FG layers' effect on nonlinear free vibrations of sandwich auxetic cylinders

This study develops a novel semi-analytical framework to investigate the nonlinear free vibration behavior of functionally graded (FG) auxetic cylinders, which are increasingly used in aerospace, automotive, and biomedical applications for their potential in weight reduction and enhanced dynamic performance. The cylinder consists of one auxetic core layer and two inner and outer FG layers, with material properties varying continuously through the thickness. Utilizing the First-order Shear Deformation Theory (FSDT) and von Kármán strain relations, a system of four coupled nonlinear partial differential equations is derived using the Hamilton principle, and they are solved using the multiple-scale method for general boundary conditions. The key contributions of this work include: the integration of auxetic behavior and material gradation into a unified nonlinear vibration model, the derivation of a closed-form semi-analytical solution that captures the effects of transverse shear deformation and geometric nonlinearity, and the detailed exploration of frequency-amplitude relationships and nonlinear vibration characteristics. The results offer a valuable tool for designing lightweight and high-performance cylindrical structures with optimized dynamic characteristics. To evaluate the accuracy of the semi-analytical model, the results are compared with other literature results.