Forced Vibration of Class of Nonlinear Dissipative Beams

An exact solution employing a Galerkin-type approach is presented for the steady-state motion of a class of dissipative Bernoulli-Euler beams provided with nonlinear auxiliary mass dampers. The beams are viscously damped and the excitation is furnished in the form of distributed, or concentrated loads, or both, that vary sinusoidally. The nonlinear damper may be applied to any point in the system. Experimental studies with a mechanical model corroborate the theoretical results. Results of the analysis are applied to cantilever and simply-supported beams subjected to base excitation, uniform load, and discrete force excitation at various points along the beams. The effects of all system parameters and mass ratio are determined. It is found that the damper under consideration is an efficient device for reducing the vibration of continuous systems, particularly cantilevered structures.