On dynamic of imperfect GNP nanocomposite joined hemisphere-cylinder shells on Winkler foundation

Abstract

This paper aims to analyze the frequencies related to the poriferous nanocomposite joined hemisphere-cylinder shells (JHCS) resting on the Winkler foundation for the first time. In detail, the Winkler foundation is used to model the soil’s behavior surrounding the JHCS. Graphene nanoplatelet (GNP) is a nano-size material that enhances a matrix to make GNP nanocomposites (GNPNs). Additionally, nine different functionally graded (FG) distribution forms along the thickness of the JHCS are used to mark the efficiency of GNP through the GNPN. In addition, two distribution models along the thickness of the JHCS, covering FG and uniform models, are implemented to address the effect of the porosity along the GNPN. Supplementarily, via joining Donnell’s shell and first shear deformation theories, the primary equations of the JHCS are determined. Addedly, Hamilton’s principle finds the fundamental motion equations (FMEs) of the JHCS. The generalized differential quadrature scheme discretizes the FMEs, boundary, and joining equations. Next, via eigenvalue determination, the frequencies of the system are discovered. Finally, the influences correlated with physical values, FG forms of the GNP, edge cases, porosity models, and Winkler foundation on the frequencies correlated with the poriferous nanocomposite JHCS are evaluated.