Frequency-independent modal damping for flexural structures via a viscous "Geometric" damping model

This paper considers the damped transverse vibration of flexural structures. Viscous damping models available to date suffer from the deficiency that predicted modal damping is strongly frequency-dependent, a situation not often encountered in experiments with built-up structures. Strain-based viscous damping, which corresponds to the case of stiffness-proportional damping, yields modal damping that increases linearly with frequency. Motion-based viscous damping, which corresponds to the case of mass-proportional damping, yields modal damping that decreases linearly with frequency. The proposed model introduces a viscous "geometric" damping term in which a resisting shear force is proportional to the time rate of change of the slope. In a discretized (finite element) context, the resulting damping matrix resembles the geometric stiffness matrix used to account for the effects of membrane loads on lateral stiffness. For an illustrative example of a simply-supported beam, this model yields constant modal damping that is independent of frequency. For some boundary conditions, the corresponding mode shapes are real. These conclusions are verified through additional finite element analysis. Such a viscous damping model should prove useful to researchers and engineers who need a time-domain damping model that exhibits realistic frequency-independent damping.