This paper presents an investigation into the importance of micromechanical models in the analysis of forced vibrations of multi-layered microplates under a moving load. The microplate has a core fabricated from functionally graded materials and face sheets consisting of metal foam. The problem is modelled via a quasi-3D shear deformable method and the modified couple stress theory. This study assumes that the core material follows a power gradation pattern. Various micromechanical models, i.e., the Hashin-Shtrikman bounds, Voigt-Reuss-Hill, Voigt, Reuss, and Tamura, are applied to estimate the material characteristics of the core. The face sheets, composed of metal foams, possess closed- and open-cell solid porosities. System's response of time history type is determined by numerically solving the coupled motion equations obtained using a force-moment balance method. A finite element analysis is conducted for a simplified plate system, and the agreement between the numerical results, via the proposed theoretical approach and the theory developed in this paper, is found to be very good. The results show that the micromechanical models influence the modelled mechanical properties of the core layer, consequently impacting the numerical results for the moving-load excited response of the multi-layered microsystem.

中文翻译：

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基于各种微机械模型的多层不完美微板的移动负载激励动力学

本文研究了微机械模型在移动载荷下多层微板受迫振动分析中的重要性。该微板具有由功能梯度材料制成的核心和由金属泡沫组成的面板。该问题通过准 3D 剪切变形方法和修正的力偶应力理论进行建模。本研究假设核心材料遵循功率梯度模式。各种微机械模型，即 Hashin-Shtrikman 边界、Voigt-Reuss-Hill、Voigt、Reuss 和 Tamura，被应用于估计核心的材料特性。面板由金属泡沫组成，具有闭孔和开孔固体孔隙。通过对力-力矩平衡法获得的耦合运动方程进行数值求解来确定系统的时程型响应。对简化板系统进行了有限元分析，发现通过所提出的理论方法和本文开发的理论得到的数值结果非常吻合。结果表明，微机械模型影响核心层的模拟机械性能，从而影响多层微系统移动负载激励响应的数值结果。