably lower than that using the conventional beam theory. It is also shown that the amplitude of both the axial stress and shear stress is considerably decreased by the increase of the material length scale parameter. A numerical study is carried out to highlight the influence of various parameters such as the moving mass velocity and the the ratio of the total beam length to its height on the dynamic response of the microbeams.