Tuning methodology of nonlinear vibration absorbers coupled to nonlinear mechanical systems

A large body of literature exists regarding linear and nonlinear dynamic absorbers, but the vast majority of it deals with linear primary structures. However, nonlinearity is a frequent occurrence in engineering applications. Therefore, the present paper focuses on the mitigation of vibrations of nonlinear primary systems using nonlinear dynamic absorbers. Because most existing contributions about their design rely on extensive parametric studies, which are computationally demanding, or on analytic methods, which may be limited to small-amplitude motions, this study proposes a tuning procedure which is computationally tractable and can treat strongly nonlinear regimes of motion. The proposed methodology relies on a frequency-energy based approach followed by bifurcation analysis. The results are illustrated using a one-degree-of-freedom primary system, which can, for instance, represent the vibrations of a specific mode of a multi-degree-of-freedom structure.