Large amplitude forced vibrations of multi-stepped beams carrying concentric masses

The general purpose of the present study is to investigate the geometrically non-linear forced vibration of multi-stepped beams carrying masses. This study was carried out on the basis of Euler-Bernoulli beam theory and Von Karman's assumptions of geometric non-linearity. The linear problem is firstly solved, and then the discrete expressions of total strain and kinetic energies are derived. By applying Hamilton's principle, the problem is reduced to a non-linear algebraic system solved by a multi-mode approach. The numerical results are discussed following parametric studies, where the effect of varying section, inertia, length ratios and mass magnitude on the non-linear dynamic behaviour of the beam-mass system is illustrated.