Response of functionally graded beams subjected to a moving load and different types of attachments

This paper develops an analytical solution for the dynamic response of a Euler-Bernoulli functionally graded (FG) beam subjected to a load moving with constant velocity and different types of attachments. The classical beam theory (CBT) is used to derive the equation of motion. The material properties of the beam are considered to vary continuously in the transverse direction according to an exponential and a power law models. The stress distribution is evaluated and the location of the neutral axis of the FG beam is obtained. Different types of attachments connected to the beam at specific locations are analysed. The effect of using FG materials to enhance the properties of the beam, resulting in a decreased response of the beam, is made clear. Also, the effect of the restoring force of attachments in reducing the dynamic response of the beam is discussed.