A procedure for calculating the damping in multi-element space structures

A procedure is outlined for estimating the damping in a multi-element space structure by incorporating distributed material damping and discrete nonlinear joint properties into a linear analysis. Tests have been conducted in which the transient response of a truss member is measured in free fall in a vacuum in order to obtain precise material damping characteristics. The force-state mapping technique is then used to identify the localized nonlinearities in joints by mapping the force transmitted through the joint as a function of the full mechanical state of the joint. The identified nonlinear joint parameters are then linearized using an equivalent energy approach which finds the equivalent linear stiffness and linear viscous damping by equating the integrated work done and energy dissipated by the nonlinearity to those of a spring and damper undergoing sinusoidal motion. The distributed material damping and localized nonlinear effects are then incorporated to form a linearized damped finite element model. Finally, an eigenvalue perturbation analysis is developed to explore the effect of introducing damping at the joints on the overall dynamics of the truss, and to obtain design guidance on where supplemental joint damping might optimally be added.