Vibration of Toroidal Shell Segments Made of Porosity-Dependent Nanocomposite Foam Subjected to a Moving Load

This research deals with the analysis of moving-load dynamic response of toroidal shell segments subjected to a moving mass with constant velocity. It is assumed that the toroidal shells are made from a porosity-dependent composite aluminum reinforced with graphene nanoplatelets (GNPs). The shell is composed of six composite layers with the same thickness reinforced with GNPs while each of them has different values of porosity. The distribution of porosities in the shell thickness can be formulated by implementing five different profiles such as FG-X, FG-O, FG-V, FG-A, and UD. The nonlinear strain–displacement formulations are generated on the basis of the first-order shear deformation theory considering the von Kármán kinematic assumption. The system of nonlinear equations of motion is determined for the nanocomposite toroidal shell under moving load by implementing the Hamilton principle. The Ritz solution method is implemented in this research to solve the obtained system of time-dependent differential equations. Results of this research are validated by a comparison of the natural frequencies of a simple case of toroidal shells (cylindrical shell). Then, several examples are generated and presented to estimate the time-dependent response of the metal-based nanocomposite toroidal shells under the action of a moving load. The effects of material properties as well as the effects of geometrical parameters on the shell’s moving-load response are investigated and illustrated in detail.