This study presents a novel analytical framework to investigate the large amplitude vibration of sandwich doubly curved shells with an auxetic honeycomb core, a subject less explored compared to beams and plates. The primary aim is to reveal how the negative Poisson’s ratio (NPR) and specific geometric parameters of the auxetic core can be tailored to control the nonlinear frequency response of the shell. Employing von Karman geometric nonlinear theory alongside Donnell’s shallow shell formulation, the governing equations are derived. The homotopy perturbation method (HPM) is employed to solve nonlinear governing equations, revealing optimal auxetic geometries for dynamic performance. The impact of various cellular configurations exhibiting positive and NPRs on the vibrational characteristics of the auxetic-cored shells is thoroughly examined. The results offer critical insights for the optimal design of advanced curved sandwich structures with tailored dynamic performance.

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