Damping models for Timoshenko beams with applications to spacecraft wiring harnesses

Power and data cabling are attached to a spacecraft bus structure at many points and can account for a significant fraction of a spacecraft's dry mass. This combination leads to coupled spacecraft and cable dynamics that require a model to predict the effects of this interaction. While current models can accurately predict vibration frequencies, typical proportional damping models are inadequate. Instead, a viscous damping model that produces approximately frequency-independent modal damping in Euler-Bernoulli and shear beams is considered. The relevant viscous damping terms (as well as those commonly employed in proportional damping approaches) are extended and modified for application to Timoshenko beams. The inclusion of rotary inertia does add some frequency-dependence; however, careful selection of damping coefficients can produce a large range of approximately frequency-independent modal damping. As transverse shear and rotary inertia effects become large, this range decreases, with the terms producing modal damping values that increase or decrease with mode number in a fashion similar to typical proportional damping models, but at a much lower rate. When transverse shear and rotary inertia effects approach zero, collapses to the one that provides frequency-independent modal damping for the Euler-Bernoulli beam.