Mass and Stiffness Effects of Harnessing Cables on Structural Dynamics: Continuum Modeling

摘要

Dynamic analysis of satellite structures comprises an important part of their design. One such example is an inflatable deployable structure. Although prized for their small volume, mass, and subsequent launch costs, these structures are quite susceptible to disturbances in a space environment that can jitter their mission accuracy. Therefore, it is important to have models to accurately predict their vibrations response to these disturbances. One important aspect to include in these models is the effect of signal and power cables surrounding the host structure that has been traditionally ignored or accounted for using ad hoc models. Obtaining simple analytical solutions that can predict the dynamic behavior of these structures has numerous advantages for their vibrations control and modeling before their launch. Although damping plays an important role in the dynamics of these structures, the presented paper pertains only to the mass and stiffness effects of these cables. The structures are modeled as beam structures harnessed with cables and the governing partial differential equations of motion for different coordinates of vibrations, such as bending, longitudinal, and torsional modes, are derived for the harnessed structure. Two wrapping patterns for the cables are considered. Natural frequencies and the resultant frequency response functions are presented, and the results are compared to a finite element solution.