General Models for Linear Damping

The standard model for damping is the linear viscous dashpot which produces a force proportional to velocity. Although other sources of linear damping are known to exist, such as that due to viscoelasticity, it is not clear what range of mathematical forms damping models can take. Here it is suggested that there are only three types of damping model. These models are deduced by examining three configurations of mechanical components. These configurations include combinations of springs and dashpots and, most significantly, a semi-infinite beam. It is found that these models are best examined in the Laplace or s-plane so that features of the damping models may be expressed in terms of complex variable theory. The three types of damping model revealed by this analysis correspond to poles lying off the imaginary axis, poles on the negative real axis and pole like forms on the negative real axis that give rise to branch cuts. It is conjectured that these are the complete set of mathematical models that describe damping.