Damping Mechanisms in Cable-Harnessed Structures for Space Applications: Analytical Modeling

Abstract

Recent developments in the aerospace industry have driven focus towards accurately modeling the effects of the cables and electronic cords on space structures. In the past, researchers have modeled the mass and stiffness effects of these cables but primarily overlooked their damping effects through careful analytical model developments. The objective of the current work is to present analytical models for cable-harnessed structures that also include the damping effects in their vibration response. Obtaining simple, low-order and high-fidelity models are highly advantageous in designing robust vibration real-time control algorithms for structures. Additionally, the analytical models are useful tools in providing insight and better understanding the dynamics of space structures as they are often difficult to be tested prior to launch due to their large size and at best only a few components may be tested. Motivated by the space applications, this work considers beam structures wrapped with cables which are modeled using beam and string theory assumptions. Two different damping models namely Kelvin-Voigt and hysteretic damping are considered. The homogenization approach is used as a starting point for structures of periodic wrapping patterns. Using the variational principle, the governing partial differential equation for the transverse coordinate of vibrations is found for three cable patterns and the results are compared to those from the Distributed Transfer Function Method (DTFM). Finally, the effects of several structural parameters are studied on the overall system damping.

Fully Coupled Vibrations of Cable-Harnessed Beams with a Non-Periodic Wrapping Pattern

“…Higherorder strain-displacement relations were developed, [9], and the model was experimentally validated [10]. The models developed by Martin and Salehian [9,10], however, ignored damping due to the cables, which was later introduced by Agrawal and Salehian [11], primarily for predicting accurate amplitudes in the frequency response in the resonant frequency region. In the studies described so far [9][10][11], the models ignore the effect of coordinate coupling.…”

“…The eigenvalue problem to obtain the natural frequencies remains unaffected due to this operation [9,10] and hence, those decoupled terms are omitted in the final strain energy expression, Equation (9). The coefficients of Equations ( 9) and ( 10) are presented in Equation (11). The developed model for the nonhomogenous structure can be reduced to that of the homogenous structure by considering the same material properties for the beam (…”