Constructing Backbone Curves from Free-Decay Vibrations Data in Multi-Degrees of Freedom Oscillatory Systems

Abstract

Backbone curves are often the best representation of the nonlinear behavior for the vibrations of mechanical systems. Several approaches for obtaining them are present in literature, either analytical, numerical or experimental ones. However, they often make assumptions that unavoidably limit the range of applicability, such as the dynamics of the underlying conservative system and the modeling of damping terms. Here, we describe a mathematical theory and the corresponding numerical methodology that is able to rigorously extract backbone curves from free-decay vibrations data and that can overcome some of the main limitations of existing methods. We illustrate our findings with synthetic and real experiment vibration measurements.