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This study investigated the natural vibration of a sandwich conical-conical shell that is partially supported by Winkler–Pasternak foundations. The sandwich system comprises an open-cell foam (OCF) core and laminated composite face sheets reinforced with graphene platelets using functionally graded models (FG-GPLRC). To account for through-the-thickness shear deformations and rotary inertias, the first-order theory of shells is combined with Donnell-type kinematic assumptions. Hamilton’s principle is utilized to establish the general motion equations and related boundary and continuity conditions. The resulting system of equations is discretized using the semi-analytical generalized differential quadrature (GDQ) approach. An eigenvalue problem is formulated to analyze the corresponding mode shapes and vibration frequencies for the shell ends and continuity criteria under various boundary conditions. Parametric experiments are conducted for sandwich conical-conical shells partially supported by Winkler–Pasternak foundations. This study examined the impact of multiple factors on the frequency of a joined shell structure, including the total thickness, FG-GPL face sheet thickness, various boundary conditions, the length of each cone segment, and the Winkler and shear elastic foundation. Notably, this research also analyzed the effects of a partial elastic foundation on the structure’s frequency for the first time.
Qiu et al. (Thu,) studied this question.