In this research, the natural frequency responses of joined hemispherical–cylindrical–conical shells made of composite three-phase materials have been dealt with in the framework of First-Order Shear Deformation Theory (FOSDT). The joined hemispherical–cylindrical–conical shells are assumed to be made of hybrid porous nanocomposite material with three phases including a matrix of epoxy, macroscale carbon fiber, and nanoscale 3D Graphene Foams (3GFs). For getting the equivalent mechanical properties of the Hybrid Matrix (HM) including polymer epoxy and 3GFs, the well-known rule of the mixture is used. In addition, the effect of porosity throughout the HM is considered using two novel and one well-known porosity distribution pattern. Moreover, the HM is reinforced with transversely isotropic macroscale carbon fibers in which the Halpin–Tsai scheme is used for multiscale homogenization procedure. The governing equations of motion associated with hybrid porous nanocomposite joined hemispherical–cylindrical–conical structures are figured out by implementing Donnell-type shell formulation and Hamilton’s approach. Moreover, an efficient and well-known semi-analytical solution method entitled Generalized Differential Quadrature Method (GDQM) is employed to solve the governing differential equations. To verify the proposed formulation some well-known benchmarks, especially those are composed of homogenous materials have been analyzed, and a good agreement has been achieved. Besides, some other new and applicable problems are considered to investigate the effects of different parameters including various boundary conditions, patterns of porosity distributions, and geometric properties of structure on the vibration behavior of joined shells.

在这项研究中，由复合三相材料制成的连接的半球-圆柱-圆锥壳的固有频率响应已经在一阶剪切变形理论（FOSDT）的框架内进行了处理。假设连接的半球-圆柱-圆锥壳由具有三相的混合多孔纳米复合材料制成，包括环氧树脂基质、宏观碳纤维和纳米级 3D 石墨烯泡沫 (3GFs)。为了获得混合基体 (HM) 的等效机械性能，包括聚合物环氧树脂和 3GF，使用了众所周知的混合物规则。此外，使用两种新颖且一种众所周知的孔隙度分布模式来考虑整个 HM 中孔隙度的影响。而且，HM 用横向各向同性的宏观碳纤维增强，其中 Halpin-Tsai 方案用于多尺度均化过程。通过实施 Donnell 型壳公式和 Hamilton 方法，计算出与混合多孔纳米复合材料连接的半球-圆柱-圆锥结构相关的运动控制方程。此外，采用名为广义微分正交法（GDQM）的有效且众所周知的半解析解方法来求解控制微分方程。为了验证所提出的配方，对一些众所周知的基准，特别是那些由均质材料组成的基准进行了分析，并取得了良好的一致性。除了，