Here, dynamic responses and frequency analysis of the graphene origami (GOri)-reinforced multilayer functionally graded thick cylindrical shells have been studied using the element free Galerkin (EFG) method and layer-wise (LW) Carrera unified formulation (CUF). To this end, the three-dimensional equation of motion in cylindrical coordinates is derived using the principle of virtual displacements (PVD). The thick cylindrical shell is assumed to be composed of several individual layers, each of which is made of homogeneous GOri-enabled metallic metamaterials. The effective macroscopic mechanical properties of each layer are estimated by the genetic programming (GP)-assisted Halpin–Tsai micromechanical model. The LW-CUF with various order expansions are utilized to accurately describe the displacement fields at each layer and enforce inter laminar continuity. The stiffness and mass matrices are derived by using the EFG method. Newmark method is employed to solve the algebraic governing equation of motions for obtaining dynamic responses of the cylindrical shell subjected to impulsive loads. Comparison of results obtained from the proposed method with other analytical and numerical solutions in literature confirms the validity and efficiency of proposed methodology. Finally, the effect of graphene content, graphene folding degree, and layer distribution patterns on dynamic behavior of cylindrical shells are studied in detail.

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