This investigation delves into the free vibration characteristics of coupled nested conical shells (CNCSs) made of porous composite materials. These two conical shells are connected by a mid-layer of elastic springs. The composite materials used in the shells consist of epoxy, nanofillers, and fibers. Two types of nanofillers are considered: Graphene Nanoplatelets (GNPs) and Carbon Nanotubes (CNTs), while E-glass fiber is used as the fiber. The nanofillers are distributed in four different patterns within the shell section. Porosity is uniformly distributed along the shell section and characterized by a coefficient. The rule of mixtures is employed to ascertain the equivalent material properties of the hybrid materials, while the Chamis approach is utilized for three-phase materials. First-order shear deformation theory (FSDT) and Donnell\\\\\\\'s theory are utilized for modeling the conical shells. The governing equations of motion are established through Hamilton\\\\\\\'s principle are solved using the generalized differential quadrature method (GDQM). Seven different boundary conditions (BCs) are considered to encompass the full range of BCs for CNCSs and four type of BCs for single truncated conical shell (STCS). The solution\\\\\\\'s accuracy is verified, and the effects of various parameters on the natural frequency parameter (NFP) of the shell are investigated, such as BCs, circumferential wave number (n), nanofillers pattern, semi-vertex angle, nanofillers angle, and mid-layer stiffness. Initially, a comprehensive investigation into the vibration behavior of a STCS is presented, followed by an analysis of the NFP of the CNCSs. The results demonstrate that the stiffness of the elastic mid-layer significantly influences the NFP of the system. The orientation of the nanofillers in the shell can increase or decrease the NFP. Additionally, the relationship between mode number and n depends on the type of BCs of the shells.

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