Investigation of Viscous Damping Terms for a Timoshenko Beam

摘要

Data cabling has become a significant portion of a spacecraft's dry mass and can no longer be neglected in structural dynamics models. At higher-frequency modes, the cable dynamics can interact with the bus structure to which they are attached, affecting the overall dynamics of the spacecraft. Experimental testing has shown an increased damping ratio for cabled versus non-cabled structures, indicating the need for a spacecraft dynamics model that accurately includes the effects of data cable damping. Previous work has modeled cables as shear beams with structural and proportional damping terms. Structural damping models have a tendency to overestimate system damping in higher-frequency modes, while proportional damping results in unrealistic frequency-dependent damping. A time-domain viscous damping model reflecting the frequency-independent nature of spacecraft cables is desired. The addition of viscous damping in the form of a "geometric-based" term produced nearly frequency-independent damping in Euler-Bernoulli beams and a similar result in shear beams. This work investigated the effects of a geometric-based damping term in the Timoshenko beam equations. Ten damping terms were included in a Timoshenko beam finite element model and categorized as motion-, rotation-, and strain-based damping. This research shows two trends of modal damping dominated by bending or shear, with no single damping term producing frequency-independent modal damping. The damping results provide further insight into the creation of a frequency-independent damping model.