Vibration modals of composite auxetic honeycomb sandwich cylindrical shells

Abstract The vibration modals of composite sandwich cylindrical shells with auxetic honeycomb cells arrayed in the circumferential direction and axial direction were studied theoretically and numerically. The equivalent moduli and relative density of auxetic cores were derived and validated. Subsequently, the differences in these physical quantities caused by the number of layers were taken into consideration. Based on these works, a verified third order shear deformation theory (TSDT) was applied to deduce the free vibration governing equations of sandwich cylindrical shells. Specially, the effects of deepness terms were not ignored. To prove the accuracy of the theory, four finite element modellings of composite sandwich cylindrical shells with different numbers of auxetic cells arrayed in the circumferential direction were established for vibration analysis. Additionally, cylindrical shells with auxetic cells arrayed in the axial direction were modeled to verify the theory. The frequencies of composite sandwich cylindrical shells calculated by theory were a good fit with those obtained from the numerical method. Thus, the influences of dimensions on vibration modals of composite sandwich cylindrical shells were discussed by TSDT. The sensitivity analysis showed that the number of layers, the radius of cylindrical shells, and the thickness of auxetic cores had a great influence on the frequencies of composite auxetic cylindrical shells. Highlights The governing equations of cylindrical shells were deduced by TSDT. Effects of layers on the equivalent stiffnesses of the auxetic core were considered. Effects of dimensions on vibration modal of cylindrical shells were studied.