Analytical responses of functionally graded beam under moving mass using Caputo and Caputo–Fabrizio fractional derivative models

Abstract

In this article, a functionally graded simply supported Euler–Bernoulli beam subjected to moving mass is considered in which the beam-damping is described using fractional Kelvin–Voigt model. A comparison between Caputo and Caputo–Fabrizio fractional derivatives for obtaining the analytical dynamic response of the beam is carried out. The equation of motion is solved by the decomposition method with the cooperation of the Laplace transform. Two verification studies were performed to check the validity of the solutions. The results show that the grading order, the velocity of the moving mass and the fractional derivative order have significant effects on the beam deflection, whereas the difference between the results of the two fractional derivative models is expressed by the determination of the correlation coefficient.