The increasing demand for lightweight, high-strength structures in advanced engineering applications, such as aerospace and marine systems, necessitates the development of robust models to predict the vibrational behavior of complex multi-segment shell structures. This study introduces a novel numerical–analytical framework for the free vibration analysis of joined hemispherical–cylindrical–conical (JCCH) triple-shell systems constructed from three-phase porous nanocomposites reinforced with three-dimensional graphene foam (3DGF) and AS4 carbon fibers. By integrating first-order shear deformation theory (FSDT), Hamilton’s principle, and the generalized differential quadrature (GDQ) method, the proposed model accounts for material porosity, elastic foundation stiffness, and diverse boundary conditions, addressing a critical gap in the literature regarding the coupled effects of these parameters. The framework achieves high accuracy with minimal computational cost, validated against established benchmarks with discrepancies below 2 %. Parametric analyses reveal that increasing foundation stiffness from 106 to 109 N/m3 elevates natural frequencies by up to 35 % under clamped–clamped conditions, while higher porosity levels (up to 0.65) reduce frequencies by approximately 15 % in free–free configurations. The model’s ability to optimize vibrational performance through tailored material and geometric parameters positions it as a powerful tool for designing high-performance, lightweight structures in cutting-edge engineering applications.

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