Performance of nonlinear vibration absorbers for multi-degrees-of-freedom systems using nonlinear normal modes

Linear vibration absorbers are a valuable tool used to suppress vibrations due to harmonic excitation in structural systems. While limited evaluation of the performance of nonlinear vibration absorbers for nonlinear structures exists in the literature for single mode structures, none exists for multi-mode structures. Consequently, nonlinear multiple-degrees-of-freedom structures are evaluated. The theory of nonlinear normal modes is extended to include consideration of modal damping, excitation and small linear coupling, allowing estimation of vibration absorber performance. The dynamics of the N + 1-degrees-of-freedom system are shown to reduce to those of a two-degrees-of-freedom system on a four-dimensional nonlinear modal manifold, thereby simplifying the analysis. Quantitative agreement is shown to require a higher-order model which is recommended for future investigation.