This paper aims to investigate the free and forced vibration behavior of a sandwich beam with functionally graded porous core and composite face layers embedded with shape memory alloy (SMA). Three different porosity patterns are assumed through the thickness direction of the core, and composite face layers are reinforced with carbon nanotubes (CNT). The sandwich beam is resting on an elastic foundation which is simulated by Vlasov’s model. By using Hamilton’s principle and first-order shear deformation theory, the governing equations of motion are derived. The analytical solution is presented to solve the equations of motion using Navier’s solution. Results are verified with corresponding literatures. Finally, the effects of important parameters such as temperature, volume fraction of SMA, porosity distribution, weight fraction of CNT, and geometric parameters are explored in detail.

中文翻译：

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Vlasov 基础上考虑多孔芯和 SMA 混合复合材料面层的夹层梁自由和受迫振动分析

本文旨在研究具有功能梯度多孔芯和嵌入形状记忆合金 (SMA) 的复合面层的夹层梁的自由和受迫振动行为。通过芯的厚度方向假设三种不同的孔隙率模式，并且复合面层用碳纳米管 (CNT) 增强。夹层梁位于弹性基础上，该基础由 Vlasov 模型模拟。利用哈密顿原理和一阶剪切变形理论，推导出运动控制方程。提供解析解以使用 Navier 解来求解运动方程。结果与相应文献进行了验证。最后，温度、SMA 体积分数、孔隙率分布、CNT 重量分数等重要参数的影响，