Persistent and ghost nonlinear normal modes in the forced response of non-smooth systems

Abstract

Non-smooth systems may exhibit bifurcations characterized by the onset of superabundant modes in internal resonance conditions. These modes are characterized by peculiar shape that can emerge in the forced response of the system. This paper presents an investigation on the evidence of the nonlinear normal modes in the forced system response. The study is carried out on a two-degrees-of-freedom system characterized by piecewise linear restoring forces, by means of a theoretical analysis as well as numerical simulations and experimental tests. As a result, the nonlinear normal modes of the considered system are classified among persistent, and ghost; the former are those influencing the response, while the latter ones, even if stable, cannot be directly excited by external forces. Finally, criteria to distinguish between ghost and persistent modes are proposed.