Vibration reduction on beams subjected to moving loads using linear and nonlinear dynamic absorbers

The present work is focused on the analysis of the effectiveness of dynamic vibration absorbers applied to beams excited by moving loads. The goal is to test the performance of nonlinear dampers in comparison with the classical linear damper. Simply supported beams are analysed using the Euler–Bernoulli theory, the partial differential equation governing the beam dynamics are reduced to an ordinary differential equation set by means of the Galerkin–Bubnov method, and a multimode expansion of the displacement field allows accurate analysis of the problem. The performance of the dynamic dampers in vibration reduction is estimated through two indicators, the maximum amplitude of vibration, and the portion of energy dissipated by the dynamic damper. The same indicators are used as objective functions for developing an optimisation approach. Two conservation laws are found for the optimal parameters and beam geometry for nonlinear (cubic) dynamic dampers.