In this paper, the vibration problem of a rectangular plate rested on a viscoelastic substrate and consisting of porous metal foam is solved via an analytical method with respect to the influences of various porosity distributions. Three types of porosity distribution across the thickness are covered, namely uniform, symmetric and asymmetric. The strain–displacement relations of the plate are assumed to be derived on the basis of a refined higher-order shear deformation plate theory. Then, the achieved relations will be incorporated with the Hamilton’s principle in order to reach the Euler–Lagrange equations of the structure. Next, the well-known Galerkin’s method is utilized to calculate the natural frequencies of the system. The influences of both simply supported and clamped boundary conditions are included. In order to show the accuracy of the presented method, the results of present research are compared with those reported by former published papers. The reported results show that an increase in the porosity coefficient can dramatically decrease the frequency of the plate. Also, the stiffness of the system can be lesser decreased, while a symmetrically porous metal foam is used to manufacture the plate.

中文翻译：

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粘弹性基材上多孔泡沫金属板的振动分析

在本文中，基于各种孔隙率分布的影响，通过分析方法解决了放置在粘弹性基底上并由多孔金属泡沫组成的矩形板的振动问题。涵盖了三种类型的孔隙度分布在厚度上，即均匀、对称和不对称。假定板的应变-位移关系是根据改进的高阶剪切变形板理论推导出来的。然后，将获得的关系与哈密顿原理结合，以达到结构的欧拉-拉格朗日方程。接下来，利用著名的伽辽金方法来计算系统的固有频率。包括简支和夹紧边界条件的影响。为了显示所提出方法的准确性，将目前的研究结果与以前发表的论文报告的结果进行了比较。报告的结果表明孔隙率系数的增加可以显着降低板的频率。此外，系统的刚度可以减少较少，而对称多孔金属泡沫用于制造板。