Dynamics of an axially functionally graded beam under axial load

This paper considers the dynamics of a simply supported beam under axial time–dependent load. The beam is made of an axially functionally graded material. The motion equations are deduced from the equilibrium in deformed configuration and no restriction is made on the amplitude of the transversal displacement, but that naturally imposed by the inextensibility assumption that is adopted in the present study. The transversal motion equation, that is a partial differential equation, is approximated by its Taylor expansion until third order and then discretized through the Galerkin procedure