In this paper, the nonlocal strain gradient theory and a new quasi 3D plate theory are employed to investigate the wave propagation in functionally graded (FG) porous graphene platelets (GPLs)-reinforced nanoplates on elastic foundations subjected to in-plane mechanical load and magnetic field. The present theory takes into account the shear deformation as well as the thickness stretching effect. The internal porosities and the GPLs are uniformly or non-uniformly distributed into the matrix according to four different types. The properties of the nanocomposites plates are calculated by utilizing the modified Halpin-Tsai pattern. Lorentz magnetic force is derived from Maxwell’s equations for the conducting material. The motion equations are derived employing Hamilton’s principle according to a new shear and normal deformations plate theory. Detailed parametric investigations on the wave frequency and phase velocity of the porous GPLs-reinforced nanoplates are implemented considering the influences of porosity coefficient, GPLs weight fraction, magnetic parameter and foundation stiffnesses on the results. It can be found that an increment occurs in the wave frequency with increasing the GPLs weight fraction and magnetic field parameter. While, it decreases as the pore coefficient increases.

本文采用非局部应变梯度理论和新的准3D板理论研究了功能梯度（FG）多孔石墨烯血小板（GPLs）增强的纳米板在弹性基础上承受平面机械载荷和磁场的波传播领域。本理论考虑了剪切变形以及厚度拉伸效应。根据四种不同类型，内部孔隙率和GPL均匀或不均匀地分布在基质中。通过使用改良的Halpin-Tsai模式计算纳米复合材料板的性能。洛伦兹磁力是根据导电材料的麦克斯韦方程式得出的。根据新的剪切和法向变形板理论，采用汉密尔顿原理导出了运动方程。考虑到孔隙率系数，GPL重量分数，磁参数和基础刚度对结果的影响，对多孔GPL增强纳米板的波频率和相速度进行了详细的参数研究。可以发现，随着GPL的重量分数和磁场参数的增加，波频率会增加。同时，它随着孔隙系数的增加而降低。