In this paper, the nonlinear dynamic responses of ring-stiffened truncated conical sandwich shells-like aerospace structures fabricated by perfectly bonded graphene platelets (GPLs) reinforced composite porous core and face sheets (GPLRC-PC-FS) under asymmetric internal ring-shaped moving load are investigated. The sandwich shells have edge point supports, which are simulated using the translational and rotational artificial springs. In addition to the open cell porosities, closed cells are also considered and analyzed. The spatially discretized nonlinear motion equations are derived based on the first-order shear deformation theory (FSDT) under the von Kármán geometric nonlinearity assumptions using the Ritz method with Chebyshev polynomials as its admissible basis functions. Then, Newmark's time integration scheme along with the Newton–Raphson method is employed to obtain the shell dynamic responses. After demonstrating the robustness and accuracy of the approach, the influence of rings number, their size and arrangement, core porosity distribution and structure, face sheets, GPLs parameters, moving load velocity and boundary conditions on the shell responses are studied. The results show that the shell dynamic behaviors are significantly affected by porosity, but almost are independent of the type of porosity distribution pattern and its structure (open and closed cell porosities). It is shown that the shell deflection can be minimized by suitably choosing the number of rings, their dimensions and arrangement. Moreover, the nonlinear behaviors of the shells have a significant correlation with the number of point supports and by adjusting the support stiffnesses, the nonlinear dynamic responses of the shells can be reduced.