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Abstract
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Up to now, no research has yet been presented on the vibrational properties of a new auxetic butterfly-shaped honeycomb structure. The findings of this study have the potential to inform the design and optimization of advanced nanoscale materials and nanostructures used in various engineering applications. This article focuses on analyzing the free vibration characteristics of butterfly-shaped honeycomb (BSH) auxetic doubly curved nanoshells. We employ high-order shear deformation theory based on nonlocal strain gradient theory (NSGT) and Hamilton’s principle to derive the equations of motion. Using Navier's solution, we address the vibration behavior of the BSH nanoshells. The numerical findings from this study are compared to those from existing literature to assess the accuracy and reliability of the proposed formulas. Additionally, we thoroughly investigate the effects of the nonlocal parameter, strain gradient length scale, curvature radius, and the geometric dimensions of the butterfly-shaped auxetic structure on the behavior of the BSH nanoshell.
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