An efficient finite element model based on three nodded element has been developed for the vibration analysis of sandwich arches with graded metallic cellular (GMC) core. The present formulation is based on the higher-order shear deformation theory and orthogonal curvilinear coordinate axes. The arch consists of two isotropic face sheets and a GMC core layer. The internal pores in the core layer follow the different types of distributions. The material properties of the GMC core layer of the sandwich arches vary in the thickness direction as a function in terms of porosity coefficient and mass density. Three types of porosity distributions have been considered to accomplish the vibration responses of sandwich arches. The present formulation is validated with limited results available in the literature. Few new results are computed and the effects of different influencing parameters such as porosity coefficient [Formula: see text], porosity distribution type, the thickness-to-length ratio [Formula: see text], boundary conditions and opening angle [Formula: see text] on the free vibration characteristics of sandwich arches with the GMC core are observed. The present finite element model gives better convergence and more accurate results than a conventional two nodded element-based finite element model.

中文翻译：

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梯度金属蜂窝芯夹心拱自由振动分析的高效三点有限元公式

基于三点单元的有效有限元模型已被开发用于梯度金属蜂窝（GMC）芯夹层拱的振动分析。本公式基于高阶剪切变形理论和正交曲线坐标轴。拱由两个各向同性面板和一个 GMC 核心层组成。核心层的内部孔隙遵循不同类型的分布。夹层拱门的 GMC 芯层的材料特性在厚度方向上随孔隙率系数和质量密度的变化而变化。已经考虑了三种类型的孔隙率分布来完成夹层拱门的振动响应。目前的配方已通过文献中可用的有限结果进行验证。计算的新结果很少，不同影响参数的影响，如孔隙率系数[公式：见文本]、孔隙率分布类型、厚长比[公式：见文本]、边界条件和张角[公式：见text] 对 GMC 芯夹层拱的自由振动特性进行了观察。本有限元模型比传统的基于两个节点的有限元模型具有更好的收敛性和更准确的结果。