تحلیل ارتعاشات آزاد پوسته‌ی استوانه‌ای با ساختار آگزتیک پروانه‌ای شکل به روش تفاضل مربعات دیفرانسیل

In this paper, the free vibrations of a cylindrical butterfly shell were studied. Auxetic structures refer to lattice structures that, unlike conventional structures, have a negative Poisson's ratio. Among the negative Poisson structures that have received attention in recent years, the butterfly aesthetic can be mentioned. Based on the classical theory of shells and using Hamilton's principle, the vibration equations of the butterfly-shaped cylindrical shell were obtained. The governing equations were solved using the quadratic differential numerical solution method, and the natural frequencies were obtained. For validation, the results of the implemented method were first compared for a cylindrical shell with the results obtained from a finite element simulation using Abaqus software. The main objective of this research is to evaluate the effect of the geometric characteristics of the auxetic structure on the vibration performance of the shell under clamped boundary conditions. The proposed model provides a detailed understanding of how natural frequencies are changed by auxetic geometries, thereby providing valuable insights into the design of high-performance shells.