A complex solution on the dynamic response of sandwich graphene-reinforced aluminum-based composite beams with copper face sheets under two moving constant loads on an elastic foundation

An analytical solution was used to investigate the elastic response of a sandwich beam with a graphene-reinforced aluminum-based composite (GRAC) on an elastic foundation using copper as the face layer of the functionally graded composite beam and a simply supported boundary condition. Mantari's higher-order shear deformation theory was utilized to derive the equations, which were solved in Laplace space and then converted into space–time using Laplace inversion. The exact response of the GRAC sandwich beam was obtained by considering the displacement at the mid-span of the sandwich beam. Two moving loads with different speed ratios were applied at a single point, and the effect of various parameters, including the spring constant, the speed ratio, the percentage of graphene, the moving load speed, and the distribution pattern, was investigated. This study aimed to eliminate any overlap and improve the accuracy of the results. The exact solving method presented has not been reported in other articles so far. Additionally, due to the difficulty of solving mathematical equations, this method is only applicable to simple boundary conditions.