Understanding Damping in Linear Multi-Degree of Freedom Systems

A system with damping is much more difficult to model than an undamped system. In particular, the effect of damping on a multi-degree-of-freedom system is not a straightforward extension of the damped found in single-degree-of-freedom systems. The complications of a multi-degree-of-freedom system are first examined by investigating the acoustic modes of a pipe with energy leaking from one boundary. This system can be modelled exactly. It is found that individual modes of vibration cannot be separated and are always coupled by damping effects which may involve some modes being active and not passive. Furthermore if damping sinks are increased the damping ratios can either increase or decrease. The damping of systems with fewer degrees-of-freedom are then examined to determine how damping coupling behaves. It is found that a two-degree-of-freedom system exhibits increasing and decreasing damping values as the magnitude of a damping sink is varied.