Free vibration behavior of bio-inspired helicoidal laminated sandwich skew plates: finite element-assisted higher-order zigzag theory

Introduction Helicoidal (Bouligand) architectures found in natural biological systems have attracted considerable attention for enhancing the mechanical performance of laminated composite structures without increasing material usage or weight. Although the static and impact behavior of helicoidal laminates has been extensively investigated, studies on the free vibration characteristics of bio-inspired helicoidal laminated sandwich skew plates remain limited. This study aims to evaluate the dynamic performance of cross- and double‐helicoidal laminated sandwich skew plates and compare their vibration behavior with conventional cross‐ply laminates. Methods The free vibration behavior of bio‐inspired cross‐helicoidal and double‐helicoidal laminated sandwich skew plates was analyzed using a finite element formulation based on higher‐order zigzag theory. The governing equations were derived through Hamilton's principle. Skew geometry was rigorously incorporated using Jacobian‐based coordinate transformations and boundary transformation matrices. A comprehensive parametric investigation was performed to assess the effects of skew angle, side‐to‐thickness ratio, core thickness ratio, interply angle, and boundary conditions on the natural frequencies of the structures. Results The results indicate that helicoidal layup configurations significantly enhance the dynamic stiffness of laminated sandwich skew plates compared with conventional cross‐ply laminates. Among the configurations examined, the cross‐helicoidal CH12 arrangement exhibited the highest vibration performance, achieving up to 14.7% higher natural frequencies than cross-ply laminates under simply supported boundary conditions (a/h = 100, skew angle = 0°). Under cantilever boundary conditions, frequency improvements of approximately 9–10% were observed. Furthermore, increasing the skew angle generally increased the structural stiffness and natural frequencies for most boundary conditions. However, cantilever plates demonstrated a non-monotonic response due to the interaction between geometric effects and stiffness variations. Discussion and Conclusions The study demonstrates that bio‐inspired helicoidal architectures provide superior vibration characteristics and enhanced dynamic stiffness relative to conventional laminate designs. The observed improvements are attributed to the more efficient distribution of fiber orientations, which enhances structural rigidity and resistance to deformation. These findings highlight the potential of helicoidal laminated sandwich skew plates for lightweight engineering applications requiring improved vibration resistance and dynamic performance, such as aerospace, marine, and advanced structural systems.