بررسی نانوپوسته‌های استوانه‌ای آگزتیک پروانه‌ای: تحلیل دینامیکی غیرموضعی ارتعاشات آزاد و بهینه‌سازی پارامترهای هندسی برای کاربردهای نانومکانیکی

This research investigates the vibrational behavior of a novel auxetic structure featuring a butterfly-shaped honeycomb architecture, which demonstrates significant potential for applications in the design and optimization of advanced materials and structures at the nanoscale. In this paper, the free vibration characteristics of cylindrical nanoshells fabricated from this auxetic material are thoroughly analyzed. The governing equations are derived using a higher-order shear deformation theory within the framework of nonlocal elasticity theory, employing Hamilton’s principle. These equations are solved analytically via Navier’s method to obtain the vibrational response of the nanoshells. Subsequently, the influence of key parameters—including the nonlocal parameter and the geometric dimensions of the butterfly-shaped unit cells—on the dynamic response of the nanoshells is comprehensively examined and discussed. The results reveal that while the nonlocal parameter consistently reduces the natural frequencies of the butterfly auxetic nanoshells due to its softening effect, the geometric parameters exert a significantly stronger and more decisive influence on the dynamic behavior of the structure.