Multidimensional Vibrations of Cable-Harnessed Beam Structures with Periodic Pattern: Modeling and Experiment

Abstract

The dynamics of space structures is significantly impacted by the presence of power and electronic cables. Robust physical model is essential to investigate how the host structure dynamics is influenced by cable harnessing. All the developed models only considered the decoupled bending motion. Initial studies by authors point out the importance of coordinate coupling in structures with straight longitudinal cable patterns. In this article, an experimentally validated mathematical model is developed to analyze the fully coupled dynamics of beam with a more complex cable wrapping pattern which is periodic in nature. The effects of cable wrapping pattern and geometry on the system dynamics are investigated through the proposed coupled model. Homogenization-based mathematical modeling is developed to obtain an analogous solid beam that represents the cable wrapped system. The energy expressions obtained for fundamental repeating segment are transferred into the global coordinates consisting of several periodic elements. The coupled partial differential equations (PDE) are obtained for an analogous solid structure. The advantage of the proposed analytical model over the existing models to analyze the vibratory motion of beam with complex cable wrapping pattern has been shown through experimental validation.

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

“…The wrapping angle is different in each element. This represents a more realistic case of cable attachment pattern than the periodic wrapping patterns previously studied by the authors [19]. The system shown in Figure 1b represents a homogenous cable harnessed structure where each fundamental element has the same material properties for the beam and cable.…”

“…The pattern consists of multiple fundamental elements, each comprising a diagonal cable section and a lumpedmass cable section. In structures with more cables and fewer fundamental elements, the effect of coupling will be more significant [13,19]. The coupling also depends on the material properties of the host structure and the cable.…”

“…In the case of non-periodic CH beams in this paper, the wrapping angle and, in some cases, the material properties vary from one element to the other. A homogenization approach developed by the authors before [19] cannot be applied in this case. As a result, continuity conditions at the interface of the two elements must be applied.…”