Dynamic behaviour of bidirectional functionally graded sandwich beams under a moving mass with partial foundation supporting effect

Dynamic analysis of bidirectional functionally graded sandwich beams under a moving mass with the effect of partial support by a Pasternak foundation is presented on the basis of a quasi-3D theory. The face layers of the sandwich beams are made of bidirectional functionally graded material (FGM), while the core is axially FGM. The material properties of the skin layers are varied smoothly in both the axial and transverse directions by power gradation laws, and they are evaluated by both Voigt and Mori-Tanaka micromechanical models. A finite element formulation is derived and employed to construct the equation of motion of the beams. Dynamic characteristics, including the dynamic deflections, dynamic magnification factors and stress distribution, are computed with the aid of the Newmark method. The numerical results reveal that the ratio of the foundation supporting part to the total beam length plays an important role in the dynamic response of the beams. The influence of the micromechanical model on the dynamic response of the beams is found to be dependent on the foundation stiffness and the power-law indexes. The effects of the material gradation, the foundation and loading parameters on the dynamic behaviour of the beams are examined in detail and highlighted.