Folded structures hold significant importance in aerospace technology due to their distinct design, effectively reconciling strength with a lightweight framework. Within aerospace applications, these structures fulfill diverse roles, serving as pivotal elements in aircraft wings, fuselage sections, and essential components of spacecraft and satellites. This study delves into the free vibration behavior of folded sandwich plates composed of a porous core and functionally graded carbon nanotube-reinforced composite (FG-CNTRC) coatings, resting on a two-parameter elastic foundation. Leveraging first-order shear deformation plate theory (FSDT), elasto-dynamic equations are established for each individual plate segment. Utilizing the two-dimensional generalized differential quadrature method (2D-GDQM), these equations are discretized. Subsequently, by applying boundary conditions to all six edges, including traditional clamped, simply supported, and free configurations, and incorporating continuity conditions for displacements, forces, and moments at the joint borders, natural frequencies and modal shapes are extracted for the folded plate structure. The validity of the proposed formulation and results is demonstrated by comparing them with numerical examples for both composite flat and folded plates. This comparison provides strong support for the accuracy and reliability of the present study. The study comprehensively examines the influence of various parameters on natural frequencies, including modal shape visualizations under different boundary configurations, plate thickness, crank angle, porosity parameter, core thickness, foundation stiffness, and CNTs distribution type.

中文翻译：

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基于两参数弹性基础的多孔芯材和 FG-CNTRC 涂层折叠夹层板的固有频率和模态形状

折叠结构由于其独特的设计，能够有效地协调强度与轻质框架，因此在航空航天技术中具有重要意义。在航空航天应用中，这些结构发挥着不同的作用，作为飞机机翼、机身部分以及航天器和卫星的重要部件的关键元件。本研究深入研究了由多孔芯和功能梯度碳纳米管增强复合材料 (FG-CNTRC) 涂层组成的折叠夹层板的自由振动行为，该夹层板基于双参数弹性基础。利用一阶剪切变形板理论 (FSDT)，为每个单独的板段建立弹动力方程。利用二维广义微分求积法 (2D-GDQM)，对这些方程进行离散化。随后，通过对所有六个边应用边界条件，包括传统的夹紧、简支和自由配置，并结合接头边界处的位移、力和力矩的连续性条件，提取折板结构的固有频率和模态形状。通过与复合材料平板和折叠板的数值例子进行比较，证明了所提出的公式和结果的有效性。这一比较为本研究的准确性和可靠性提供了强有力的支持。该研究全面考察了各种参数对固有频率的影响，包括不同边界配置、板厚度、曲柄角、孔隙率参数、核心厚度、基础刚度和碳纳米管分布类型下的模态形状可视化。