Natural frequency investigation of graphene oxide powder nanocomposite cylindrical shells surrounded by Winkler/Pasternak/Kerr elastic foundations with a focus on various boundary conditions

For the first time, the present research examines the free vibration responses, Natural Frequencies (NFs), of Graphene Oxide Powder (GOP) nanocomposite cylindrical shells surrounded by three types of elastic foundations considering different Boundary Conditions (BCs). To support this, the effects of various BCs are examined on the NFs related to the GOP Nanocomposite Cylindrical Shells (GOPNCS). In addition, elastic foundations are characterized by three factors: Winkler, Pasternak, and Kerr. Addedly, First-order Shear Deformation Theory (FSDT) and Donnell's shell theory are combined to discover the fundamental formulations related to the GOPNCS structures. Then, the equations of motion related to the GOPNCS are formulated employing Hamilton's principle. In subsequent, the equations associated with the previous step are discretized by implementing the Generalized Differential Quadrature Method (GDQM), counted as the mesh reduction method. Afterward, the standard eigenvalue determination is employed to determine the NFs associated with the GOPNCS. Ultimately, multiple benchmarks are answered to authenticate the scheme recommended for determining the NFs of the GOPNCS. Further, numerous original problems are arranged and highlight the effects of changes in material and geometrical features, various BCs, and three types of elastic foundations on the NFs related to the GOPNCS.