The Difficulty of Modelling Damping in Linear Dynamic Systems

The consequences of including damping in linear dynamic systems are investigated. One unexpected consequence is that, unlike an undamped system, modes cannot be found which uncouple the system and can be considered individually. In particular, most damped modes are a source of energy even though only passive damping is being considered. The methodology used is to investigate various sources of damping that have analytical models thus avoiding a dependence on measured data. It is suggested that all damping can be categorised into one of three types which have descriptions in terms of complex variables as i) off-axis pole pairs, ii) symmetry axis poles and iii) symmetry axis branch cuts. One physical example for each type of damping mechanism is identified and analysed. The types of damping covered include viscoelastic materials as well as combinations of dampers and springs in multi-degree of freedom configurations. An important physical model is that of the semi-infinite beam which takes energy off to infinity as well as adding stiffness or inertia to a structure.