A Comparison Between the Linear and Nonlinear Dynamic Vibration Absorber for a Timoshenko Beam

Dynamic vibration absorbers (DVAs) play an important role in the energy dissipation of a vibrating system. Undesirable vibrations of structures can be reduced by using the absorbers. This paper investigates the effect of an attached energy sink on the energy dissipation of a simply supported beam subjected to harmonic excitation. The aim is to design an optimal linear energy sink (LES) and a nonlinear energy sink (NES) and then compare them with each other. Each absorber includes a spring, a mass, and a damper. For each absorber, the optimum mass, stiffness, and damping coefficients are obtained in order to minimize the beam’s maximum amplitude at the resonant frequencies. The optimization problem is minimizing the maximum amplitude of the beam subjected to an arbitrary harmonic force excitation. For consideration of the effects of rotary inertia and shear deformation, the Timoshenko beam theory is used. The mathematical model of beam with DVA is verified by using the ANSYS WORKBENCH software. Finally, by considering the uncertainty on the DVA parameters it was observed that the LES is more robust than the NES.