Dynamic instability of three-layered cylindrical shells containing an FGM interlayer

• Dynamic instability of FG layered shells under periodic axial loads are investigated.
• The basic equations for three-layered shells containing an FG interlayer are derived.
• Governing equations are reduced Mathieu–Hill equation using the Galerkin method.
• Expression for boundaries of unstable regions of FG layered cylindrical shell are found.
• Effects of variations of FG interlayer on boundaries of unstable regions are studied.

In this study, the dynamic instability of three-layered cylindrical shells containing a functionally graded (FG) interlayer subjected to static and time dependent periodic axial compressive loads are investigated. The governing relations, modified Donnell type dynamic stability and deformation compatibility equations are derived. The governing equations are reduced Mathieu–Hill equation by using Galerkin׳s method and the expressions for boundaries of unstable regions of three-layered cylindrical shell with an FG interlayer are found. Finally, the effects of variations of volume fractions of FG interlayer and shell characteristics on the magnitudes of boundaries of unstable regions are studied numerically.