Damping Models for Shear Beams with Applications to Spacecraft Wiring Harnesses

Spacecraft wiring harnesses can fundamentally alter a spacecraft\u27s structural dynamics, necessitating a model to predict the coupled dynamic response of the structure and attached cabling. Although a beam model including first-order transverse shear can accurately predict vibration resonance frequencies, current time domain damping models are inadequate. For example, common proportional damping models result modal damping that depends unrealistically on the frequency. Inspired by a geometric rotation-based viscous damping model that provides frequency independent modal damping in an Euler-Bernoulli formulation, a viscous damping model with terms associated with the shear and bending angles is presented. The model provides modal damping that is approximately constant in the bending-dominated regime (low mode numbers), increasing by at most 6% for a particular selection of bending and shear angle-based damping coefficients. In the shear-dominated regime (high mode numbers), damping values increase linearly with mode number and in proportion to the shear angle-based damping coefficient. A key feature of this shear beam damping model is its ready finite element implementation using only matrices commonly developed for an Euler-Bernoulli beam. Such an analysis using empirically determined damping coefficients generates damping values that agree well with existing spacecraft wiring harness cable data