<p>This research investigates the nonlinear vibration behavior of bidirectional functionally graded sandwich conical shells (BDFG-SC) incorporating a porous foam core. This work addresses the critical need for lightweight yet robust structural components in advanced applications, such as the aerospace and automotive industries, where precise control of dynamic responses under operational loads is paramount. The nonlinear governing equations, derived using the First-order Shear Deformation Theory (FSDT) and von Kármán nonlinear strain relations, were solved using the Galerkin discretization and the homotopy perturbation method. A key novelty of this study lies in the comprehensive parametric analysis that explores the intricate effects of the foam porosity coefficient, porosity distribution patterns, FG power indices, semi-vertex angle, and various boundary conditions on both the fundamental natural frequencies and the nonlinear backbone curves. The results reveal significant influences of these parameters, highlighting observed transitions between hardening and softening nonlinear response regimes. Specifically, this study provides novel insights into how tailoring material distributions and structural geometry can be leveraged to tune the dynamic characteristics of these shells, offering valuable guidance for the design of next-generation lightweight structures with optimized vibration performance. The accuracy of the proposed formulation was validated against existing literature.</p>