Metric Damping of MDOF Systems in High Transient Motion

This paper deals with damping due to transient motion in the case of multi-degree-of-freedom (MDOF) system. The main aim of this research is to make the method presented by the authors in a previous paper available for MDOF systems. An method based on relativity concepts is developed in order to identify and evaluate a metric damping due to time-varying forcing frequency. An additional dimension for each degree of freedom (DOF) is introduced. The variational problem of the metric of a Riemannian space gives the geodesic equations, i.e., equations of motion that, after time integration carried out with several types of numerical schemes, permit one to predict the forced transient response of a 3-DOF system. The proposed metric approach makes the experimental results correspond with the simulated results.