Free Vibrations of a New Three-Phase Composite Cylindrical Shell

The novel concept of a functionally graded three-phase composite structure is derived from the urgent need to improve the mechanical properties of traditional two-phase composite structures in aviation. In this paper, we study the free vibrations of a new functionally graded three-phase composite cylindrical shell reinforced synergistically with graphene platelets and carbon fibers. We calculate the equivalent elastic properties of the new three-phase composite cylindrical shell using the Halpin-Tsai and Mori-Tanaka models. The governing equations of this three-phase composite cylindrical shell are derived by using first-order shear deformation theory and Hamilton’s principle. We obtain the natural frequencies and mode shapes of the new functionally graded three-phase composite cylindrical shell under artificial boundary conditions. By comparing the results of this paper with the numerical results of finite element software, the calculation method is verified. The effects of the boundary spring stiffness, GPL mass fraction, GPL functionally graded distributions, carbon fiber content, and the carbon fiber layup angle on the free vibrations of the functionally graded three-phase composite cylindrical shell are analyzed in depth. The conclusions provide a certain guiding significance for the future application of this new three-phase composite structure in the aerospace and engineering fields.