Perturbation analysis of resonant and non-resonant excitations of a beam equipped with a nonlinear vibration absorber

In the current paper the impact of the presence of a damped nonlinear Dynamic Vibration Absorber on dynamic behavior of an Euler-Bernoulli clamped-free beam is investigated under resonant and non-resonant excitations. Accordingly, the governing equations of motion are derived and converted to the form of non-dimensional equations. Then, these equations are solved using the Multiple Scales Method after applying the Galerkin Method. It is assumed that the Dynamic Vibration Absorber damping is linear, and its stiffness is composed of two parts, a linear and a third order nonlinear one. Resonant and non-resonant cases have been taken into account for sinusoidal excitation. The influence of the Dynamic Vibration Absorber parameters on the system vibrational behavior is provided. Obtained results illustrate the possibility that under specific circumstances the nonlinear dynamic vibration absorber could have a better performance in suppressing the oscillation amplitude than a similar linear one in jumping phenomenon region. In addition, the results show that in non-resonant frequency regions, there is no major difference in system vibrational behavior in presence of linear damped, undamped and nonlinear vibration absorbers. Furthermore, in comparison with similar linear case, the nonlinearity of the absorber stiffness relocates the resonant frequencies, and makes changes in the non-resonant frequency region.