LAUSR

Abstract This paper performs nonlinear vibration analysis of metal foam circular cylindrical shells reinforced with graphene platelets. An improved Donnell nonlinear shell theory is employed to formulate the present model. The graphene platelet reinforced material properties are evaluated by the Halpin–Tsai equation. Different types of porosity and graphene platelet (GPL) distribution are taken into account. Governing equations are derived via Hamilton's principle and then they are transformed to ordinary differential equations using the Galerkin method. Afterwards, nonlinear frequencies of the system are solved by using the multiple scale method. Our findings demonstrate that GPL reinforced metal foam (GPLRMF) shells exhibit hardening-spring vibration characteristics. The nonlinear to linear frequency ratio of the shell closely relates to the porosity distributions and GPL patterns. The effect of geometrical size of graphene platelets on nonlinear vibration characteristics of GPLRMF cylindrical shells is also highlighted.