A Comprehensive Parametric Analysis of Geometric Effects on the Natural Frequencies of Auxetic and Honeycomb Beams

This paper Presents a comprehensive finite element method (FEM) study of the free vibration behavior of auxetic and honeycomb beams, using Euler–Bernoulli beam theory (EBBT). For the first time, a systematic parametric analysis is conducted to investigate the impact of unit cell (UC) geometry, including connection angle, link length, and thickness, on the natural frequency of both beam types by considering more than 22,000 different UC geometries. In this regard, a novel and adjustable UC design is employed to directly compare the auxetic and honeycomb configurations. The study also explores the influence of UC row numbers and orientations on the natural frequency of these beams. The results declare that variations in each of them lead to nonlinear increases or decreases in natural frequencies. As well, for most cases under identical conditions, the natural frequencies for honeycomb beams are found to be higher than those for auxetic beams. These findings address a significant gap in the literature and provide valuable insights for the design of lightweight, vibration-resistant structures in applications such as aerospace, automotive, and smart systems. Furthermore, this work contributes to the advancement of parametric design in auxetic and honeycomb beams, offering a framework to support dynamic and vibration performance improvements in engineering applications.