The purpose of this study is to investigate the free vibration behavior of stepped sandwich cylinders with auxetic honeycomb cores using semi-analytical and numerical approaches. The study aims to develop efficient formulations based on the first-order shear deformation theory and evaluate the effects of key geometric parameters, including inclination angle, thickness ratio, relative thickness and length ratio, on the natural frequencies and dynamic characteristics of the structure.
The formulation is based on the first-order shear deformation theory to model the free vibration behavior of stepped sandwich cylinders with auxetic honeycomb cores. The governing equations are derived using energy principles, including kinetic and potential energy expressions. The problem is solved using both semi-analytical and numerical approaches. In the semi-analytical framework, the Rayleigh–Ritz method is applied with trigonometric basis functions, and an extended formulation employs Legendre polynomials with Lagrange multipliers to enforce boundary conditions. In addition, a one-dimensional ring finite element is developed, and its mass and stiffness matrices are obtained via the energy method. The resulting eigenvalue problems are solved to determine natural frequencies.
The results show that the proposed semi-analytical and finite element formulations are in excellent agreement with available literature, confirming their accuracy and reliability. It is observed that increasing the inclination angle and relative thickness, as well as decreasing the length ratio, leads to a reduction in the natural frequencies of the stepped sandwich cylinder. A higher core-to-face sheet thickness ratio also generally lowers the frequencies. Furthermore, increasing the length ratio reduces the natural frequencies for all thickness configurations. At low length ratios, the effect of the auxiliary–cylinder thickness ratio is non-monotonic, whereas at high length ratios, it leads to a consistent increase in frequencies.
This study presents a comprehensive vibration analysis of stepped sandwich cylinders with auxetic honeycomb cores using both semi-analytical and numerical frameworks. The originality lies in the integration of Rayleigh–Ritz formulations with trigonometric and Legendre basis functions alongside a Lagrange multiplier approach, enabling flexible enforcement of boundary conditions. In addition, a dedicated one-dimensional ring finite element is developed for efficient numerical modeling. The combined methodology provides a robust and accurate tool for analyzing complex stepped cylindrical structures. The findings offer valuable insights into how geometric parameters and core configurations influence dynamic behavior, supporting improved design of lightweight, high-performance sandwich cylindrical structures.
