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Abstract
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This study presents a novel analytical investigation into the free vibration behavior of doubly curved panels composed of graphene-origami metamaterials (GOMMs), resting on a Kerr-type elastic foundation and exposed to a thermal environment. The model captures the mechanical complexity of GOMM-based composite shells by incorporating spatially varying metamaterial distributions, variable folding degrees, and thermomechanical coupling. The First-order Shear Deformation Theory (FSDT) is employed to formulate the displacement field, while the governing equations of motion are derived using Hamilton’s principle. Navier’s solution approach is adopted to solve the resulting eigenvalue problem under simply supported boundary conditions. Various GOMM distribution patterns—including Uniform, Symmetric-A, Symmetric-B, Nonsymmetric, and functionally graded layouts—are examined concerning thermal effects, foundation stiffness, and geometric parameters. Results reveal that both the natural frequencies and their sensitivity to thermal and mechanical parameters are significantly influenced by the folding degree and spatial configuration of GOMMs. Among all patterns, the Symmetric-A and A-type graded distributions deliver the highest stiffness and thermal resilience, while nonsymmetric and X-patterns offer enhanced tunability. These findings offer critical insights for the design of thermally stable, vibration-controlled structures in aerospace, mechanical, and smart adaptive systems where lightweight and tunable performance are essential.
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