Dynamics of functionally graded beams carrying a moving load with influence of porosities and partial foundation support

The novelty of the present work is to study the simultaneous influence of porosities and partial Pasternak foundation support on dynamics of functionally graded (FG) beams carrying a moving load. The beams are made from an open-cell steel foam with symmetric and asymmetric porosity distributions in the thickness direction. Based on a refined third-order shear deformation theory, a two-node beam element with ten degrees of freedom is derived and employed to construct the discretized equation of motion for the beams. Dynamic characteristics, including the time histories for mid-span deflection, dynamic magnification factor (DMF) and the stress distribution, are computed with the aid of the Newmark method. The numerical result reveals that the foundation supporting length has an important role on the dynamics of the beams, and the dependence of the DMF upon the porosity coefficient is governed by the foundation supporting length.  It is also found that the asymmetric porosity distribution has more impact on the dynamic response of the beams than the symmetric one does, and the difference between the DMFs obtained from the two porosity distributions is more significant for the beam with a higher porosity coefficient. The effects of the porosities, the foundation support and the moving load velocity on the dynamic behavior of the beams are examined in detail and highlighted