Frequency response of rotating two-directional functionally graded GPL-reinforced conical shells on elastic foundation

In this article, a semi-analytical solution is provided to investigate the free vibration characteristics of rotating truncated conical shells surrounded by Winkler–Pasternak type foundation. It assumed that material shell composed epoxy as matrix and graphene nanoplatelets (GPLs) reinforcement dispersed in both thickness length directions shell. The modeled based on first-order shear deformation theory equivalent mechanical properties are evaluated using rule mixture Halpin–Tsai model. governing equations derived implementing Hamilton’s principle incorporating centrifugal acceleration, Coriolis initial hoop tension. Utilizing trigonometric functions, an analytical presented solve circumferential direction numerical longitudinal utilizing differential quadrature method. convergence accuracy present results examined with those available literature. A parametric study check influences boundary conditions, rotational speed, wave number, mass fraction dispersion pattern GPLs, Winkler coefficients foundation natural frequencies concluded increment GPLs increases scattering near inner surface small radius have higher reinforcing effect.