Abstract In this study, the dynamic buckling of bi-directional functionally graded porous (BD-FG) truncated conical shell resting on an elastic foundation is investigated for different boundary conditions. The structure is under an axial compression loading at the two ends. First order shear deformation theory (FSDT) and Hamilton's principle are used to derive the governing equations. The material characteristics change according to modified power-law model across thickness and along length directions for even and uneven distributions of porosity pattern. The governing equations are solved numerically by means of the Generalized Differential Quadrature method. Afterwards, the Bolotin’s method is employed for attaining the dynamic instability region of structure. The results are compared and validated with those cases from published papers. Subsequently, the effect of circumferential half wave number, geometrical parameters, power-law indexes, porosity volume fraction, boundary conditions, static load factor and elastic foundation parameters on the dynamic instability region are investigated.

中文翻译：

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不同边界条件下双向功能梯度多孔截锥壳的动态屈曲分析

摘要 在这项研究中，研究了基于弹性基础的双向功能梯度多孔 (BD-FG) 截锥壳在不同边界条件下的动态屈曲。结构两端承受轴向压缩载荷。一阶剪切变形理论（FSDT）和哈密顿原理用于推导控制方程。材料特性根据修改的幂律模型在厚度和长度方向上发生变化，以实现均匀和不均匀分布的孔隙率模式。控制方程通过广义微分求和法进行数值求解。之后，采用Bolotin 方法获得结构的动态不稳定区域。将结果与已发表论文中的案例进行比较和验证。