Dynamical response of a cantilever beam under moving mass with fractional damping

Abstract

Abstract In the present paper, the dynamical response of a cantilever beam with fractional damping excited by the moving mass load is studied. First, the vibration equation of the cantilever beam is established by adopting Euler-Bernoulli beam theory. Then, the established equation is discretized by using Galerkin discretization. The discrete equation is difficult to solve due to the fractional damping. Based on the generalized harmonic function technology, the fractional damping force is approximated by a damping force and a conservative force. Then, an efficient algorithm is used to calculated the truncated equation to derive the dynamical response. The displacement at the end of the cantilever beam is calculated, and the influence of fractional damping coefficients is analysed.