Damping mechanisms and models in structural dynamics

Several aspects of damping models for dynamic analysis of structures are investigated. First the causality condition for structural response is used to identify rules for the use of complex-valued frequency dependent material models, illustrated by the shortcomings of the elastic hysteretic model. Basic properties of fractional derivatives and their use in the representation of damping are then reviewed, and its is demonstrated that the frequency dependent fractional damping force describes a cicle - depending on damping exponent - in the complex plane.

Finally an asymptoitic result for the damping obtained in flexibal systems like cables and beams by isolated dampers is derived, and it is demonstrated that also this case leads to circles in the complex plane for viscous as well as for fractional damper properties.