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.

基于准3D理论，在Pasternak基础局部支撑的作用下，研究了双向移动功能梯度夹层梁在移动质量作用下的动力学分析。夹层梁的表层由双向功能梯度材料（FGM）制成，而芯层则由轴向FGM制成。皮层的材料特性通过功率梯度定律在轴向和横向上均平滑变化，并且通过Voigt和Mori-Tanaka微力学模型对它们进行了评估。推导了有限元公式，并将其用于构建梁的运动方程。借助Newmark方法计算了动态特性，包括动态挠度，动态放大系数和应力分布。数值结果表明，基础支撑部分与梁总长度的比值在梁的动力响应中起着重要作用。发现微力学模型对梁动力响应的影响取决于基础刚度和幂律指标。详细检查并强调了材料等级，基础和荷载参数对梁动力特性的影响。