Transient vibration of a fractional viscoelastic cantilever beam with an eccentric mass element at the end

Abstract

The work focuses on the transient forced vibration of a cantilever beam with a rigid eccentric mass element attached at the free end. The Euler-Bernoulli beam theory and the viscoelastic fractional Kelvin-Voigt material model are adopted. The equation of motion of the beam is derived using Hamilton's principle. The first eigenfunction of linear vibrations is used as an approximate solution for the nonlinear vibrations. The equations of motion of the system are solved numerically. The impact of the order of the fractional derivative on the beam transient linear and nonlinear vibrations is studied.